Research ArticleModified Discrete Grey Wolf Optimizer Algorithm forMultilevel Image Thresholding

Linguo Li12 Lijuan Sun1 Jian Guo1 Jin Qi3 Bin Xu3 and Shujing Li2

1School of Computer Nanjing University of Posts and Telecommunications Nanjing 210003 China2College of Information Engineering Fuyang Normal University Fuyang 236041 China3School of Internet of Things Nanjing University of Posts and Telecommunication Nanjing 210003 China

Correspondence should be addressed to Linguo Li llg-1212163com

Received 1 July 2016 Revised 21 November 2016 Accepted 6 December 2016 Published 3 January 2017

Academic Editor Cheng-Jian Lin

Copyright copy 2017 Linguo Li et alThis is an open access article distributed under theCreativeCommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The computation of image segmentation has become more complicated with the increasing number of thresholds and the optionand application of the thresholds in image thresholding fields have become anNP problem at the same timeThe paper puts forwardthe modified discrete grey wolf optimizer algorithm (MDGWO) which improves on the optimal solution updating mechanism ofthe search agent by the weights Taking Kapurrsquos entropy as the optimized function and based on the discreteness of threshold inimage segmentation the paper firstly discretizes the grey wolf optimizer (GWO) and then proposes a new attack strategy by usingthe weight coefficient to replace the search formula for optimal solution used in the original algorithm The experimental resultsshow that MDGWO can search out the optimal thresholds efficiently and precisely which are very close to the result examined byexhaustive searches In comparison with the electromagnetism optimization (EMO) the differential evolution (DE) the ArtificalBee Colony (ABC) and the classical GWO it is concluded that MDGWO has advantages over the latter four in terms of imagesegmentation quality and objective function values and their stability

1 Introduction

Image segmentation involves the technique and process ofsegmenting an image into several particular unique areasand extracting useful or interested targets [1] These areas ortargets are the keys for image analysis and understandingWith the in-depth research of image segmentation tech-nology image segmentation techniques have been widelyapplied in various fields such as medical analysis [2] imageclassification [3] object recognition [4] image copy detection[5] and motion estimation [6]

In recent yearsmany researchers have conductedmassiveresearch on image segmentation However there has been notheory of segmentation so far which is universally applicableThere are many algorithms for image segmentation andclassical ones are classified as algorithms based on thresholdedge area and others which are combinedwith other specifictheories [7 8] As a commonly used image segmentationalgorithm threshold segmentation selects proper threshold

to divide image into different areas or classes Numerousdifferent thresholding approaches have been reported in theliterature Basically thresholdingmethods fall into two kindsparametric and nonparametric [9 10] Parametric methodsare time-consuming and computationally expensive whilenonparametric methods try to determine the optimal thresh-old value by optimizing some standards [10] By introducingthe optimization methods nonparametric methods reducethe time consumption and computation and show betterrobustness and accuracy Based on the above analysis thepaper will take nonparametric methods to analyze and studymultilevel image segmentation

It has proved to be feasible to determine the optimalthreshold value by analyzing the histogram characteristicsor optimizing objective functions [9] These nonparametricmethods can be achieved by optimizing objective functionsThe commonly used optimization functions include maxi-mization of the entropy [11] maximization of the between-class variance (eg Otsursquos method) [12] the use of the fuzzy

HindawiComputational Intelligence and NeuroscienceVolume 2017 Article ID 3295769 16 pageshttpsdoiorg10115520173295769

2 Computational Intelligence and Neuroscience

similarity measure [13] and minimization of the Bayesianerror [14] Among them Kapurrsquos optimal entropy thresh-old method does not require prior knowledge which canobtain desirable segmentation result for the nonideal bimodalhistogram of images which make it the most widely usedmethod [4] All of these techniques were originally usedfor bilevel thresholding and then extended to multilevelthresholding areas However after thesemethods are used formultilevel thresholding (MT) the computational complexitygrows exponentially Therefore numerical evolutionary andswarm-based intelligent optimizations are much preferred inMT [3]

Optimization algorithm [15] is mainly used to solve theproblem of the option of the threshold value and reducethe time consumption from the increase of the numberof the thresholds Genetic algorithm (GA) [16] is an earlymethod used in the image thresholding With the constantlyemerging of the optimization algorithms a large numberof MT methods based on optimization algorithms followFujun et al [17] put forward an improved adaptive geneticalgorithm (IAGA) image segmentation method this methodcan adjust control parameters adaptively according to the sizeof individual fitness and dispersion degree of the populationwhich keeps the diversity of the population and improvesthe convergence speed evolutionary algorithms which areinspired by swarm behavior such as Particle Swarm Opti-mization (PSO) [18] and artificial colony algorithm (ABC)[19] are also widely used in image segmentation problemOliva et al [20] used EMO algorithm for MT problem andalso applied HAS algorithm [17] to MT tasks there are manyother optimization algorithms which are also used to dealwith this kind of problem and the results are also satisfactorysuch as DE CS BF and FFA [21ndash25]

As a newly proposed optimization algorithm the GWO[26] algorithm mimics the leadership hierarchy and huntingmechanism of grey wolves in nature Four types of greywolves (120572 120573 120575 120596) are employed as the leadership hierar-chy The main steps are hunting searching for prey encir-cling and attacking Compared to well-known evolutionary-based algorithms such as PSO GSA DE EP and ES theGWO algorithm shows better global convergence and higherrobustness Moreover the GWO has high performance insolving challenging problems in unknown search spaces andthe results on semireal and real problems also prove thatGWOcan show high performance not only on unconstrainedproblems but also on constrained problems [26] This paperby making an analysis of GWO tries to determine theoptimal threshold for image segmentation discretizes thecontinuous GWO algorithm and then proposes modifieddiscrete GWO algorithm Original GWO algorithm mainlysolves the problem of continuity but the image thresholdingis a discrete problem for different thresholds therefore GWOalgorithm has to be discretized In addition this paper hasalso improved thewolves attack strategy (ie determining theoptimal solution) While the original GWO used the averageof the optimal three wolves as the best solution the proposedalgorithm in this paper abandons the average optimizationstrategy in the process of determining the optimal solutionand calculates the different weights on the basis of wolves

fitness function and at the same time gives the highestweightto the dominant wolf so as to improve the convergence Theexperimental results show that the algorithm determines theappropriate thresholds quickly and has better segmentationeffect high efficiency and accuracy Finally the simulationexperiment verifies the superiority of MOGWO Moreoverit is the first time that MDGWO algorithm is applied tomultilevel image segmentation

The rest of the paper is organized as follows Section 2introduces Kapurrsquos entropy and related work of intelligentoptimization in the field of MT Section 3 presents theformulation of MT and Kapurrsquos entropy objective functionThe detailed process and pseudocode of the initializingencircling hunting and attacking behaviors inMDGWO arepresented in Section 4 Section 5 analyzes the superiority ofMDGWO based on numerous experiments in combinationwith Figures and Tables Section 6 concludes

2 Related Works

In recent years image segmentation methods based onintelligent optimization takes Otsursquos method between-classvariance Tsallis entropy and Kapurrsquos entropy for objectivefunctions These methods optimized the threshold throughoptimization algorithm and obtained better results on imagesegmentation [4] Moreover Akay [27] compared ABCwith PSO by employing between-class variance and Kapurrsquosentropy as objective functions Kapurrsquos entropy-based ABCshowed better performance when the number of thresholdsincreases and reduced time complexity Bhandari [28] et alconducted comparative analysis in detail between KapurrsquosOtsu and Tsallis functions The results show that in remotesensing image segmentation Kapurrsquos entropy-based algo-rithm performs better than the rest generally Ghamisi [29]et al analyzed the performances of Particle Swarm Opti-mization (PSO) Darwinian Particle Swarm Optimization(DPSO) and Fractional-Order Darwinian Particle SwarmOptimization (FODPSO) in MT By comparing them to Bac-teria Foraging (BF) algorithm and genetic algorithms (GA)PODPSO shows better performance in overcoming localoptimization and computational speed Electromagnetismwas introduced for MT by Horng [19] which comparedit to Kapurrsquos entropy and Otsursquos method respectively Theexperimental results show that Kapurrsquos entropy is moreefficient Before that they verified the same test experimentthrough Harmony Search Optimization and obtained similarresults [20] In our previous work [30] we also take DiscreteGrey Wolf Optimizer (GWO) as the tool with fuzzy theoryand fuzzy logic to achieve image segmentation Comparedwith EMO and DE our method shows better performancein segmentation quality and stability Based on the aboveanalysis the algorithmwhich takes Kapurrsquos entropy for objec-tive function shows better performance By taking Kapurrsquosentropy as the optimization goal the paper analyzes andstudies the application of GWO in MT

Wolf Pack Algorithm (WPA) is a new swarm intelli-gent method proposed by Wu et al in 2013 [25ndash29 31ndash33] According to the wolf pack intelligent behavior the

Computational Intelligence and Neuroscience 3

researchers abstracted three intelligent behaviors scoutingcalling and besieging and two intelligent rules winner-take-all generation rule of leadwolf and stronger-survive renewingrule of wolf packThe experiments show thatWPA has betterconvergence and robustness especially for high-dimensionalfunctions In the same year Q Zhou and Y Zhou [34]proposed Wolf Colony Search Algorithm based on LeaderStrategy (LWCA) The idea of the algorithm originated fromthe phenomenon that there exists individual competitionsamong the wolf pack The strongest wolf was selected asthe leader of the wolves the wolves hunted prey under theleadership of the leader so that they could be more effectivein capturing prey The experiments show that the algorithmhas better performance on convergence speed and accuracyand it is difficult to trap-in local minimum CoincidentallyMirjalili et al [26] proposed grey wolf optimizer (GWO)inspired by grey wolves in 2014 In GWO algorithm The120572 wolf is also called the dominant wolf the level of otherthree types decreases in turn and the 120596 is the lowest-level wolf In addition the three main steps of huntingsearching for prey encircling prey and attacking prey areimplemented Compared to well-known heuristics such asPSO GSA DE EP and ES [35ndash38] the GWO algorithmshows better convergence and higher local optima avoidanceIn 2014 Muangkote et al [39] proposed an improved greywolf optimizer method (IGWO) The strategy on parameterselection of IGWO improves the search capability and thehybridization strategy increases the diversity of the agentZhu et al [40] proposed to combine GWO with differencealgorithm for solving the global optimization problem in2015

By introducing MDGWO to MT the paper solves theproblem of thresholds option by taking Kapurrsquos entropy forobjective functionThe proposed algorithm shows better seg-mentation result high efficiency and accuracy and stability ofthe range of threshold

3 Formulation of the MultilevelImage Thresholding

MT needs to set a set of threshold values 119905119894 based on thatthe image can be segmented into different regions By meansof intelligent optimization to obtain the optimal thresholdvalue the process of image segmentation has to be formulatedbefore taking image elements or image features as parametersto determine the optimized objective functions with thepurpose of getting close to the optimal threshold value

31 Pixel Grouping Based on Thresholding Supposing thateach image has 119871 grey levels the thresholding conversionis a process in which the pixels of image are divided intodifferent classes or groups according to the grey levels Thiskind of classification has to choose a threshold (th) or followthe following rules

1198621 larr997888 119901 if 0 ≪ 119901 lt th1198622 larr997888 119901 if th ≪ 119901 lt 119871 minus 1 (1)

where 119901 indicates the grey level of a pixel in image 119868119892 119901 =0 1 2 119871 minus 1 1198621 1198622 is the class of pixel 119901 and th is thethreshold

Equation (1) is the description of bilevel thresholding ForMT problem the description is

1198621 larr997888 119901 if 0 ≪ 119901 lt th11198622 larr997888 119901 if th1 ≪ 119901 lt th2119862119894 larr997888 119901 if th119894minus1 ≪ 119901 lt th119894

119862119896+1 larr997888 119901 if th119896 ≪ 119901 lt 119871 minus 1

(2)

where th1 th2 th119894 th119894+1 th119896 indicates different thresh-olds Therefore MT can be described as the problem ofsolving the set of th Kapurrsquos entropy is a well-knownmethodused to solve this kind of problem by maximizing theobjective function to determine the optimal threshold

32 Concept of Kapurrsquos Entropy for Image SegmentationKapurrsquos entropy is one of the early methods used in bilevelthresholding and it has been applied in MT field by scholarsKapurrsquos entropy is an effective image segmentation techniquebased on threshold and probability distributions of imagehistogramWhen the optimal threshold is allocated correctlythe entropy is the biggest of all Entropy is used tomeasure thecompactness and separability between classesThepurpose ofthe method is to find the optimal threshold and produce themaximum entropy This method extracts the brightness level119871 from a greyscale image or a RGB image The probabilitydistribution of brightness value is calculated as follows

119875ℎ119886119894

= ℎ119886119894SP

SPsum119894=1

119875ℎ119886119894

= 1119886 =

1 2 3 if RGB Image1 if Grayscale Image

(3)

where 119894 indicates a specific brightness level ranging from 0 to119871minus1 parameter 119886 is used to judge whether the image is a greyimage or a RGB image SP is the total of pixels and ℎ119886119894 is thepixel number of the brightness level 119894 in 119886 For the simplestsegmentation there are two classes defined as follows

1198621 = 119875ℎ11988611205961198860 (th)

119875ℎ119886th1205961198860 (th) 1198622 = 119875ℎ119886th+11205961198861 (th)

119875ℎ1198861198711205961198861 (th)

(4)

4 Computational Intelligence and Neuroscience

where1205960(th)1205961(th) are the probability distribution of11986211198622respectively the equation is as follows

1205961198860 (th) = thsum119894=1

119875ℎ119886119894

1205961198861 (th) = 119871sum

119894=th+1119875ℎ119886119894

(5)

Therefore the objective function of Kapurrsquos entropy canbe defined as

119891 (th) = 1198671198861 + 1198671198862 119886 =

1 2 3 if RGB Image1 if Grayscale Image

(6)

where entropy1198671 and entropy1198672 are derived by (4)

1198671198861 = thsum119894=1

119875ℎ1198861198941205961198860 ln(119875ℎ119886

1198941205961198860 ) 1198671198862 = 119871sum

119894=th+1

119875ℎ1198861198941205961198861 ln(119875ℎ119886

1198941205961198861 ) (7)

where 119875ℎ119886119894

is the probability distribution of strength grades by(3) and 1205960(th) 1205961(th) are the probability distribution of 11986211198622 respectively

Naturally the entropy-based method can be extended tomultithresholdingmethod In this case image can be dividedinto 119896 classes with 119896 minus 1 thresholds Therefore multilevelthresholding objective function can be defined as follows

119891 (TH) = 119896sum119894=1

119867119886119894 119886 =

1 2 3 if RGB Image1 if Grayscale Image

(8)

where TH = [th1 th2 th119896minus1] is a vector containingmultiple thresholds and each entropy is calculated withthe corresponding threshold respectively And (7) can beextended to the calculation of 119896 entropies as follows

1198671198861 = th1sum119894=1

119875ℎ1198861198941205961198860 ln(119875ℎ119886

1198941205961198860 ) 1198671198862 = th2sum

119894=th1+1

119875ℎ1198861198941205961198861 ln(119875ℎ119886

1198941205961198861 )

119867119886119896 = 119871sum119894=th119896minus1+1

119875ℎ119886119894120596119886119896minus1

ln( 119875ℎ119886119894120596119886119896minus1

)

(9)

where the probabilities of 119896 classes are calculated by (10)finally it needs to categorize the pixels into correspondingclasses and complete the multilevel image segmentation by(2)

1205961198860 (th) = th1sum119894=1

119875ℎ119886119894

1205961198861 (th) = th2sum

119894=th1+1119875ℎ119886119894

120596119886119896minus1 (th) = 119871sum119894=th119896minus1+1

119875ℎ119886119894

(10)

As mentioned above multilevel thresholding is formu-lated tomaximize Kapurrsquos entropy and the objective functionis shown in (8) As previously mentioned this paper willuse the MDGWO to optimize the objective function theoptimization algorithm is the key to the quality of imagesegmentation

4 Image Segmentation Based on MDGWO

41 Standard Grey Wolf Optimizer Grey wolfs (Canis lupus)belongs to Canidae family which are considered as apexpredators meaning that they are at the top of the foodchain They have a very strict social dominant hierarchy Thealgorithm divides the wolves into four types 120572 120573 120575 and 120596The social behavior of each type wolves can be summarizedas follows

The leaders are amale and a female called alphaThey arethe most brilliant wolves and the best in terms of managingthe packThe alphawolf is also called the dominant wolf sincehisher orders should be followed by the pack uncondition-ally The location of alpha presents the best solution of theproblem

The second level in the hierarchy of grey wolves isbeta The betas are subordinate wolves that help the alphain decision-making or other pack activities The beta wolfshould respect the alpha but commands the other lower-level wolves as well It plays the role of an advisor to thealpha and discipliner for the pack The beta reinforces alpharsquoscommands throughout the pack and gives feedback to thealpha

The third level in the hierarchy of grey wolves is deltaDelta wolves have to submit to alphas and betas but theydominate the omega scouts sentinels elders hunters andcaretakers who belong to this category They are responsiblefor watching the boundaries of the territory warning the packin case of any danger protecting and guaranteeing the safetyof the pack helping the alphas and betas when hunting preyand providing food for the pack and caring for the weak illand wounded wolves in the pack

The lowest ranking grey wolf is omega It may seem theomega is not an important individual in the pack but it has

Computational Intelligence and Neuroscience 5

Table 1 The corresponding relationships between MDGWO andimage segmentation

MDGWO Image segmentationPositions Threshold segmentation solutionAlpha Pos Optimal solutionAlpha score The largest fitness valueFitness Fitness function valueBest R Best fitness

been observed that the whole pack face internal fighting andproblems in case of losing the omega which is harmful to thegroup structure

In addition to the social hierarchy of wolves grouphunting is another interesting social behavior of grey wolvesThemain phases of greywolf hunting are as follows searchingfor the prey tracking chasing and approaching the preypursuing encircling and harassing the prey until it stopsmoving attacking toward the prey

In order to mathematically model the social hierarchy ofwolves in GWO [26] the fittest solution is considered as thealpha (120572) Consequently the second and third best solutionsare named beta (120573) and delta (120575) respectively The rest ofthe candidate solutions are assumed to be omega (120596) In theGWO algorithm the hunting (optimization) is guided by 120572120573 and 120575 The 120596 wolves follow these three wolves

In addition to the above four abstract models this paperproposes MDGWO based on the standard GWO settings forMT In the improved algorithm the corresponding relation-ships between grey wolf hunting and image segmentation areshown in Table 1

42 The Initialization of MDGWO The size of the wolf packis assumed as SN SN candidate solutions (the location ofthe wolves is the threshold values) are generated randomly inthe initialization phase Different from the GWO the imagethreshold is a set of discrete integers by rounding toward zero

997888rarr119883119894 = lfloorrand (SN 1) sdot (119906119887 minus 119897119887) + 119897119887rfloor (11)

where 119906119887 and 119897119887 are the upper limit and the lower limit ofparameters (namely boundaries of parameter)

After the initialization of candidate solutions MDGWOjudges whether the initial solution 997888rarr119883119894 is in the range of[119906119887 119897119887] If it is the fitness value will be calculated otherwisethe search agent will be put back in the search space (ieguaranteeing the initial solution in the range of [119906119887 119897119887])by (12) and then the fitness value will be recalculated byrounding toward zero

997888rarr119883119894 = lfloor(997888rarr119883119894 sdot (119906 + 119897)) + 119906119887 sdot 119906 + 119897119887 sdot 119897rfloor (12)

where 119906 = 997888rarr119883119894 gt 119906119887 119897 = 997888rarr119883119894 lt 119897119887

In the all fitness values calculated by (13) of candidatesolutions MDGWO chooses three optimal candidate solu-tions to assign to997888rarr119883120572997888rarr119883120573997888rarr119883120575 and records all the fitness valuesand candidate functions (namely locations of the wolves)

Fitness (997888rarr119883119894) = 1(1 + 119891 (997888rarr119883119894)) (119891 (997888rarr119883119894) ge 0)

1 + 100381610038161003816100381610038161003816119891 (997888rarr119883119894)100381610038161003816100381610038161003816 (119891 (997888rarr119883119894) ge 0) (13)

where997888rarr119883119894 is one of the candidate solutions which include a setof thresholds then 119891(997888rarr119883119894) is calculated by Kapurrsquos function asshown in (8)

43 Iterative Process After the initialization all the searchagents have to update their current locations for optimize thecandidate solutions over the course of iteration In the rangeof the maximum iteration (Max iter) all the update processand optimization process will be completed

431 Encircling Prey Grey wolves encircle prey before thehunt In the mathematical model the wolf pack has to updatethe position (namely the threshold value) constantly so thatthey can approach the prey In the algorithm all the agentposition updated by (15) over the course of encirclement

= 100381610038161003816100381610038161003816 sdot 997888997888rarr119883119901 (119905) minus (119905)100381610038161003816100381610038161003816 (14)

(119905 + 1) = 997888997888rarr119883119901 (119905) minus sdot (15)

where 119905 indicates the current iteration and are coefficientvectors 997888997888rarr119883119901 is the position vector of the prey and indicatesthe position vector of a grey wolf The vectors and arecalculated as follows

= 2 119890 sdot 997888rarr1199031 minus 119890 (16)

= 2997888rarr1199032 (17)

where components of 119890 are linearly decreased from 2 to 0 overthe course of iterations and997888rarr1199031 997888rarr1199032 are random vectors in [0 1]The detailed selection of the two vectors can be found in [26]

432 The Behavior of Hunting The hunt is usually guided bythe alphaThebeta and deltamight also participate in huntingoccasionally However in an abstract search space we haveno idea about the location of the optimum (prey) In order tomathematically simulate the hunting behavior of grey wolvesit is supposed that the alpha beta and delta have betterknowledge about the potential location of prey Thereforethe algorithm saves the first three best solutions obtainedso far and obliges the other search agents (including theomegas) to update their positions according to the positionof the best search agents The original GWO algorithm inliterature [26] calculates the updated parameter of searchagents by the first three best solutions and then updates thelocation of search agents (namely new candidate solutions)

6 Computational Intelligence and Neuroscience

if 10038161003816100381610038161003816A10038161003816100381610038161003816lt 1

(a)

if 10038161003816100381610038161003816A10038161003816100381610038161003816gt 1

(b)

Figure 1 Attacking prey of grey wolf

according to their average value As for the specific formulasand the detailed calculation please refer to literature [26]In order to approach the best solution more quickly theproposed algorithm in this paper improves the current bestsolution in solutions updating by weighting method Theupdate formulations are as shown in (20) and correlationcoefficients are calculated by (18) (19) where 1198601 1198602 1198603 arecalculated by (16)997888rarr119863120572 = 100381610038161003816100381610038161003816997888rarr1198621 sdot 997888rarr119883120572 minus 100381610038161003816100381610038161003816 997888rarr119863120573 = 100381610038161003816100381610038161003816997888rarr1198622 sdot 997888rarr119883120573 minus 100381610038161003816100381610038161003816 997888rarr119863120575 = 100381610038161003816100381610038161003816997888rarr1198623 sdot 997888rarr119883120575 minus 100381610038161003816100381610038161003816

(18)

997888rarr1198831 = 997888rarr119883120572 minus 997888rarr1198601 sdot 997888rarr119863120572997888rarr1198832 = 997888rarr119883120573 minus 997888rarr1198602 sdot 997888rarr119863120573997888rarr1198833 = 997888rarr119883120575 minus 997888rarr1198603 sdot 997888rarr119863120575(19)

(119905 + 1) = 1199081 sdot 997888rarr1198831 + 1199082 sdot 997888rarr1198832 + 1199083 sdot 997888rarr1198833 (20)

where 1199081 1199082 1199083 are the corresponding weights which arecalculated by

1199081 = 1198911119865 1199082 = 1198912119865 1199083 = 1198913119865

(21)

where 1198911 1198912 1198913 calculated by (13) are the correspondingfitness values of120572120573 120575119865 = 1198911+1198912+1198913This paper emphasizes

that different from GWO updating search agents MDGWOuses (20) and (21) to update the location of search agentsby weighting method for the first time it is also the majorcontribution to the improved GWO

433 Attacking Prey The grey wolves finish the hunt byattacking the prey when it stops moving In order to mathe-matically model approaching the prey we decrease the valueof 119890 Note that the fluctuation range of is also decreasedby 119890 In other words is a random value in the interval[minus119890 119890] where 119890 is decreased from 2 to 0 over the course ofiterations When random values of are in [minus1 1] the nextposition of a search agent can be in any position betweenits current position and the position of the prey that is thesearch agent will approach the best solution gradually asshown in Figure 1

At the same time for the purpose of mathematical modeldivergence we utilize with random values greater than 1or less than minus1 to oblige the search agent to diverge from theprey As shown in Figure 1(b) gt 1 forces the grey wolves todiverge from the prey to hopefully find a better prey

44 Pseudocode of MDGWO The application of MDGWOalgorithm in image segmentation mainly lies in optimizingKapurrsquo entropy to obtain the best threshold therefore thefitness function as shown in (13) will be calculated based onKapurrsquos entropy

Step 1 Read image 119869 if 119869 is a RGB image then it will beprocessed by three channel of 119869R 119869G 119869B and store the datain ℎR ℎG ℎB respectively if 119869 is a grey image then read thegrey value and store it in ℎgrStep 2 According to (3) calculate image grey values andprobability distribution histogram

Computational Intelligence and Neuroscience 7

Step 3 Initialize the population of grey wolves parameter 119890 and Max iter

Step 4 Initialize the population 997888rarr119883119894 (119894 = 1 2 SN)randomly 997888rarr119883119894 = rand (SN 1) sdot (119906119887 minus 119897119887) + 119897119887 (22)

Step 5 Use (11) to discretize 997888rarr119883119894 that is being roundedtoward zero Use (12) to adjust the singular data beyond theboundaries of search space

Step 6 Calculate objective functions of each search agent byusing (8) And calculate the fitness value of each search agenton the basis of objective functions

Step 7 According to the fitness values assigning first threebest search agents to 997888rarr119883120572 997888rarr119883120573 997888rarr119883120575 respectivelyStep 8 Updating encircling parameters based on997888rarr119883120572997888rarr119883120573997888rarr119883120575which include calculating 997888rarr1198601 997888rarr1198602 997888rarr1198603 by (16) 997888rarr1198621 997888rarr1198622 997888rarr1198623 by(17) and 997888rarr119863120572 997888rarr119863120573 997888rarr119863120575 by (18)Step 9 Update the position of search agents based on (19) and(20) for the next hunting

Step 10 Add one to circular point if 119902 ge Max iter ormeet thestop condition of the algorithm the iteration will be finishedand skip to Step 11 otherwise skip to Step 5

Step 11 Set the location of the wolf that has the best objectivefunction as the best threshold of segmentation

Step 12 Input best threshold and images before and aftersegmentation

5 Experiments and Discussion

51 Parameters Settings The proposed algorithm has beentested under a set of benchmark images Some of theseimages are widely used in the multilevel image segmenta-tion literature to test different methods (Cameraman LenaBaboon and Maize) Others are chosen on purpose fromthe Berkeley Segmentation Data Set and Benchmarks 500(BSD500 for short see [41]) as shown in Figure 2 Theexperiments were carried out on a Lenovo Laptop with anIntel Core i5 processor and 4GBmemoryThe algorithmwasdeveloped via the signal processing toolbox image processingtoolbox and global optimization toolbox of Matlab R2011bAccording to relevant literatures manymethods were provedto have certain advantages compared with previous meth-ods This paper chooses the best advantageous method ascomparison objective the earlier or inferior literatures willno longer be used for the analysis Based on quantities ofcontrast experiments this paper will verify the superiority ofMDGWO in image segmentation by comparison of imagedata chart and so forth In the following sections MDGWOwill be compared with the algorithm using electromagnetism

optimization (EMO) proposed in [20] the differential evo-lution (DE) [27] the Artifical Bee Colony (ABC) [10] andthe original grey wolf optimizer The EMO DE and ABC arethe latest intelligent optimization methods by using Kapurrsquosentropy so far The comparison with GWO is mainly used totest the advantages of MDWGO

In order to avoid the randomness of results we useappropriate statistical metrics to compare the effectiveness ofthese algorithms According to [19 20] and the experimentstest thresholds are th = 2 3 4 5 [1ndash3] and the stop criterionof each experiment is 150 iterations the detailed settings ofparameters are showed in Table 2

For verifying the stability we use (23) to calculate thestandard deviation (STD) at the end of each test Once theSTD value increases the algorithms becomes more instablecorrespondingly [29]

STD = radicMax itersum119894=1

(120579119894 minus 120576)2Max iter

(23)

In addition the peak signal to noise ratio (PSNR [20]) isused to compare the similarity between the segmented imageand original image according to the mean square error (MSE[26]) of each pixel

PSNR = 20 log10 ( 255MSE

) (dB) (24)

MSE = radicsumro119894=1sumco119895=1 (119868119886119900 (119894 119895) minus 119868119886th (119894 119895))

ro times co (25)

where 119868119886119900 is the original image 119868119886th is the segmented image and119886 depends on the type of image (grey image or RGB image)ro co are respectively the total number of rows and columnsin an image

Because Kapurrsquos entropy is based on histogram of theimage this paper provides test images and the correspondinghistograms From Figure 2 it can be seen that each imagehas the only distinctive histogram which can guarantee theuniversality and commonality of the algorithm More impor-tantly most of these histograms do not follow the bimodalcharacteristic therefore the difficulty level of optimizationincreases accordingly

52 The Image Segmentation Result Based on MDGWO withDifferent Thresholds In order to reflect the segmentationeffect Figures 3 and 4 illustrate the segmentation results oforiginal images in Figure 2when the threshold is 2 3 4 and 5respectively The experiments indicate that the segmentationresults turn out to be finer and there are alsomore segmentedareas when the number of thresholds is larger and vice versaIn extreme cases when the threshold is 2 the algorithmis reduced to be binary image segmentation (foreground-background segmentation) Certainly that how many areasare segmented is related to the applications and requirementsthis method only needs to set the corresponding number ofthresholds (th) Besides giving the MDGWO segmentationresults like [20] Figures 3 and 4 also mark the position

8 Computational Intelligence and Neuroscience

Table 2 Parameters settings of MDGWO

Parameters Population size Threshold Number of iterations Run time Lower bound Upper boundValue 50 2 3 4 5 150 35 1 256

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

000100020003000400050006000700080009

001

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 3000

0002000400060008

0010012001400160018

002

times10minus3

Histogram of left col ImageImage Histogram of left col

(a) Cameraman (b) Lena

(c) Baboon (d) Butterfly

(e) Maize (f) Starfish

(g) Smiling Girl (h) Surfing

Figure 2 The original images and their histograms

of the threshold in each histogram Compared with otherMT methods it is difficult to find the difference in termsof the segmentation effect Therefore Section 54 lists thethresholds PSNR STD and MEAN for comparisons ofMDGWO results and other techniques

53 The Comparison of MDGWO in Multilevel Image Thresh-olding with Different Objective Functions In Section 1 wesummarize the relevant objective functions The commonlyused optimization functions include maximization of theentropy andmaximization of the between-class variance (egOtsursquos method) In [27] the authors respectively analyze

these objective functions and compare Kapur and Otsusystematically The experiment results show that Kapurrsquosentropy gets the best effectiveness Therefore in order toverify MDGWOrsquos efficiency we compare the thresholds andPSNR between Otsu and Kapur in Table 3

As shown inTable 3 the threshold distribution ofKapur ismore dispersed and wider in most cases However the effectof image thresholding cannot be seen from the thresholddistribution directly Therefore we focus on analysis thePSNR between Otsu and Kapur In terms of PSNR the Kapurmethod produces higher PSNR values on most items inFigure 2 except for the Sea Star Imagewith 119896 = 3 5 and SurferImage with 119896 = 4

Computational Intelligence and Neuroscience 9

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005001

0015002

0025

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

000100020003000400050006000700080009

001

0 50 100 150 200 250 3000

000100020003000400050006000700080009

001

0 50 100 150 200 250 3000

000100020003000400050006000700080009

001

0 50 100 150 200 250 3000

000100020003000400050006000700080009

001

Image

Cam

eram

anLe

naBa

boon

Butte

rfly

th = 2 th = 3 th = 4 th = 5

Figure 3 The segmentation results of (a)ndash(d) in Figure 2 and their thresholds in histograms

10 Computational Intelligence and Neuroscience

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0002000400060008

0010012001400160018

002

0 50 100 150 200 250 3000

0002000400060008

0010012001400160018

002

0 50 100 150 200 250 3000

0002000400060008

0010012001400160018

002

0 50 100 150 200 250 30000002000400060008

0010012001400160018

002

times10minus3

times10minus3

times10minus3

times10minus3

Image th = 2 th = 3 th = 4 th = 5

Mai

zeSt

arfis

hSm

iling

Girl

Surfi

ng

Figure 4 The segmentation results of (e)ndash(h) in Figure 2 and their thresholds in histograms

Computational Intelligence and Neuroscience 11

Table 3 The comparison of MDGWOrsquos efficiency between Otsu and Kapur

Image 119896 Otsu thresholds PSNR Kapur thresholds PSNR

Cameraman

2 70 144 119475 44 106 1446293 58 119 156 129933 44 98 148 1993374 40 93 139 170 160180 39 83 119 156 2116845 35 81 121 149 174 163710 23 58 94 125 159 231191

Lena

2 92 151 131029 93 163 1471643 80 126 171 157626 70 121 172 1751444 75 114 145 180 164291 43 81 127 171 2017295 73 109 136 161 189 167206 41 73 103 141 178 218208

Baboon

2 97 149 124396 78 141 1603023 83 123 160 137731 46 103 151 1863404 70 105 136 167 149493 34 75 117 159 2051985 66 98 125 150 175 160012 29 64 100 134 170 220929

Butterfly

2 100 152 124400 87 150 1493253 81 118 159 142563 62 104 152 1855394 73 101 129 164 146987 49 88 128 168 2107115 69 95 121 149 177 164688 48 80 113 145 180 224539

Maize

2 92 168 136677 84 165 1404073 76 128 187 152676 59 113 171 1658534 65 104 150 200 167309 45 80 125 187 1898185 56 86 123 164 208 185649 39 74 108 147 198 208792

Sea Star

2 85 157 148445 81 160 1485953 69 120 178 176040 60 111 172 1745834 59 99 137 187 194039 46 89 131 184 1944875 51 85 117 150 193 214000 47 83 118 150 196 209681

Smiling Girl

2 60 123 131358 88 145 1800333 47 100 131 128470 44 91 145 1911484 28 74 111 136 156914 24 67 100 145 2007595 20 63 95 124 158 18 2260 44 83 115 152 203 217937

Surfer

2 92 162 125401 52 141 1643433 71 111 177 160569 52 103 168 1893434 47 81 118 179 208786 49 86 131 185 2072185 46 77 105 143 196 216071 24 53 88 126 183 218961

The average value of Kapur is improved averagely by2224 compared to Otsu by checking against the cor-responding PSNR values which are obtained from theMDGWO The maximum value is increased by 5342 forCameraman Image when 119896 = 3 Therefore the Kapurmethod is significantly better than the Otsu method and wealso mainly analyze the effectiveness of Kapurrsquos method inSection 54

54TheComparison ofQuality Assessment by PSNR STD andMEAN This paper adopts PSNR standard to evaluate thesegmentation quality in comparisonwith otherMTmethodsTables 4ndash6 illustrate the PSNR values under different thresh-olds ofMDGWOGWOEMODEABC and theMEANandSTD of objective functions As shown in Table 4 it can be

seen from the PSNR values that MDGWO gets the highestevaluation in most cases Thus it proves that MDGWO getsbetter results on image segmentation In addition when thenumber of thresholds increases it shows superior PSNRvalue In detail the MDGWO algorithm produces higherPSNR values on all items in Table 4 except for the SmilingGirl Image with 119896 = 5 and Surfer Image with 119896 = 4 on theresult of DE

As shown in Table 4 the average value of MDGWO isimproved averagely by 1316 compared toGWOby checkingagainst the corresponding PSNR valuesThemaximum valueis increased by 4505 for Butterfly Image when 119896 = 5

ComparingwithMTEMO the average value ofMDGWOis improved averagely by 1156 by checking against the cor-responding PSNR valuesThemaximumvalue is increased by3994 for Surfer Image when 119896 = 2

12 Computational Intelligence and Neuroscience

Table 4 PSNR metrics of MTEMO DE ABC GWO and MDGWO

Image 119896 MTEMO DE ABC GWO MDGWO

Cameraman

2 13626 12584 13920 14279 144633 18803 17584 14462 19696 199344 20586 20111 2081 20809 211685 20661 21282 2240 22404 23119

Lena

2 14672 8823 14590 14680 147163 17247 14386 17197 17416 175144 18251 16151 18559 19762 201735 20019 16720 20321 21299 21820

Baboon

2 16016 8103 16007 16024 160353 16016 12596 18592 18632 186344 18485 13178 18417 20480 205195 20507 13135 20224 22060 22092

Butterfly

2 11065 8702 14402 14762 149323 14176 13028 14504 17873 185534 16725 13028 16189 21021 210715 19026 14786 19286 21485 22453

Maize

2 13633 10549 13590 13950 140403 15229 13022 15295 16201 165854 16280 14270 16346 18713 189815 17211 15079 17046 20410 20879

Sea Star

2 14398 8610 14395 14809 148853 16987 14078 16981 17431 174584 18304 16191 18427 19421 194485 20165 16474 20330 20887 20968

Smiling Girl

2 13420 14986 13514 17989 180033 18254 11243 18069 18742 191144 18860 14556 18826 19823 200755 19840 22980 19769 21214 21793

Surfer

2 11744 9737 11878 16154 164343 18584 11638 18762 18895 189344 19478 21866 19647 20234 207215 20468 19576 20479 21699 21896

By comparing with DE the average value of MDGWO isimproved averagely by 3814 by checking against the cor-responding PSNR values The maximum value is increasedby 9789 for Baboon Image when 119896 = 2 The PSNR of theSmiling Girl with 119896 = 5 and Surfer Image with 119896 = 4 areslightly lower but the gap is not significant

Comparing between ABC and MDGWO the averagevalue of MDGWO is improved averagely by 1055 by check-ing against the corresponding PSNR values The maximumvalue is increased by 3836 for Surfer Image when 119896 = 2

From the perspective of STDwhich is shown in Table 5 itcan be observed that MDGWO shows obviously advantagesover MTEMO DE ABC and GWOThe smaller the STD isthe smaller the change of fitness functions over the course ofiterations will be that is the better stability of segmentation

Therefore the results show that MDGWO obtains excitingeffect in stability So MDGWOrsquos stability is better

Compared with GWO the average value of MDGWO isimproved averagely by 7352 compared to GWO by check-ing against the corresponding STD values The maximumvalue is increased by 9644 for Baboon Image when 119896 = 3and the minimum value is increased by 2492 for BaboonImage when 119896 = 3

By comparing with MTEMO the average value ofMDGWO is improved averagely by 4788 The maximumvalue is increased by 87 for Lena Image when 119896 = 2 and theminimum value is increased by 06 for Surfer Image when119896 = 3

Comparing between DE andMDGWO the average valueofMDGWO is improved averagely by 9560Themaximum

Computational Intelligence and Neuroscience 13

Table 5 STD metrics of MTEMO DE ABC GWO and MDGWO

Image 119896 MTEMO DE ABC GWO MDGWO

Camerman

2 01849 12592 01235 01697 004623 01649 17601 02122 02287 007584 02943 21995 03003 03627 006595 02999 26579 02784 04278 01964

Lena

2 00969 12902 00349 01536 001263 01665 17822 01300 03570 002644 02800 22104 01872 05965 009395 02515 25992 01827 05946 01570

Baboon

2 00108 12862 00358 02171 001023 00393 17678 00202 04376 001564 01727 22126 01610 02986 011845 02868 26239 02660 05377 02316

Butterfly

2 00903 12708 00750 02179 004653 02207 17429 02952 02712 020364 02482 22368 03906 04808 024155 02900 26571 04818 05096 02684

Maize

2 00356 13501 00218 03571 001883 01222 18612 00901 02225 002704 02305 23230 02605 03903 009275 02502 27461 03834 04584 01677

Sea Star

2 01073 13547 01088 01728 002903 01497 18741 01752 02028 003744 01596 23307 01817 05032 011195 02639 27550 02180 04550 01437

Smiling Girl

2 00377 12516 00318 01834 001113 00955 17311 00577 01712 002424 01966 21878 01094 02508 007815 01550 25989 02768 05273 01302

Surfer

2 00579 13213 00303 02681 002453 01002 18337 01646 03014 009964 03382 23317 01686 03162 014245 03690 27846 02580 03815 01706

value is increased by 9921 for Baboon Image when 119896 =2 The minimum value is increased by 8832 for ButterflyImage when 119896 = 3

Comparing with ABC the average value of MDGWOis improved averagely by 4590 The maximum value isincreased by 7970 for Lena Image when 119896 = 3 and theminimum value is increased by 1293 for Baboon Imagewhen 119896 = 5

As far as MEAN is concerned this parameter presentsthe average value of fitness function over the course ofiterations in Table 6 which reflects the algorithm stability tosome extent But its accuracy of evaluation is relatively lowwhich can only reflect the fuzzy stability of the algorithmThe experiment data is offered here just in response to theparameter provided in literature [20] In comparison withGWO MTEWO DE and ABC in Table 6 it can be safely

assumed that inmost casesMDGWOobtains higherMEANof fitness function Moreover the difference is extremelysmall when MDGWOrsquos MEAN is lower

From the analyses of Tables 3ndash6 together with the visualeffects of Figures 2 3 and 4 it can be observed thatMDGWO method obtains better segmentation effect andhas advantage in optimal process accuracy stability androbustnessThereforeMDGWO is aMT algorithmwith highaccuracy and high segmentation quality

6 Conclusion

This paper proposes a modified discrete grey wolf optimizerwhich is used to optimize the image histograms and realizethe multilevel image segmentation Based on the high effi-ciency of GWO in the course of optimization and stability

14 Computational Intelligence and Neuroscience

Table 6 MEANmetrics of MTEMO DE ABC GWO and MDGWO

Image 119896 MTEMO DE ABC GWO MDGWO

Camerman

2 17584 124212 177638 14634 174713 21976 173764 223059 21107 219194 26586 217520 268409 24927 274805 30506 262505 308328 30436 30548

Lena

2 17831 127730 178139 17809 183963 22120 176428 220832 22074 228564 25999 218784 260615 25318 264475 29787 257311 299664 29252 30381

Baboon

2 17625 127333 176760 17679 186193 22269 175005 221276 22129 229494 26688 219010 263912 26194 269005 30800 259681 303464 30067 30076

Butterfly

2 16681 125796 174205 17425 177233 21242 172545 222209 21585 224984 25179 220176 263794 25267 261905 28611 261795 306533 29492 29899

Maize

2 18631 133566 186316 18604 195423 23565 184245 232496 22941 239394 27529 229813 273931 26936 278425 31535 271709 312127 31023 30694

Sea Star

2 18754 134104 187295 18321 195873 23323 185516 232738 23245 239014 27582 230719 275057 27136 282105 31562 272551 314919 31167 31958

Smiling Girl

2 17334 123892 173129 17136 180353 21904 171339 218601 21253 219804 26040 216541 259904 25050 265975 30089 257130 300225 29870 30574

Surfer

2 18339 130786 183393 18283 188693 23231 181492 232889 23243 241354 27863 230548 278017 27275 274475 31823 274979 317335 31384 31325

this paper successfully applies the MDGWO to the field ofMT by improving the location selection mechanism of 120572 120573and 120575 during the hunting and using weight to optimize thefinal position of prey (best threshold)TheMDGWOmethodnot only obtains better segmentation quality but also showsobvious superiority over GWO MTEMO DE and ABC instability accuracy and multilevel thresholding

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work was supported in part by the National NaturalScience Foundation of China (no 61300239 no 71301081and no 61572261) the Postdoctoral Science Foundation (no

2014M551635 and no 1302085B) the Innovation Project ofGraduate Students Foundation of Jiangsu Province (KYLX150841) the Higher Education Revitalization Plan Foundationof Anhui Province (no 2013SQRL102ZD no 2015xdjy196no 2015jyxm728 no 2016jyxm0774 and no 2016jyxm0777)and Natural Science Fund for Colleges and Universities inJiangsu Province (no16KJB520034) A Project Funded by thePriority Academic Program Development of Jiangsu HigherEducation Institutions (PAPD) and Jiangsu CollaborativeInnovation Center on Atmospheric Environment and Equip-ment Technology (CICAEET)

References

[1] M Sonka V Hlavac and R Boyle Image Processing Analysisand Machine Vision Cengage Learning 2014

[2] S Masood M Sharif A Masood M Yasmin and M RazaldquoA survey on medical image segmentationrdquo Current MedicalImaging Reviews vol 11 no 1 pp 3ndash14 2015

Computational Intelligence and Neuroscience 15

[3] PGhamisiM S Couceiro FM LMartins and J A Benedikts-son ldquoMultilevel image segmentation based on fractional-orderdarwinian particle swarm optimizationrdquo IEEE Transactions onGeoscience and Remote Sensing vol 52 no 5 pp 2382ndash23942014

[4] M Waseem Khan ldquoA survey image segmentation techniquesrdquoInternational Journal of Future Computer and Communicationvol 3 no 2 pp 89ndash93 2014

[5] J Li X Li B Yang and X Sun ldquoSegmentation-based imagecopy-move forgery detection schemerdquo IEEE Transactions onInformation Forensics and Security vol 10 no 3 pp 507ndash5182015

[6] Z Pan J Lei Y Zhang X Sun and S Kwong ldquoFast motionestimation based on content property for low-complexityH265HEVC encoderrdquo IEEE Transactions on Broadcasting vol62 no 3 pp 675ndash684 2016

[7] X Chen S Feng and D Pan ldquoAn improved approach oflung image segmentation based on watershed algorithmrdquo inProceedings of the the 7th International Conference on InternetMultimedia Computing and Service pp 1ndash5 Zhangjiajie ChinaAugust 2015

[8] Y Zheng B Jeon D Xu Q M J Wu and H Zhang ldquoImagesegmentation by generalized hierarchical fuzzy C-means algo-rithmrdquo Journal of Intelligent and Fuzzy Systems vol 28 no 2pp 961ndash973 2015

[9] V Osuna-Enciso E Cuevas and H Sossa ldquoA comparison ofnature inspired algorithms for multi-threshold image segmen-tationrdquo Expert Systems with Applications vol 40 no 4 pp 1213ndash1219 2013

[10] T Kurban P Civicioglu R Kurban and E Besdok ldquoCompari-son of evolutionary and swarmbased computational techniquesfor multilevel color image thresholdingrdquo Applied Soft Comput-ing Journal vol 23 pp 128ndash143 2014

[11] J N Kapur P K Sahoo and A K C Wong ldquoA new methodfor gray-level picture thresholding using the entropy of thehistogramrdquo Computer Vision Graphics and Image Processingvol 29 no 3 pp 273ndash285 1985

[12] N Otsu ldquoA threshold selection method from gray-level his-togramsrdquo Automatica vol 11 no 285ndash296 pp 23ndash27 1975

[13] X Li Z Zhao and H D Cheng ldquoFuzzy entropy thresholdapproach to breast cancer detectionrdquo Information Sciences -Applications vol 4 no 1 pp 49ndash56 1995

[14] J Kittler and J Illingworth ldquoMinimum error thresholdingrdquoPattern Recognition vol 19 no 1 pp 41ndash47 1986

[15] Y Xue S Zhong T Ma and J Cao ldquoA hybrid evolution-ary algorithm for numerical optimization problemrdquo IntelligentAutomation amp Soft Computing vol 21 no 4 pp 473ndash490 2015

[16] P-Y Yin ldquoA fast scheme for optimal thresholding using geneticalgorithmsrdquo Signal Processing vol 72 no 2 pp 85ndash95 1999

[17] W Fujun L Junlan L Shiwei Z Xingyu Z Dawei and TYanling ldquoAn improved adaptive genetic algorithm for imagesegmentation and vision alignment used in microelectronicbondingrdquo IEEEASMETransactions onMechatronics vol 19 no3 pp 916ndash923 2014

[18] S Banerjee and N D Jana ldquoBi level kapurs entropy basedimage segmentation using particle swarm optimizationrdquo inProceedings of the 3rd International Conference on ComputerCommunication Control and InformationTechnology (C3IT rsquo15)pp 1ndash4 Hooghly India February 2015

[19] M-H Horng ldquoMultilevel thresholding selection based on theartificial bee colony algorithm for image segmentationrdquo ExpertSystems with Applications vol 38 no 11 pp 13785ndash13791 2011

[20] D Oliva E Cuevas G Pajares D Zaldivar and V OsunaldquoA multilevel thresholding algorithm using electromagnetismoptimizationrdquo Neurocomputing vol 139 pp 357ndash381 2014

[21] S Sarkar G R Patra and S Das ldquoA differential evolutionbased approach for multilevel image segmentation using mini-mum cross entropy thresholdingrdquo in Swarm Evolutionary andMemetic Computing pp 51ndash58 Springer Berlin Germany 2011

[22] Y Xue Y Zhuang T Ni S Ni and X Wen ldquoSelf-adaptivelearning based discrete differential evolution algorithm forsolving CJWTA problemrdquo Journal of Systems Engineering andElectronics vol 25 no 1 pp 59ndash68 2014

[23] S Agrawal R Panda S Bhuyan and B K Panigrahi ldquoTsallisentropy based optimal multilevel thresholding using cuckoosearch algorithmrdquo Swarm and Evolutionary Computation vol11 pp 16ndash30 2013

[24] PD Sathya andRKayalvizhi ldquoOptimalmultilevel thresholdingusing bacterial foraging algorithmrdquo Expert Systems with Appli-cations vol 38 no 12 pp 15549ndash15564 2011

[25] S Ayas H Dogan E Gedikli and M Ekinci ldquoMicroscopicimage segmentation based on firefly algorithm for detectionof tuberculosis bacteriardquo in Proceedings of the 23rd SignalProcessing and Communications Applications Conference (SIUrsquo15) pp 851ndash854 Malatya Turkey May 2015

[26] S Mirjalili S M Mirjalili and A Lewis ldquoGrey wolf optimizerrdquoAdvances in Engineering Software vol 69 pp 46ndash61 2014

[27] B Akay ldquoA study on particle swarm optimization and artificialbee colony algorithms for multilevel thresholdingrdquo Applied SoftComputing vol 13 no 6 pp 3066ndash3091 2013

[28] A K Bhandari A Kumar and G K Singh ldquoModified artificialbee colony based computationally efficient multilevel thresh-olding for satellite image segmentation using Kapurrsquos Otsu andTsallis functionsrdquo Expert Systems with Applications vol 42 no3 pp 1573ndash1601 2015

[29] P Ghamisi M S Couceiro J A Benediktsson and N M FFerreira ldquoAn efficientmethod for segmentation of images basedon fractional calculus and natural selectionrdquo Expert Systemswith Applications vol 39 no 16 pp 12407ndash12417 2012

[30] L Li L Sun W Kang J Guo C Han and S Li ldquoFuzzymultilevel image thresholding based on modified discrete greywolf optimizer and local information aggregationrdquo IEEE Accessvol 4 pp 6438ndash6450 2016

[31] H-S Wu F-M Zhang and L-S Wu ldquoNew swarm intelligencealgorithm-wolf pack algorithmrdquo Xi Tong Gong Cheng Yu DianZi Ji ShuSystems Engineering and Electronics vol 35 no 11 pp2430ndash2438 2013

[32] H Wu and F Zhang ldquoA uncultivated wolf pack algorithm forhigh-dimensional functions and its application in parametersoptimization of PID controllerrdquo in Proceedings of the IEEECongress on Evolutionary Computation (CEC rsquo14) pp 1477ndash1482Beijing China July 2014

[33] H-S Wu and F-M Zhang ldquoWolf pack algorithm for uncon-strained global optimizationrdquo Mathematical Problems in Engi-neering vol 2014 Article ID 465082 17 pages 2014

[34] Q Zhou and Y Zhou ldquoWolf colony search algorithm based onleader strategyrdquo Application Research of Computers vol 9 pp2629ndash2632 2013

[35] G M Komaki and V Kayvanfar ldquoGrey Wolf Optimizer algo-rithm for the two-stage assembly flow shop scheduling problemwith release timerdquo Journal of Computational Science vol 8 pp109ndash120 2015

16 Computational Intelligence and Neuroscience

[36] L I Wong M H Sulaiman M R Mohamed and M SHong ldquoGrey Wolf Optimizer for solving economic dispatchproblemsrdquo in Proceedings of the IEEE International Conferenceon Power and Energy (PECon rsquo14) pp 150ndash154 KuchingMalaysia December 2014

[37] A Chaman-Motlagh ldquoSuperdefect photonic crystal filter opti-mization using Grey Wolf Optimizerrdquo IEEE Photonics Technol-ogy Letters vol 27 no 22 pp 2355ndash2358 2015

[38] P Q Dzung N T Tien N Dinh Tuyen and H Lee ldquoSelectiveharmonic elimination for cascaded multilevel inverters usinggrey wolf optimizer algorithmrdquo in Proceedings of the 9thInternational Conference on Power Electronics and ECCE Asia(ICPE rsquo15-ECCE Asia) June 2015

[39] N Muangkote K Sunat and S Chiewchanwattana ldquoAnimproved grey wolf optimizer for training q-Gaussian RadialBasis Functional-link netsrdquo in Proceedings of the InternationalComputer Science and Engineering Conference (ICSEC rsquo14) pp209ndash214 Khon Kaen Thailand August 2014

[40] A Zhu C Xu Z Li J Wu and Z Liu ldquoHybridizing grey Wolfoptimization with differential evolution for global optimizationand test scheduling for 3D stacked SoCrdquo Journal of SystemsEngineering and Electronics vol 26 no 2 pp 317ndash328 2015

[41] P ArbelaezMMaire C Fowlkes and JMalik ldquoContour detec-tion and hierarchical image segmentationrdquo IEEE Transactionson Pattern Analysis and Machine Intelligence vol 33 no 5 pp898ndash916 2011

Submit your manuscripts athttpswwwhindawicom

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Applied Computational Intelligence and Soft Computing

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Industrial EngineeringJournal of

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Human-ComputerInteraction

Advances in

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Computational Intelligence and Neuroscience 3

researchers abstracted three intelligent behaviors scoutingcalling and besieging and two intelligent rules winner-take-all generation rule of leadwolf and stronger-survive renewingrule of wolf packThe experiments show thatWPA has betterconvergence and robustness especially for high-dimensionalfunctions In the same year Q Zhou and Y Zhou [34]proposed Wolf Colony Search Algorithm based on LeaderStrategy (LWCA) The idea of the algorithm originated fromthe phenomenon that there exists individual competitionsamong the wolf pack The strongest wolf was selected asthe leader of the wolves the wolves hunted prey under theleadership of the leader so that they could be more effectivein capturing prey The experiments show that the algorithmhas better performance on convergence speed and accuracyand it is difficult to trap-in local minimum CoincidentallyMirjalili et al [26] proposed grey wolf optimizer (GWO)inspired by grey wolves in 2014 In GWO algorithm The120572 wolf is also called the dominant wolf the level of otherthree types decreases in turn and the 120596 is the lowest-level wolf In addition the three main steps of huntingsearching for prey encircling prey and attacking prey areimplemented Compared to well-known heuristics such asPSO GSA DE EP and ES [35ndash38] the GWO algorithmshows better convergence and higher local optima avoidanceIn 2014 Muangkote et al [39] proposed an improved greywolf optimizer method (IGWO) The strategy on parameterselection of IGWO improves the search capability and thehybridization strategy increases the diversity of the agentZhu et al [40] proposed to combine GWO with differencealgorithm for solving the global optimization problem in2015

By introducing MDGWO to MT the paper solves theproblem of thresholds option by taking Kapurrsquos entropy forobjective functionThe proposed algorithm shows better seg-mentation result high efficiency and accuracy and stability ofthe range of threshold

3 Formulation of the MultilevelImage Thresholding

MT needs to set a set of threshold values 119905119894 based on thatthe image can be segmented into different regions By meansof intelligent optimization to obtain the optimal thresholdvalue the process of image segmentation has to be formulatedbefore taking image elements or image features as parametersto determine the optimized objective functions with thepurpose of getting close to the optimal threshold value

31 Pixel Grouping Based on Thresholding Supposing thateach image has 119871 grey levels the thresholding conversionis a process in which the pixels of image are divided intodifferent classes or groups according to the grey levels Thiskind of classification has to choose a threshold (th) or followthe following rules

1198621 larr997888 119901 if 0 ≪ 119901 lt th1198622 larr997888 119901 if th ≪ 119901 lt 119871 minus 1 (1)

where 119901 indicates the grey level of a pixel in image 119868119892 119901 =0 1 2 119871 minus 1 1198621 1198622 is the class of pixel 119901 and th is thethreshold

Equation (1) is the description of bilevel thresholding ForMT problem the description is

1198621 larr997888 119901 if 0 ≪ 119901 lt th11198622 larr997888 119901 if th1 ≪ 119901 lt th2119862119894 larr997888 119901 if th119894minus1 ≪ 119901 lt th119894

119862119896+1 larr997888 119901 if th119896 ≪ 119901 lt 119871 minus 1

(2)

where th1 th2 th119894 th119894+1 th119896 indicates different thresh-olds Therefore MT can be described as the problem ofsolving the set of th Kapurrsquos entropy is a well-knownmethodused to solve this kind of problem by maximizing theobjective function to determine the optimal threshold

32 Concept of Kapurrsquos Entropy for Image SegmentationKapurrsquos entropy is one of the early methods used in bilevelthresholding and it has been applied in MT field by scholarsKapurrsquos entropy is an effective image segmentation techniquebased on threshold and probability distributions of imagehistogramWhen the optimal threshold is allocated correctlythe entropy is the biggest of all Entropy is used tomeasure thecompactness and separability between classesThepurpose ofthe method is to find the optimal threshold and produce themaximum entropy This method extracts the brightness level119871 from a greyscale image or a RGB image The probabilitydistribution of brightness value is calculated as follows

119875ℎ119886119894

= ℎ119886119894SP

SPsum119894=1

119875ℎ119886119894

= 1119886 =

1 2 3 if RGB Image1 if Grayscale Image

(3)

where 119894 indicates a specific brightness level ranging from 0 to119871minus1 parameter 119886 is used to judge whether the image is a greyimage or a RGB image SP is the total of pixels and ℎ119886119894 is thepixel number of the brightness level 119894 in 119886 For the simplestsegmentation there are two classes defined as follows

1198621 = 119875ℎ11988611205961198860 (th)

119875ℎ119886th1205961198860 (th) 1198622 = 119875ℎ119886th+11205961198861 (th)

119875ℎ1198861198711205961198861 (th)

(4)

4 Computational Intelligence and Neuroscience

where1205960(th)1205961(th) are the probability distribution of11986211198622respectively the equation is as follows

1205961198860 (th) = thsum119894=1

119875ℎ119886119894

1205961198861 (th) = 119871sum

119894=th+1119875ℎ119886119894

(5)

Therefore the objective function of Kapurrsquos entropy canbe defined as

119891 (th) = 1198671198861 + 1198671198862 119886 =

1 2 3 if RGB Image1 if Grayscale Image

(6)

where entropy1198671 and entropy1198672 are derived by (4)

1198671198861 = thsum119894=1

119875ℎ1198861198941205961198860 ln(119875ℎ119886

1198941205961198860 ) 1198671198862 = 119871sum

119894=th+1

119875ℎ1198861198941205961198861 ln(119875ℎ119886

1198941205961198861 ) (7)

where 119875ℎ119886119894

is the probability distribution of strength grades by(3) and 1205960(th) 1205961(th) are the probability distribution of 11986211198622 respectively

Naturally the entropy-based method can be extended tomultithresholdingmethod In this case image can be dividedinto 119896 classes with 119896 minus 1 thresholds Therefore multilevelthresholding objective function can be defined as follows

119891 (TH) = 119896sum119894=1

119867119886119894 119886 =

1 2 3 if RGB Image1 if Grayscale Image

(8)

where TH = [th1 th2 th119896minus1] is a vector containingmultiple thresholds and each entropy is calculated withthe corresponding threshold respectively And (7) can beextended to the calculation of 119896 entropies as follows

1198671198861 = th1sum119894=1

119875ℎ1198861198941205961198860 ln(119875ℎ119886

1198941205961198860 ) 1198671198862 = th2sum

119894=th1+1

119875ℎ1198861198941205961198861 ln(119875ℎ119886

1198941205961198861 )

119867119886119896 = 119871sum119894=th119896minus1+1

119875ℎ119886119894120596119886119896minus1

ln( 119875ℎ119886119894120596119886119896minus1

)

(9)

where the probabilities of 119896 classes are calculated by (10)finally it needs to categorize the pixels into correspondingclasses and complete the multilevel image segmentation by(2)

1205961198860 (th) = th1sum119894=1

119875ℎ119886119894

1205961198861 (th) = th2sum

119894=th1+1119875ℎ119886119894

120596119886119896minus1 (th) = 119871sum119894=th119896minus1+1

119875ℎ119886119894

(10)

As mentioned above multilevel thresholding is formu-lated tomaximize Kapurrsquos entropy and the objective functionis shown in (8) As previously mentioned this paper willuse the MDGWO to optimize the objective function theoptimization algorithm is the key to the quality of imagesegmentation

4 Image Segmentation Based on MDGWO

41 Standard Grey Wolf Optimizer Grey wolfs (Canis lupus)belongs to Canidae family which are considered as apexpredators meaning that they are at the top of the foodchain They have a very strict social dominant hierarchy Thealgorithm divides the wolves into four types 120572 120573 120575 and 120596The social behavior of each type wolves can be summarizedas follows

The leaders are amale and a female called alphaThey arethe most brilliant wolves and the best in terms of managingthe packThe alphawolf is also called the dominant wolf sincehisher orders should be followed by the pack uncondition-ally The location of alpha presents the best solution of theproblem

The second level in the hierarchy of grey wolves isbeta The betas are subordinate wolves that help the alphain decision-making or other pack activities The beta wolfshould respect the alpha but commands the other lower-level wolves as well It plays the role of an advisor to thealpha and discipliner for the pack The beta reinforces alpharsquoscommands throughout the pack and gives feedback to thealpha

The third level in the hierarchy of grey wolves is deltaDelta wolves have to submit to alphas and betas but theydominate the omega scouts sentinels elders hunters andcaretakers who belong to this category They are responsiblefor watching the boundaries of the territory warning the packin case of any danger protecting and guaranteeing the safetyof the pack helping the alphas and betas when hunting preyand providing food for the pack and caring for the weak illand wounded wolves in the pack

The lowest ranking grey wolf is omega It may seem theomega is not an important individual in the pack but it has

Computational Intelligence and Neuroscience 5

Table 1 The corresponding relationships between MDGWO andimage segmentation

MDGWO Image segmentationPositions Threshold segmentation solutionAlpha Pos Optimal solutionAlpha score The largest fitness valueFitness Fitness function valueBest R Best fitness

been observed that the whole pack face internal fighting andproblems in case of losing the omega which is harmful to thegroup structure

In addition to the social hierarchy of wolves grouphunting is another interesting social behavior of grey wolvesThemain phases of greywolf hunting are as follows searchingfor the prey tracking chasing and approaching the preypursuing encircling and harassing the prey until it stopsmoving attacking toward the prey

In order to mathematically model the social hierarchy ofwolves in GWO [26] the fittest solution is considered as thealpha (120572) Consequently the second and third best solutionsare named beta (120573) and delta (120575) respectively The rest ofthe candidate solutions are assumed to be omega (120596) In theGWO algorithm the hunting (optimization) is guided by 120572120573 and 120575 The 120596 wolves follow these three wolves

In addition to the above four abstract models this paperproposes MDGWO based on the standard GWO settings forMT In the improved algorithm the corresponding relation-ships between grey wolf hunting and image segmentation areshown in Table 1

42 The Initialization of MDGWO The size of the wolf packis assumed as SN SN candidate solutions (the location ofthe wolves is the threshold values) are generated randomly inthe initialization phase Different from the GWO the imagethreshold is a set of discrete integers by rounding toward zero

997888rarr119883119894 = lfloorrand (SN 1) sdot (119906119887 minus 119897119887) + 119897119887rfloor (11)

where 119906119887 and 119897119887 are the upper limit and the lower limit ofparameters (namely boundaries of parameter)

After the initialization of candidate solutions MDGWOjudges whether the initial solution 997888rarr119883119894 is in the range of[119906119887 119897119887] If it is the fitness value will be calculated otherwisethe search agent will be put back in the search space (ieguaranteeing the initial solution in the range of [119906119887 119897119887])by (12) and then the fitness value will be recalculated byrounding toward zero

997888rarr119883119894 = lfloor(997888rarr119883119894 sdot (119906 + 119897)) + 119906119887 sdot 119906 + 119897119887 sdot 119897rfloor (12)

where 119906 = 997888rarr119883119894 gt 119906119887 119897 = 997888rarr119883119894 lt 119897119887

In the all fitness values calculated by (13) of candidatesolutions MDGWO chooses three optimal candidate solu-tions to assign to997888rarr119883120572997888rarr119883120573997888rarr119883120575 and records all the fitness valuesand candidate functions (namely locations of the wolves)

Fitness (997888rarr119883119894) = 1(1 + 119891 (997888rarr119883119894)) (119891 (997888rarr119883119894) ge 0)

1 + 100381610038161003816100381610038161003816119891 (997888rarr119883119894)100381610038161003816100381610038161003816 (119891 (997888rarr119883119894) ge 0) (13)

where997888rarr119883119894 is one of the candidate solutions which include a setof thresholds then 119891(997888rarr119883119894) is calculated by Kapurrsquos function asshown in (8)

43 Iterative Process After the initialization all the searchagents have to update their current locations for optimize thecandidate solutions over the course of iteration In the rangeof the maximum iteration (Max iter) all the update processand optimization process will be completed

431 Encircling Prey Grey wolves encircle prey before thehunt In the mathematical model the wolf pack has to updatethe position (namely the threshold value) constantly so thatthey can approach the prey In the algorithm all the agentposition updated by (15) over the course of encirclement

= 100381610038161003816100381610038161003816 sdot 997888997888rarr119883119901 (119905) minus (119905)100381610038161003816100381610038161003816 (14)

(119905 + 1) = 997888997888rarr119883119901 (119905) minus sdot (15)

where 119905 indicates the current iteration and are coefficientvectors 997888997888rarr119883119901 is the position vector of the prey and indicatesthe position vector of a grey wolf The vectors and arecalculated as follows

= 2 119890 sdot 997888rarr1199031 minus 119890 (16)

= 2997888rarr1199032 (17)

where components of 119890 are linearly decreased from 2 to 0 overthe course of iterations and997888rarr1199031 997888rarr1199032 are random vectors in [0 1]The detailed selection of the two vectors can be found in [26]

432 The Behavior of Hunting The hunt is usually guided bythe alphaThebeta and deltamight also participate in huntingoccasionally However in an abstract search space we haveno idea about the location of the optimum (prey) In order tomathematically simulate the hunting behavior of grey wolvesit is supposed that the alpha beta and delta have betterknowledge about the potential location of prey Thereforethe algorithm saves the first three best solutions obtainedso far and obliges the other search agents (including theomegas) to update their positions according to the positionof the best search agents The original GWO algorithm inliterature [26] calculates the updated parameter of searchagents by the first three best solutions and then updates thelocation of search agents (namely new candidate solutions)

6 Computational Intelligence and Neuroscience

if 10038161003816100381610038161003816A10038161003816100381610038161003816lt 1

(a)

if 10038161003816100381610038161003816A10038161003816100381610038161003816gt 1

(b)

Figure 1 Attacking prey of grey wolf

according to their average value As for the specific formulasand the detailed calculation please refer to literature [26]In order to approach the best solution more quickly theproposed algorithm in this paper improves the current bestsolution in solutions updating by weighting method Theupdate formulations are as shown in (20) and correlationcoefficients are calculated by (18) (19) where 1198601 1198602 1198603 arecalculated by (16)997888rarr119863120572 = 100381610038161003816100381610038161003816997888rarr1198621 sdot 997888rarr119883120572 minus 100381610038161003816100381610038161003816 997888rarr119863120573 = 100381610038161003816100381610038161003816997888rarr1198622 sdot 997888rarr119883120573 minus 100381610038161003816100381610038161003816 997888rarr119863120575 = 100381610038161003816100381610038161003816997888rarr1198623 sdot 997888rarr119883120575 minus 100381610038161003816100381610038161003816

(18)

997888rarr1198831 = 997888rarr119883120572 minus 997888rarr1198601 sdot 997888rarr119863120572997888rarr1198832 = 997888rarr119883120573 minus 997888rarr1198602 sdot 997888rarr119863120573997888rarr1198833 = 997888rarr119883120575 minus 997888rarr1198603 sdot 997888rarr119863120575(19)

(119905 + 1) = 1199081 sdot 997888rarr1198831 + 1199082 sdot 997888rarr1198832 + 1199083 sdot 997888rarr1198833 (20)

where 1199081 1199082 1199083 are the corresponding weights which arecalculated by

1199081 = 1198911119865 1199082 = 1198912119865 1199083 = 1198913119865

(21)

where 1198911 1198912 1198913 calculated by (13) are the correspondingfitness values of120572120573 120575119865 = 1198911+1198912+1198913This paper emphasizes

that different from GWO updating search agents MDGWOuses (20) and (21) to update the location of search agentsby weighting method for the first time it is also the majorcontribution to the improved GWO

433 Attacking Prey The grey wolves finish the hunt byattacking the prey when it stops moving In order to mathe-matically model approaching the prey we decrease the valueof 119890 Note that the fluctuation range of is also decreasedby 119890 In other words is a random value in the interval[minus119890 119890] where 119890 is decreased from 2 to 0 over the course ofiterations When random values of are in [minus1 1] the nextposition of a search agent can be in any position betweenits current position and the position of the prey that is thesearch agent will approach the best solution gradually asshown in Figure 1

At the same time for the purpose of mathematical modeldivergence we utilize with random values greater than 1or less than minus1 to oblige the search agent to diverge from theprey As shown in Figure 1(b) gt 1 forces the grey wolves todiverge from the prey to hopefully find a better prey

44 Pseudocode of MDGWO The application of MDGWOalgorithm in image segmentation mainly lies in optimizingKapurrsquo entropy to obtain the best threshold therefore thefitness function as shown in (13) will be calculated based onKapurrsquos entropy

Step 1 Read image 119869 if 119869 is a RGB image then it will beprocessed by three channel of 119869R 119869G 119869B and store the datain ℎR ℎG ℎB respectively if 119869 is a grey image then read thegrey value and store it in ℎgrStep 2 According to (3) calculate image grey values andprobability distribution histogram

Computational Intelligence and Neuroscience 7

Step 3 Initialize the population of grey wolves parameter 119890 and Max iter

Step 4 Initialize the population 997888rarr119883119894 (119894 = 1 2 SN)randomly 997888rarr119883119894 = rand (SN 1) sdot (119906119887 minus 119897119887) + 119897119887 (22)

Step 5 Use (11) to discretize 997888rarr119883119894 that is being roundedtoward zero Use (12) to adjust the singular data beyond theboundaries of search space

Step 6 Calculate objective functions of each search agent byusing (8) And calculate the fitness value of each search agenton the basis of objective functions

Step 7 According to the fitness values assigning first threebest search agents to 997888rarr119883120572 997888rarr119883120573 997888rarr119883120575 respectivelyStep 8 Updating encircling parameters based on997888rarr119883120572997888rarr119883120573997888rarr119883120575which include calculating 997888rarr1198601 997888rarr1198602 997888rarr1198603 by (16) 997888rarr1198621 997888rarr1198622 997888rarr1198623 by(17) and 997888rarr119863120572 997888rarr119863120573 997888rarr119863120575 by (18)Step 9 Update the position of search agents based on (19) and(20) for the next hunting

Step 10 Add one to circular point if 119902 ge Max iter ormeet thestop condition of the algorithm the iteration will be finishedand skip to Step 11 otherwise skip to Step 5

Step 11 Set the location of the wolf that has the best objectivefunction as the best threshold of segmentation

Step 12 Input best threshold and images before and aftersegmentation

5 Experiments and Discussion

51 Parameters Settings The proposed algorithm has beentested under a set of benchmark images Some of theseimages are widely used in the multilevel image segmenta-tion literature to test different methods (Cameraman LenaBaboon and Maize) Others are chosen on purpose fromthe Berkeley Segmentation Data Set and Benchmarks 500(BSD500 for short see [41]) as shown in Figure 2 Theexperiments were carried out on a Lenovo Laptop with anIntel Core i5 processor and 4GBmemoryThe algorithmwasdeveloped via the signal processing toolbox image processingtoolbox and global optimization toolbox of Matlab R2011bAccording to relevant literatures manymethods were provedto have certain advantages compared with previous meth-ods This paper chooses the best advantageous method ascomparison objective the earlier or inferior literatures willno longer be used for the analysis Based on quantities ofcontrast experiments this paper will verify the superiority ofMDGWO in image segmentation by comparison of imagedata chart and so forth In the following sections MDGWOwill be compared with the algorithm using electromagnetism

optimization (EMO) proposed in [20] the differential evo-lution (DE) [27] the Artifical Bee Colony (ABC) [10] andthe original grey wolf optimizer The EMO DE and ABC arethe latest intelligent optimization methods by using Kapurrsquosentropy so far The comparison with GWO is mainly used totest the advantages of MDWGO

In order to avoid the randomness of results we useappropriate statistical metrics to compare the effectiveness ofthese algorithms According to [19 20] and the experimentstest thresholds are th = 2 3 4 5 [1ndash3] and the stop criterionof each experiment is 150 iterations the detailed settings ofparameters are showed in Table 2

For verifying the stability we use (23) to calculate thestandard deviation (STD) at the end of each test Once theSTD value increases the algorithms becomes more instablecorrespondingly [29]

STD = radicMax itersum119894=1

(120579119894 minus 120576)2Max iter

(23)

In addition the peak signal to noise ratio (PSNR [20]) isused to compare the similarity between the segmented imageand original image according to the mean square error (MSE[26]) of each pixel

PSNR = 20 log10 ( 255MSE

) (dB) (24)

MSE = radicsumro119894=1sumco119895=1 (119868119886119900 (119894 119895) minus 119868119886th (119894 119895))

ro times co (25)

where 119868119886119900 is the original image 119868119886th is the segmented image and119886 depends on the type of image (grey image or RGB image)ro co are respectively the total number of rows and columnsin an image

Because Kapurrsquos entropy is based on histogram of theimage this paper provides test images and the correspondinghistograms From Figure 2 it can be seen that each imagehas the only distinctive histogram which can guarantee theuniversality and commonality of the algorithm More impor-tantly most of these histograms do not follow the bimodalcharacteristic therefore the difficulty level of optimizationincreases accordingly

52 The Image Segmentation Result Based on MDGWO withDifferent Thresholds In order to reflect the segmentationeffect Figures 3 and 4 illustrate the segmentation results oforiginal images in Figure 2when the threshold is 2 3 4 and 5respectively The experiments indicate that the segmentationresults turn out to be finer and there are alsomore segmentedareas when the number of thresholds is larger and vice versaIn extreme cases when the threshold is 2 the algorithmis reduced to be binary image segmentation (foreground-background segmentation) Certainly that how many areasare segmented is related to the applications and requirementsthis method only needs to set the corresponding number ofthresholds (th) Besides giving the MDGWO segmentationresults like [20] Figures 3 and 4 also mark the position

8 Computational Intelligence and Neuroscience

Table 2 Parameters settings of MDGWO

Parameters Population size Threshold Number of iterations Run time Lower bound Upper boundValue 50 2 3 4 5 150 35 1 256

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

000100020003000400050006000700080009

001

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 3000

0002000400060008

0010012001400160018

002

times10minus3

Histogram of left col ImageImage Histogram of left col

(a) Cameraman (b) Lena

(c) Baboon (d) Butterfly

(e) Maize (f) Starfish

(g) Smiling Girl (h) Surfing

Figure 2 The original images and their histograms

of the threshold in each histogram Compared with otherMT methods it is difficult to find the difference in termsof the segmentation effect Therefore Section 54 lists thethresholds PSNR STD and MEAN for comparisons ofMDGWO results and other techniques

53 The Comparison of MDGWO in Multilevel Image Thresh-olding with Different Objective Functions In Section 1 wesummarize the relevant objective functions The commonlyused optimization functions include maximization of theentropy andmaximization of the between-class variance (egOtsursquos method) In [27] the authors respectively analyze

these objective functions and compare Kapur and Otsusystematically The experiment results show that Kapurrsquosentropy gets the best effectiveness Therefore in order toverify MDGWOrsquos efficiency we compare the thresholds andPSNR between Otsu and Kapur in Table 3

As shown inTable 3 the threshold distribution ofKapur ismore dispersed and wider in most cases However the effectof image thresholding cannot be seen from the thresholddistribution directly Therefore we focus on analysis thePSNR between Otsu and Kapur In terms of PSNR the Kapurmethod produces higher PSNR values on most items inFigure 2 except for the Sea Star Imagewith 119896 = 3 5 and SurferImage with 119896 = 4

Computational Intelligence and Neuroscience 9

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005001

0015002

0025

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

000100020003000400050006000700080009

001

0 50 100 150 200 250 3000

000100020003000400050006000700080009

001

0 50 100 150 200 250 3000

000100020003000400050006000700080009

001

0 50 100 150 200 250 3000

000100020003000400050006000700080009

001

Image

Cam

eram

anLe

naBa

boon

Butte

rfly

th = 2 th = 3 th = 4 th = 5

Figure 3 The segmentation results of (a)ndash(d) in Figure 2 and their thresholds in histograms

10 Computational Intelligence and Neuroscience

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0002000400060008

0010012001400160018

002

0 50 100 150 200 250 3000

0002000400060008

0010012001400160018

002

0 50 100 150 200 250 3000

0002000400060008

0010012001400160018

002

0 50 100 150 200 250 30000002000400060008

0010012001400160018

002

times10minus3

times10minus3

times10minus3

times10minus3

Image th = 2 th = 3 th = 4 th = 5

Mai

zeSt

arfis

hSm

iling

Girl

Surfi

ng

Figure 4 The segmentation results of (e)ndash(h) in Figure 2 and their thresholds in histograms

Computational Intelligence and Neuroscience 11

Table 3 The comparison of MDGWOrsquos efficiency between Otsu and Kapur

Image 119896 Otsu thresholds PSNR Kapur thresholds PSNR

Cameraman

2 70 144 119475 44 106 1446293 58 119 156 129933 44 98 148 1993374 40 93 139 170 160180 39 83 119 156 2116845 35 81 121 149 174 163710 23 58 94 125 159 231191

Lena

2 92 151 131029 93 163 1471643 80 126 171 157626 70 121 172 1751444 75 114 145 180 164291 43 81 127 171 2017295 73 109 136 161 189 167206 41 73 103 141 178 218208

Baboon

2 97 149 124396 78 141 1603023 83 123 160 137731 46 103 151 1863404 70 105 136 167 149493 34 75 117 159 2051985 66 98 125 150 175 160012 29 64 100 134 170 220929

Butterfly

2 100 152 124400 87 150 1493253 81 118 159 142563 62 104 152 1855394 73 101 129 164 146987 49 88 128 168 2107115 69 95 121 149 177 164688 48 80 113 145 180 224539

Maize

2 92 168 136677 84 165 1404073 76 128 187 152676 59 113 171 1658534 65 104 150 200 167309 45 80 125 187 1898185 56 86 123 164 208 185649 39 74 108 147 198 208792

Sea Star

2 85 157 148445 81 160 1485953 69 120 178 176040 60 111 172 1745834 59 99 137 187 194039 46 89 131 184 1944875 51 85 117 150 193 214000 47 83 118 150 196 209681

Smiling Girl

2 60 123 131358 88 145 1800333 47 100 131 128470 44 91 145 1911484 28 74 111 136 156914 24 67 100 145 2007595 20 63 95 124 158 18 2260 44 83 115 152 203 217937

Surfer

2 92 162 125401 52 141 1643433 71 111 177 160569 52 103 168 1893434 47 81 118 179 208786 49 86 131 185 2072185 46 77 105 143 196 216071 24 53 88 126 183 218961

The average value of Kapur is improved averagely by2224 compared to Otsu by checking against the cor-responding PSNR values which are obtained from theMDGWO The maximum value is increased by 5342 forCameraman Image when 119896 = 3 Therefore the Kapurmethod is significantly better than the Otsu method and wealso mainly analyze the effectiveness of Kapurrsquos method inSection 54

54TheComparison ofQuality Assessment by PSNR STD andMEAN This paper adopts PSNR standard to evaluate thesegmentation quality in comparisonwith otherMTmethodsTables 4ndash6 illustrate the PSNR values under different thresh-olds ofMDGWOGWOEMODEABC and theMEANandSTD of objective functions As shown in Table 4 it can be

seen from the PSNR values that MDGWO gets the highestevaluation in most cases Thus it proves that MDGWO getsbetter results on image segmentation In addition when thenumber of thresholds increases it shows superior PSNRvalue In detail the MDGWO algorithm produces higherPSNR values on all items in Table 4 except for the SmilingGirl Image with 119896 = 5 and Surfer Image with 119896 = 4 on theresult of DE

As shown in Table 4 the average value of MDGWO isimproved averagely by 1316 compared toGWOby checkingagainst the corresponding PSNR valuesThemaximum valueis increased by 4505 for Butterfly Image when 119896 = 5

ComparingwithMTEMO the average value ofMDGWOis improved averagely by 1156 by checking against the cor-responding PSNR valuesThemaximumvalue is increased by3994 for Surfer Image when 119896 = 2

12 Computational Intelligence and Neuroscience

Table 4 PSNR metrics of MTEMO DE ABC GWO and MDGWO

Image 119896 MTEMO DE ABC GWO MDGWO

Cameraman

2 13626 12584 13920 14279 144633 18803 17584 14462 19696 199344 20586 20111 2081 20809 211685 20661 21282 2240 22404 23119

Lena

2 14672 8823 14590 14680 147163 17247 14386 17197 17416 175144 18251 16151 18559 19762 201735 20019 16720 20321 21299 21820

Baboon

2 16016 8103 16007 16024 160353 16016 12596 18592 18632 186344 18485 13178 18417 20480 205195 20507 13135 20224 22060 22092

Butterfly

2 11065 8702 14402 14762 149323 14176 13028 14504 17873 185534 16725 13028 16189 21021 210715 19026 14786 19286 21485 22453

Maize

2 13633 10549 13590 13950 140403 15229 13022 15295 16201 165854 16280 14270 16346 18713 189815 17211 15079 17046 20410 20879

Sea Star

2 14398 8610 14395 14809 148853 16987 14078 16981 17431 174584 18304 16191 18427 19421 194485 20165 16474 20330 20887 20968

Smiling Girl

2 13420 14986 13514 17989 180033 18254 11243 18069 18742 191144 18860 14556 18826 19823 200755 19840 22980 19769 21214 21793

Surfer

2 11744 9737 11878 16154 164343 18584 11638 18762 18895 189344 19478 21866 19647 20234 207215 20468 19576 20479 21699 21896

By comparing with DE the average value of MDGWO isimproved averagely by 3814 by checking against the cor-responding PSNR values The maximum value is increasedby 9789 for Baboon Image when 119896 = 2 The PSNR of theSmiling Girl with 119896 = 5 and Surfer Image with 119896 = 4 areslightly lower but the gap is not significant

Comparing between ABC and MDGWO the averagevalue of MDGWO is improved averagely by 1055 by check-ing against the corresponding PSNR values The maximumvalue is increased by 3836 for Surfer Image when 119896 = 2

From the perspective of STDwhich is shown in Table 5 itcan be observed that MDGWO shows obviously advantagesover MTEMO DE ABC and GWOThe smaller the STD isthe smaller the change of fitness functions over the course ofiterations will be that is the better stability of segmentation

Therefore the results show that MDGWO obtains excitingeffect in stability So MDGWOrsquos stability is better

Compared with GWO the average value of MDGWO isimproved averagely by 7352 compared to GWO by check-ing against the corresponding STD values The maximumvalue is increased by 9644 for Baboon Image when 119896 = 3and the minimum value is increased by 2492 for BaboonImage when 119896 = 3

By comparing with MTEMO the average value ofMDGWO is improved averagely by 4788 The maximumvalue is increased by 87 for Lena Image when 119896 = 2 and theminimum value is increased by 06 for Surfer Image when119896 = 3

Comparing between DE andMDGWO the average valueofMDGWO is improved averagely by 9560Themaximum

Computational Intelligence and Neuroscience 13

Table 5 STD metrics of MTEMO DE ABC GWO and MDGWO

Image 119896 MTEMO DE ABC GWO MDGWO

Camerman

2 01849 12592 01235 01697 004623 01649 17601 02122 02287 007584 02943 21995 03003 03627 006595 02999 26579 02784 04278 01964

Lena

2 00969 12902 00349 01536 001263 01665 17822 01300 03570 002644 02800 22104 01872 05965 009395 02515 25992 01827 05946 01570

Baboon

2 00108 12862 00358 02171 001023 00393 17678 00202 04376 001564 01727 22126 01610 02986 011845 02868 26239 02660 05377 02316

Butterfly

2 00903 12708 00750 02179 004653 02207 17429 02952 02712 020364 02482 22368 03906 04808 024155 02900 26571 04818 05096 02684

Maize

2 00356 13501 00218 03571 001883 01222 18612 00901 02225 002704 02305 23230 02605 03903 009275 02502 27461 03834 04584 01677

Sea Star

2 01073 13547 01088 01728 002903 01497 18741 01752 02028 003744 01596 23307 01817 05032 011195 02639 27550 02180 04550 01437

Smiling Girl

2 00377 12516 00318 01834 001113 00955 17311 00577 01712 002424 01966 21878 01094 02508 007815 01550 25989 02768 05273 01302

Surfer

2 00579 13213 00303 02681 002453 01002 18337 01646 03014 009964 03382 23317 01686 03162 014245 03690 27846 02580 03815 01706

value is increased by 9921 for Baboon Image when 119896 =2 The minimum value is increased by 8832 for ButterflyImage when 119896 = 3

Comparing with ABC the average value of MDGWOis improved averagely by 4590 The maximum value isincreased by 7970 for Lena Image when 119896 = 3 and theminimum value is increased by 1293 for Baboon Imagewhen 119896 = 5

As far as MEAN is concerned this parameter presentsthe average value of fitness function over the course ofiterations in Table 6 which reflects the algorithm stability tosome extent But its accuracy of evaluation is relatively lowwhich can only reflect the fuzzy stability of the algorithmThe experiment data is offered here just in response to theparameter provided in literature [20] In comparison withGWO MTEWO DE and ABC in Table 6 it can be safely

assumed that inmost casesMDGWOobtains higherMEANof fitness function Moreover the difference is extremelysmall when MDGWOrsquos MEAN is lower

From the analyses of Tables 3ndash6 together with the visualeffects of Figures 2 3 and 4 it can be observed thatMDGWO method obtains better segmentation effect andhas advantage in optimal process accuracy stability androbustnessThereforeMDGWO is aMT algorithmwith highaccuracy and high segmentation quality

6 Conclusion

This paper proposes a modified discrete grey wolf optimizerwhich is used to optimize the image histograms and realizethe multilevel image segmentation Based on the high effi-ciency of GWO in the course of optimization and stability

14 Computational Intelligence and Neuroscience

Table 6 MEANmetrics of MTEMO DE ABC GWO and MDGWO

Image 119896 MTEMO DE ABC GWO MDGWO

Camerman

2 17584 124212 177638 14634 174713 21976 173764 223059 21107 219194 26586 217520 268409 24927 274805 30506 262505 308328 30436 30548

Lena

2 17831 127730 178139 17809 183963 22120 176428 220832 22074 228564 25999 218784 260615 25318 264475 29787 257311 299664 29252 30381

Baboon

2 17625 127333 176760 17679 186193 22269 175005 221276 22129 229494 26688 219010 263912 26194 269005 30800 259681 303464 30067 30076

Butterfly

2 16681 125796 174205 17425 177233 21242 172545 222209 21585 224984 25179 220176 263794 25267 261905 28611 261795 306533 29492 29899

Maize

2 18631 133566 186316 18604 195423 23565 184245 232496 22941 239394 27529 229813 273931 26936 278425 31535 271709 312127 31023 30694

Sea Star

2 18754 134104 187295 18321 195873 23323 185516 232738 23245 239014 27582 230719 275057 27136 282105 31562 272551 314919 31167 31958

Smiling Girl

2 17334 123892 173129 17136 180353 21904 171339 218601 21253 219804 26040 216541 259904 25050 265975 30089 257130 300225 29870 30574

Surfer

2 18339 130786 183393 18283 188693 23231 181492 232889 23243 241354 27863 230548 278017 27275 274475 31823 274979 317335 31384 31325

this paper successfully applies the MDGWO to the field ofMT by improving the location selection mechanism of 120572 120573and 120575 during the hunting and using weight to optimize thefinal position of prey (best threshold)TheMDGWOmethodnot only obtains better segmentation quality but also showsobvious superiority over GWO MTEMO DE and ABC instability accuracy and multilevel thresholding

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work was supported in part by the National NaturalScience Foundation of China (no 61300239 no 71301081and no 61572261) the Postdoctoral Science Foundation (no

2014M551635 and no 1302085B) the Innovation Project ofGraduate Students Foundation of Jiangsu Province (KYLX150841) the Higher Education Revitalization Plan Foundationof Anhui Province (no 2013SQRL102ZD no 2015xdjy196no 2015jyxm728 no 2016jyxm0774 and no 2016jyxm0777)and Natural Science Fund for Colleges and Universities inJiangsu Province (no16KJB520034) A Project Funded by thePriority Academic Program Development of Jiangsu HigherEducation Institutions (PAPD) and Jiangsu CollaborativeInnovation Center on Atmospheric Environment and Equip-ment Technology (CICAEET)

References

[1] M Sonka V Hlavac and R Boyle Image Processing Analysisand Machine Vision Cengage Learning 2014

[2] S Masood M Sharif A Masood M Yasmin and M RazaldquoA survey on medical image segmentationrdquo Current MedicalImaging Reviews vol 11 no 1 pp 3ndash14 2015

Computational Intelligence and Neuroscience 15

[3] PGhamisiM S Couceiro FM LMartins and J A Benedikts-son ldquoMultilevel image segmentation based on fractional-orderdarwinian particle swarm optimizationrdquo IEEE Transactions onGeoscience and Remote Sensing vol 52 no 5 pp 2382ndash23942014

[4] M Waseem Khan ldquoA survey image segmentation techniquesrdquoInternational Journal of Future Computer and Communicationvol 3 no 2 pp 89ndash93 2014

[5] J Li X Li B Yang and X Sun ldquoSegmentation-based imagecopy-move forgery detection schemerdquo IEEE Transactions onInformation Forensics and Security vol 10 no 3 pp 507ndash5182015

[6] Z Pan J Lei Y Zhang X Sun and S Kwong ldquoFast motionestimation based on content property for low-complexityH265HEVC encoderrdquo IEEE Transactions on Broadcasting vol62 no 3 pp 675ndash684 2016

[7] X Chen S Feng and D Pan ldquoAn improved approach oflung image segmentation based on watershed algorithmrdquo inProceedings of the the 7th International Conference on InternetMultimedia Computing and Service pp 1ndash5 Zhangjiajie ChinaAugust 2015

[8] Y Zheng B Jeon D Xu Q M J Wu and H Zhang ldquoImagesegmentation by generalized hierarchical fuzzy C-means algo-rithmrdquo Journal of Intelligent and Fuzzy Systems vol 28 no 2pp 961ndash973 2015

[9] V Osuna-Enciso E Cuevas and H Sossa ldquoA comparison ofnature inspired algorithms for multi-threshold image segmen-tationrdquo Expert Systems with Applications vol 40 no 4 pp 1213ndash1219 2013

[10] T Kurban P Civicioglu R Kurban and E Besdok ldquoCompari-son of evolutionary and swarmbased computational techniquesfor multilevel color image thresholdingrdquo Applied Soft Comput-ing Journal vol 23 pp 128ndash143 2014

[11] J N Kapur P K Sahoo and A K C Wong ldquoA new methodfor gray-level picture thresholding using the entropy of thehistogramrdquo Computer Vision Graphics and Image Processingvol 29 no 3 pp 273ndash285 1985

[12] N Otsu ldquoA threshold selection method from gray-level his-togramsrdquo Automatica vol 11 no 285ndash296 pp 23ndash27 1975

[13] X Li Z Zhao and H D Cheng ldquoFuzzy entropy thresholdapproach to breast cancer detectionrdquo Information Sciences -Applications vol 4 no 1 pp 49ndash56 1995

[14] J Kittler and J Illingworth ldquoMinimum error thresholdingrdquoPattern Recognition vol 19 no 1 pp 41ndash47 1986

[15] Y Xue S Zhong T Ma and J Cao ldquoA hybrid evolution-ary algorithm for numerical optimization problemrdquo IntelligentAutomation amp Soft Computing vol 21 no 4 pp 473ndash490 2015

[16] P-Y Yin ldquoA fast scheme for optimal thresholding using geneticalgorithmsrdquo Signal Processing vol 72 no 2 pp 85ndash95 1999

[17] W Fujun L Junlan L Shiwei Z Xingyu Z Dawei and TYanling ldquoAn improved adaptive genetic algorithm for imagesegmentation and vision alignment used in microelectronicbondingrdquo IEEEASMETransactions onMechatronics vol 19 no3 pp 916ndash923 2014

[18] S Banerjee and N D Jana ldquoBi level kapurs entropy basedimage segmentation using particle swarm optimizationrdquo inProceedings of the 3rd International Conference on ComputerCommunication Control and InformationTechnology (C3IT rsquo15)pp 1ndash4 Hooghly India February 2015

[19] M-H Horng ldquoMultilevel thresholding selection based on theartificial bee colony algorithm for image segmentationrdquo ExpertSystems with Applications vol 38 no 11 pp 13785ndash13791 2011

[20] D Oliva E Cuevas G Pajares D Zaldivar and V OsunaldquoA multilevel thresholding algorithm using electromagnetismoptimizationrdquo Neurocomputing vol 139 pp 357ndash381 2014

[21] S Sarkar G R Patra and S Das ldquoA differential evolutionbased approach for multilevel image segmentation using mini-mum cross entropy thresholdingrdquo in Swarm Evolutionary andMemetic Computing pp 51ndash58 Springer Berlin Germany 2011

[22] Y Xue Y Zhuang T Ni S Ni and X Wen ldquoSelf-adaptivelearning based discrete differential evolution algorithm forsolving CJWTA problemrdquo Journal of Systems Engineering andElectronics vol 25 no 1 pp 59ndash68 2014

[23] S Agrawal R Panda S Bhuyan and B K Panigrahi ldquoTsallisentropy based optimal multilevel thresholding using cuckoosearch algorithmrdquo Swarm and Evolutionary Computation vol11 pp 16ndash30 2013

[24] PD Sathya andRKayalvizhi ldquoOptimalmultilevel thresholdingusing bacterial foraging algorithmrdquo Expert Systems with Appli-cations vol 38 no 12 pp 15549ndash15564 2011

[25] S Ayas H Dogan E Gedikli and M Ekinci ldquoMicroscopicimage segmentation based on firefly algorithm for detectionof tuberculosis bacteriardquo in Proceedings of the 23rd SignalProcessing and Communications Applications Conference (SIUrsquo15) pp 851ndash854 Malatya Turkey May 2015

[26] S Mirjalili S M Mirjalili and A Lewis ldquoGrey wolf optimizerrdquoAdvances in Engineering Software vol 69 pp 46ndash61 2014

[27] B Akay ldquoA study on particle swarm optimization and artificialbee colony algorithms for multilevel thresholdingrdquo Applied SoftComputing vol 13 no 6 pp 3066ndash3091 2013

[28] A K Bhandari A Kumar and G K Singh ldquoModified artificialbee colony based computationally efficient multilevel thresh-olding for satellite image segmentation using Kapurrsquos Otsu andTsallis functionsrdquo Expert Systems with Applications vol 42 no3 pp 1573ndash1601 2015

[29] P Ghamisi M S Couceiro J A Benediktsson and N M FFerreira ldquoAn efficientmethod for segmentation of images basedon fractional calculus and natural selectionrdquo Expert Systemswith Applications vol 39 no 16 pp 12407ndash12417 2012

[30] L Li L Sun W Kang J Guo C Han and S Li ldquoFuzzymultilevel image thresholding based on modified discrete greywolf optimizer and local information aggregationrdquo IEEE Accessvol 4 pp 6438ndash6450 2016

[31] H-S Wu F-M Zhang and L-S Wu ldquoNew swarm intelligencealgorithm-wolf pack algorithmrdquo Xi Tong Gong Cheng Yu DianZi Ji ShuSystems Engineering and Electronics vol 35 no 11 pp2430ndash2438 2013

[32] H Wu and F Zhang ldquoA uncultivated wolf pack algorithm forhigh-dimensional functions and its application in parametersoptimization of PID controllerrdquo in Proceedings of the IEEECongress on Evolutionary Computation (CEC rsquo14) pp 1477ndash1482Beijing China July 2014

[33] H-S Wu and F-M Zhang ldquoWolf pack algorithm for uncon-strained global optimizationrdquo Mathematical Problems in Engi-neering vol 2014 Article ID 465082 17 pages 2014

[34] Q Zhou and Y Zhou ldquoWolf colony search algorithm based onleader strategyrdquo Application Research of Computers vol 9 pp2629ndash2632 2013

[35] G M Komaki and V Kayvanfar ldquoGrey Wolf Optimizer algo-rithm for the two-stage assembly flow shop scheduling problemwith release timerdquo Journal of Computational Science vol 8 pp109ndash120 2015

16 Computational Intelligence and Neuroscience

[36] L I Wong M H Sulaiman M R Mohamed and M SHong ldquoGrey Wolf Optimizer for solving economic dispatchproblemsrdquo in Proceedings of the IEEE International Conferenceon Power and Energy (PECon rsquo14) pp 150ndash154 KuchingMalaysia December 2014

[37] A Chaman-Motlagh ldquoSuperdefect photonic crystal filter opti-mization using Grey Wolf Optimizerrdquo IEEE Photonics Technol-ogy Letters vol 27 no 22 pp 2355ndash2358 2015

[38] P Q Dzung N T Tien N Dinh Tuyen and H Lee ldquoSelectiveharmonic elimination for cascaded multilevel inverters usinggrey wolf optimizer algorithmrdquo in Proceedings of the 9thInternational Conference on Power Electronics and ECCE Asia(ICPE rsquo15-ECCE Asia) June 2015

[39] N Muangkote K Sunat and S Chiewchanwattana ldquoAnimproved grey wolf optimizer for training q-Gaussian RadialBasis Functional-link netsrdquo in Proceedings of the InternationalComputer Science and Engineering Conference (ICSEC rsquo14) pp209ndash214 Khon Kaen Thailand August 2014

[40] A Zhu C Xu Z Li J Wu and Z Liu ldquoHybridizing grey Wolfoptimization with differential evolution for global optimizationand test scheduling for 3D stacked SoCrdquo Journal of SystemsEngineering and Electronics vol 26 no 2 pp 317ndash328 2015

[41] P ArbelaezMMaire C Fowlkes and JMalik ldquoContour detec-tion and hierarchical image segmentationrdquo IEEE Transactionson Pattern Analysis and Machine Intelligence vol 33 no 5 pp898ndash916 2011

Submit your manuscripts athttpswwwhindawicom

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Distributed Sensor Networks

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Advances in

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Hindawi Publishing Corporationhttpwwwhindawicom

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International Journal of

ReconfigurableComputing

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Applied Computational Intelligence and Soft Computing

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Artificial Intelligence

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Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Electrical and Computer Engineering

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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httpwwwhindawicom Volume 2014

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International Journal of

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ArtificialNeural Systems

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RoboticsJournal of

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Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

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4 Computational Intelligence and Neuroscience

where1205960(th)1205961(th) are the probability distribution of11986211198622respectively the equation is as follows

1205961198860 (th) = thsum119894=1

119875ℎ119886119894

1205961198861 (th) = 119871sum

119894=th+1119875ℎ119886119894

(5)

Therefore the objective function of Kapurrsquos entropy canbe defined as

119891 (th) = 1198671198861 + 1198671198862 119886 =

1 2 3 if RGB Image1 if Grayscale Image

(6)

where entropy1198671 and entropy1198672 are derived by (4)

1198671198861 = thsum119894=1

119875ℎ1198861198941205961198860 ln(119875ℎ119886

1198941205961198860 ) 1198671198862 = 119871sum

119894=th+1

119875ℎ1198861198941205961198861 ln(119875ℎ119886

1198941205961198861 ) (7)

where 119875ℎ119886119894

is the probability distribution of strength grades by(3) and 1205960(th) 1205961(th) are the probability distribution of 11986211198622 respectively

Naturally the entropy-based method can be extended tomultithresholdingmethod In this case image can be dividedinto 119896 classes with 119896 minus 1 thresholds Therefore multilevelthresholding objective function can be defined as follows

119891 (TH) = 119896sum119894=1

119867119886119894 119886 =

1 2 3 if RGB Image1 if Grayscale Image

(8)

where TH = [th1 th2 th119896minus1] is a vector containingmultiple thresholds and each entropy is calculated withthe corresponding threshold respectively And (7) can beextended to the calculation of 119896 entropies as follows

1198671198861 = th1sum119894=1

119875ℎ1198861198941205961198860 ln(119875ℎ119886

1198941205961198860 ) 1198671198862 = th2sum

119894=th1+1

119875ℎ1198861198941205961198861 ln(119875ℎ119886

1198941205961198861 )

119867119886119896 = 119871sum119894=th119896minus1+1

119875ℎ119886119894120596119886119896minus1

ln( 119875ℎ119886119894120596119886119896minus1

)

(9)

where the probabilities of 119896 classes are calculated by (10)finally it needs to categorize the pixels into correspondingclasses and complete the multilevel image segmentation by(2)

1205961198860 (th) = th1sum119894=1

119875ℎ119886119894

1205961198861 (th) = th2sum

119894=th1+1119875ℎ119886119894

120596119886119896minus1 (th) = 119871sum119894=th119896minus1+1

119875ℎ119886119894

(10)

As mentioned above multilevel thresholding is formu-lated tomaximize Kapurrsquos entropy and the objective functionis shown in (8) As previously mentioned this paper willuse the MDGWO to optimize the objective function theoptimization algorithm is the key to the quality of imagesegmentation

4 Image Segmentation Based on MDGWO

41 Standard Grey Wolf Optimizer Grey wolfs (Canis lupus)belongs to Canidae family which are considered as apexpredators meaning that they are at the top of the foodchain They have a very strict social dominant hierarchy Thealgorithm divides the wolves into four types 120572 120573 120575 and 120596The social behavior of each type wolves can be summarizedas follows

The leaders are amale and a female called alphaThey arethe most brilliant wolves and the best in terms of managingthe packThe alphawolf is also called the dominant wolf sincehisher orders should be followed by the pack uncondition-ally The location of alpha presents the best solution of theproblem

The second level in the hierarchy of grey wolves isbeta The betas are subordinate wolves that help the alphain decision-making or other pack activities The beta wolfshould respect the alpha but commands the other lower-level wolves as well It plays the role of an advisor to thealpha and discipliner for the pack The beta reinforces alpharsquoscommands throughout the pack and gives feedback to thealpha

The third level in the hierarchy of grey wolves is deltaDelta wolves have to submit to alphas and betas but theydominate the omega scouts sentinels elders hunters andcaretakers who belong to this category They are responsiblefor watching the boundaries of the territory warning the packin case of any danger protecting and guaranteeing the safetyof the pack helping the alphas and betas when hunting preyand providing food for the pack and caring for the weak illand wounded wolves in the pack

The lowest ranking grey wolf is omega It may seem theomega is not an important individual in the pack but it has

Computational Intelligence and Neuroscience 5

Table 1 The corresponding relationships between MDGWO andimage segmentation

MDGWO Image segmentationPositions Threshold segmentation solutionAlpha Pos Optimal solutionAlpha score The largest fitness valueFitness Fitness function valueBest R Best fitness

been observed that the whole pack face internal fighting andproblems in case of losing the omega which is harmful to thegroup structure

In addition to the social hierarchy of wolves grouphunting is another interesting social behavior of grey wolvesThemain phases of greywolf hunting are as follows searchingfor the prey tracking chasing and approaching the preypursuing encircling and harassing the prey until it stopsmoving attacking toward the prey

In order to mathematically model the social hierarchy ofwolves in GWO [26] the fittest solution is considered as thealpha (120572) Consequently the second and third best solutionsare named beta (120573) and delta (120575) respectively The rest ofthe candidate solutions are assumed to be omega (120596) In theGWO algorithm the hunting (optimization) is guided by 120572120573 and 120575 The 120596 wolves follow these three wolves

In addition to the above four abstract models this paperproposes MDGWO based on the standard GWO settings forMT In the improved algorithm the corresponding relation-ships between grey wolf hunting and image segmentation areshown in Table 1

42 The Initialization of MDGWO The size of the wolf packis assumed as SN SN candidate solutions (the location ofthe wolves is the threshold values) are generated randomly inthe initialization phase Different from the GWO the imagethreshold is a set of discrete integers by rounding toward zero

997888rarr119883119894 = lfloorrand (SN 1) sdot (119906119887 minus 119897119887) + 119897119887rfloor (11)

where 119906119887 and 119897119887 are the upper limit and the lower limit ofparameters (namely boundaries of parameter)

After the initialization of candidate solutions MDGWOjudges whether the initial solution 997888rarr119883119894 is in the range of[119906119887 119897119887] If it is the fitness value will be calculated otherwisethe search agent will be put back in the search space (ieguaranteeing the initial solution in the range of [119906119887 119897119887])by (12) and then the fitness value will be recalculated byrounding toward zero

997888rarr119883119894 = lfloor(997888rarr119883119894 sdot (119906 + 119897)) + 119906119887 sdot 119906 + 119897119887 sdot 119897rfloor (12)

where 119906 = 997888rarr119883119894 gt 119906119887 119897 = 997888rarr119883119894 lt 119897119887

In the all fitness values calculated by (13) of candidatesolutions MDGWO chooses three optimal candidate solu-tions to assign to997888rarr119883120572997888rarr119883120573997888rarr119883120575 and records all the fitness valuesand candidate functions (namely locations of the wolves)

Fitness (997888rarr119883119894) = 1(1 + 119891 (997888rarr119883119894)) (119891 (997888rarr119883119894) ge 0)

1 + 100381610038161003816100381610038161003816119891 (997888rarr119883119894)100381610038161003816100381610038161003816 (119891 (997888rarr119883119894) ge 0) (13)

where997888rarr119883119894 is one of the candidate solutions which include a setof thresholds then 119891(997888rarr119883119894) is calculated by Kapurrsquos function asshown in (8)

43 Iterative Process After the initialization all the searchagents have to update their current locations for optimize thecandidate solutions over the course of iteration In the rangeof the maximum iteration (Max iter) all the update processand optimization process will be completed

431 Encircling Prey Grey wolves encircle prey before thehunt In the mathematical model the wolf pack has to updatethe position (namely the threshold value) constantly so thatthey can approach the prey In the algorithm all the agentposition updated by (15) over the course of encirclement

= 100381610038161003816100381610038161003816 sdot 997888997888rarr119883119901 (119905) minus (119905)100381610038161003816100381610038161003816 (14)

(119905 + 1) = 997888997888rarr119883119901 (119905) minus sdot (15)

where 119905 indicates the current iteration and are coefficientvectors 997888997888rarr119883119901 is the position vector of the prey and indicatesthe position vector of a grey wolf The vectors and arecalculated as follows

= 2 119890 sdot 997888rarr1199031 minus 119890 (16)

= 2997888rarr1199032 (17)

where components of 119890 are linearly decreased from 2 to 0 overthe course of iterations and997888rarr1199031 997888rarr1199032 are random vectors in [0 1]The detailed selection of the two vectors can be found in [26]

432 The Behavior of Hunting The hunt is usually guided bythe alphaThebeta and deltamight also participate in huntingoccasionally However in an abstract search space we haveno idea about the location of the optimum (prey) In order tomathematically simulate the hunting behavior of grey wolvesit is supposed that the alpha beta and delta have betterknowledge about the potential location of prey Thereforethe algorithm saves the first three best solutions obtainedso far and obliges the other search agents (including theomegas) to update their positions according to the positionof the best search agents The original GWO algorithm inliterature [26] calculates the updated parameter of searchagents by the first three best solutions and then updates thelocation of search agents (namely new candidate solutions)

6 Computational Intelligence and Neuroscience

if 10038161003816100381610038161003816A10038161003816100381610038161003816lt 1

(a)

if 10038161003816100381610038161003816A10038161003816100381610038161003816gt 1

(b)

Figure 1 Attacking prey of grey wolf

according to their average value As for the specific formulasand the detailed calculation please refer to literature [26]In order to approach the best solution more quickly theproposed algorithm in this paper improves the current bestsolution in solutions updating by weighting method Theupdate formulations are as shown in (20) and correlationcoefficients are calculated by (18) (19) where 1198601 1198602 1198603 arecalculated by (16)997888rarr119863120572 = 100381610038161003816100381610038161003816997888rarr1198621 sdot 997888rarr119883120572 minus 100381610038161003816100381610038161003816 997888rarr119863120573 = 100381610038161003816100381610038161003816997888rarr1198622 sdot 997888rarr119883120573 minus 100381610038161003816100381610038161003816 997888rarr119863120575 = 100381610038161003816100381610038161003816997888rarr1198623 sdot 997888rarr119883120575 minus 100381610038161003816100381610038161003816

(18)

997888rarr1198831 = 997888rarr119883120572 minus 997888rarr1198601 sdot 997888rarr119863120572997888rarr1198832 = 997888rarr119883120573 minus 997888rarr1198602 sdot 997888rarr119863120573997888rarr1198833 = 997888rarr119883120575 minus 997888rarr1198603 sdot 997888rarr119863120575(19)

(119905 + 1) = 1199081 sdot 997888rarr1198831 + 1199082 sdot 997888rarr1198832 + 1199083 sdot 997888rarr1198833 (20)

where 1199081 1199082 1199083 are the corresponding weights which arecalculated by

1199081 = 1198911119865 1199082 = 1198912119865 1199083 = 1198913119865

(21)

where 1198911 1198912 1198913 calculated by (13) are the correspondingfitness values of120572120573 120575119865 = 1198911+1198912+1198913This paper emphasizes

that different from GWO updating search agents MDGWOuses (20) and (21) to update the location of search agentsby weighting method for the first time it is also the majorcontribution to the improved GWO

433 Attacking Prey The grey wolves finish the hunt byattacking the prey when it stops moving In order to mathe-matically model approaching the prey we decrease the valueof 119890 Note that the fluctuation range of is also decreasedby 119890 In other words is a random value in the interval[minus119890 119890] where 119890 is decreased from 2 to 0 over the course ofiterations When random values of are in [minus1 1] the nextposition of a search agent can be in any position betweenits current position and the position of the prey that is thesearch agent will approach the best solution gradually asshown in Figure 1

At the same time for the purpose of mathematical modeldivergence we utilize with random values greater than 1or less than minus1 to oblige the search agent to diverge from theprey As shown in Figure 1(b) gt 1 forces the grey wolves todiverge from the prey to hopefully find a better prey

44 Pseudocode of MDGWO The application of MDGWOalgorithm in image segmentation mainly lies in optimizingKapurrsquo entropy to obtain the best threshold therefore thefitness function as shown in (13) will be calculated based onKapurrsquos entropy

Step 1 Read image 119869 if 119869 is a RGB image then it will beprocessed by three channel of 119869R 119869G 119869B and store the datain ℎR ℎG ℎB respectively if 119869 is a grey image then read thegrey value and store it in ℎgrStep 2 According to (3) calculate image grey values andprobability distribution histogram

Computational Intelligence and Neuroscience 7

Step 3 Initialize the population of grey wolves parameter 119890 and Max iter

Step 4 Initialize the population 997888rarr119883119894 (119894 = 1 2 SN)randomly 997888rarr119883119894 = rand (SN 1) sdot (119906119887 minus 119897119887) + 119897119887 (22)

Step 5 Use (11) to discretize 997888rarr119883119894 that is being roundedtoward zero Use (12) to adjust the singular data beyond theboundaries of search space

Step 6 Calculate objective functions of each search agent byusing (8) And calculate the fitness value of each search agenton the basis of objective functions

Step 7 According to the fitness values assigning first threebest search agents to 997888rarr119883120572 997888rarr119883120573 997888rarr119883120575 respectivelyStep 8 Updating encircling parameters based on997888rarr119883120572997888rarr119883120573997888rarr119883120575which include calculating 997888rarr1198601 997888rarr1198602 997888rarr1198603 by (16) 997888rarr1198621 997888rarr1198622 997888rarr1198623 by(17) and 997888rarr119863120572 997888rarr119863120573 997888rarr119863120575 by (18)Step 9 Update the position of search agents based on (19) and(20) for the next hunting

Step 10 Add one to circular point if 119902 ge Max iter ormeet thestop condition of the algorithm the iteration will be finishedand skip to Step 11 otherwise skip to Step 5

Step 11 Set the location of the wolf that has the best objectivefunction as the best threshold of segmentation

Step 12 Input best threshold and images before and aftersegmentation

5 Experiments and Discussion

51 Parameters Settings The proposed algorithm has beentested under a set of benchmark images Some of theseimages are widely used in the multilevel image segmenta-tion literature to test different methods (Cameraman LenaBaboon and Maize) Others are chosen on purpose fromthe Berkeley Segmentation Data Set and Benchmarks 500(BSD500 for short see [41]) as shown in Figure 2 Theexperiments were carried out on a Lenovo Laptop with anIntel Core i5 processor and 4GBmemoryThe algorithmwasdeveloped via the signal processing toolbox image processingtoolbox and global optimization toolbox of Matlab R2011bAccording to relevant literatures manymethods were provedto have certain advantages compared with previous meth-ods This paper chooses the best advantageous method ascomparison objective the earlier or inferior literatures willno longer be used for the analysis Based on quantities ofcontrast experiments this paper will verify the superiority ofMDGWO in image segmentation by comparison of imagedata chart and so forth In the following sections MDGWOwill be compared with the algorithm using electromagnetism

optimization (EMO) proposed in [20] the differential evo-lution (DE) [27] the Artifical Bee Colony (ABC) [10] andthe original grey wolf optimizer The EMO DE and ABC arethe latest intelligent optimization methods by using Kapurrsquosentropy so far The comparison with GWO is mainly used totest the advantages of MDWGO

In order to avoid the randomness of results we useappropriate statistical metrics to compare the effectiveness ofthese algorithms According to [19 20] and the experimentstest thresholds are th = 2 3 4 5 [1ndash3] and the stop criterionof each experiment is 150 iterations the detailed settings ofparameters are showed in Table 2

For verifying the stability we use (23) to calculate thestandard deviation (STD) at the end of each test Once theSTD value increases the algorithms becomes more instablecorrespondingly [29]

STD = radicMax itersum119894=1

(120579119894 minus 120576)2Max iter

(23)

In addition the peak signal to noise ratio (PSNR [20]) isused to compare the similarity between the segmented imageand original image according to the mean square error (MSE[26]) of each pixel

PSNR = 20 log10 ( 255MSE

) (dB) (24)

MSE = radicsumro119894=1sumco119895=1 (119868119886119900 (119894 119895) minus 119868119886th (119894 119895))

ro times co (25)

where 119868119886119900 is the original image 119868119886th is the segmented image and119886 depends on the type of image (grey image or RGB image)ro co are respectively the total number of rows and columnsin an image

Because Kapurrsquos entropy is based on histogram of theimage this paper provides test images and the correspondinghistograms From Figure 2 it can be seen that each imagehas the only distinctive histogram which can guarantee theuniversality and commonality of the algorithm More impor-tantly most of these histograms do not follow the bimodalcharacteristic therefore the difficulty level of optimizationincreases accordingly

52 The Image Segmentation Result Based on MDGWO withDifferent Thresholds In order to reflect the segmentationeffect Figures 3 and 4 illustrate the segmentation results oforiginal images in Figure 2when the threshold is 2 3 4 and 5respectively The experiments indicate that the segmentationresults turn out to be finer and there are alsomore segmentedareas when the number of thresholds is larger and vice versaIn extreme cases when the threshold is 2 the algorithmis reduced to be binary image segmentation (foreground-background segmentation) Certainly that how many areasare segmented is related to the applications and requirementsthis method only needs to set the corresponding number ofthresholds (th) Besides giving the MDGWO segmentationresults like [20] Figures 3 and 4 also mark the position

8 Computational Intelligence and Neuroscience

Table 2 Parameters settings of MDGWO

Parameters Population size Threshold Number of iterations Run time Lower bound Upper boundValue 50 2 3 4 5 150 35 1 256

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

000100020003000400050006000700080009

001

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 3000

0002000400060008

0010012001400160018

002

times10minus3

Histogram of left col ImageImage Histogram of left col

(a) Cameraman (b) Lena

(c) Baboon (d) Butterfly

(e) Maize (f) Starfish

(g) Smiling Girl (h) Surfing

Figure 2 The original images and their histograms

of the threshold in each histogram Compared with otherMT methods it is difficult to find the difference in termsof the segmentation effect Therefore Section 54 lists thethresholds PSNR STD and MEAN for comparisons ofMDGWO results and other techniques

53 The Comparison of MDGWO in Multilevel Image Thresh-olding with Different Objective Functions In Section 1 wesummarize the relevant objective functions The commonlyused optimization functions include maximization of theentropy andmaximization of the between-class variance (egOtsursquos method) In [27] the authors respectively analyze

these objective functions and compare Kapur and Otsusystematically The experiment results show that Kapurrsquosentropy gets the best effectiveness Therefore in order toverify MDGWOrsquos efficiency we compare the thresholds andPSNR between Otsu and Kapur in Table 3

As shown inTable 3 the threshold distribution ofKapur ismore dispersed and wider in most cases However the effectof image thresholding cannot be seen from the thresholddistribution directly Therefore we focus on analysis thePSNR between Otsu and Kapur In terms of PSNR the Kapurmethod produces higher PSNR values on most items inFigure 2 except for the Sea Star Imagewith 119896 = 3 5 and SurferImage with 119896 = 4

Computational Intelligence and Neuroscience 9

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005001

0015002

0025

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

000100020003000400050006000700080009

001

0 50 100 150 200 250 3000

000100020003000400050006000700080009

001

0 50 100 150 200 250 3000

000100020003000400050006000700080009

001

0 50 100 150 200 250 3000

000100020003000400050006000700080009

001

Image

Cam

eram

anLe

naBa

boon

Butte

rfly

th = 2 th = 3 th = 4 th = 5

Figure 3 The segmentation results of (a)ndash(d) in Figure 2 and their thresholds in histograms

10 Computational Intelligence and Neuroscience

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0002000400060008

0010012001400160018

002

0 50 100 150 200 250 3000

0002000400060008

0010012001400160018

002

0 50 100 150 200 250 3000

0002000400060008

0010012001400160018

002

0 50 100 150 200 250 30000002000400060008

0010012001400160018

002

times10minus3

times10minus3

times10minus3

times10minus3

Image th = 2 th = 3 th = 4 th = 5

Mai

zeSt

arfis

hSm

iling

Girl

Surfi

ng

Figure 4 The segmentation results of (e)ndash(h) in Figure 2 and their thresholds in histograms

Computational Intelligence and Neuroscience 11

Table 3 The comparison of MDGWOrsquos efficiency between Otsu and Kapur

Image 119896 Otsu thresholds PSNR Kapur thresholds PSNR

Cameraman

2 70 144 119475 44 106 1446293 58 119 156 129933 44 98 148 1993374 40 93 139 170 160180 39 83 119 156 2116845 35 81 121 149 174 163710 23 58 94 125 159 231191

Lena

2 92 151 131029 93 163 1471643 80 126 171 157626 70 121 172 1751444 75 114 145 180 164291 43 81 127 171 2017295 73 109 136 161 189 167206 41 73 103 141 178 218208

Baboon

2 97 149 124396 78 141 1603023 83 123 160 137731 46 103 151 1863404 70 105 136 167 149493 34 75 117 159 2051985 66 98 125 150 175 160012 29 64 100 134 170 220929

Butterfly

2 100 152 124400 87 150 1493253 81 118 159 142563 62 104 152 1855394 73 101 129 164 146987 49 88 128 168 2107115 69 95 121 149 177 164688 48 80 113 145 180 224539

Maize

2 92 168 136677 84 165 1404073 76 128 187 152676 59 113 171 1658534 65 104 150 200 167309 45 80 125 187 1898185 56 86 123 164 208 185649 39 74 108 147 198 208792

Sea Star

2 85 157 148445 81 160 1485953 69 120 178 176040 60 111 172 1745834 59 99 137 187 194039 46 89 131 184 1944875 51 85 117 150 193 214000 47 83 118 150 196 209681

Smiling Girl

2 60 123 131358 88 145 1800333 47 100 131 128470 44 91 145 1911484 28 74 111 136 156914 24 67 100 145 2007595 20 63 95 124 158 18 2260 44 83 115 152 203 217937

Surfer

2 92 162 125401 52 141 1643433 71 111 177 160569 52 103 168 1893434 47 81 118 179 208786 49 86 131 185 2072185 46 77 105 143 196 216071 24 53 88 126 183 218961

The average value of Kapur is improved averagely by2224 compared to Otsu by checking against the cor-responding PSNR values which are obtained from theMDGWO The maximum value is increased by 5342 forCameraman Image when 119896 = 3 Therefore the Kapurmethod is significantly better than the Otsu method and wealso mainly analyze the effectiveness of Kapurrsquos method inSection 54

54TheComparison ofQuality Assessment by PSNR STD andMEAN This paper adopts PSNR standard to evaluate thesegmentation quality in comparisonwith otherMTmethodsTables 4ndash6 illustrate the PSNR values under different thresh-olds ofMDGWOGWOEMODEABC and theMEANandSTD of objective functions As shown in Table 4 it can be

seen from the PSNR values that MDGWO gets the highestevaluation in most cases Thus it proves that MDGWO getsbetter results on image segmentation In addition when thenumber of thresholds increases it shows superior PSNRvalue In detail the MDGWO algorithm produces higherPSNR values on all items in Table 4 except for the SmilingGirl Image with 119896 = 5 and Surfer Image with 119896 = 4 on theresult of DE

As shown in Table 4 the average value of MDGWO isimproved averagely by 1316 compared toGWOby checkingagainst the corresponding PSNR valuesThemaximum valueis increased by 4505 for Butterfly Image when 119896 = 5

ComparingwithMTEMO the average value ofMDGWOis improved averagely by 1156 by checking against the cor-responding PSNR valuesThemaximumvalue is increased by3994 for Surfer Image when 119896 = 2

12 Computational Intelligence and Neuroscience

Table 4 PSNR metrics of MTEMO DE ABC GWO and MDGWO

Image 119896 MTEMO DE ABC GWO MDGWO

Cameraman

2 13626 12584 13920 14279 144633 18803 17584 14462 19696 199344 20586 20111 2081 20809 211685 20661 21282 2240 22404 23119

Lena

2 14672 8823 14590 14680 147163 17247 14386 17197 17416 175144 18251 16151 18559 19762 201735 20019 16720 20321 21299 21820

Baboon

2 16016 8103 16007 16024 160353 16016 12596 18592 18632 186344 18485 13178 18417 20480 205195 20507 13135 20224 22060 22092

Butterfly

2 11065 8702 14402 14762 149323 14176 13028 14504 17873 185534 16725 13028 16189 21021 210715 19026 14786 19286 21485 22453

Maize

2 13633 10549 13590 13950 140403 15229 13022 15295 16201 165854 16280 14270 16346 18713 189815 17211 15079 17046 20410 20879

Sea Star

2 14398 8610 14395 14809 148853 16987 14078 16981 17431 174584 18304 16191 18427 19421 194485 20165 16474 20330 20887 20968

Smiling Girl

2 13420 14986 13514 17989 180033 18254 11243 18069 18742 191144 18860 14556 18826 19823 200755 19840 22980 19769 21214 21793

Surfer

2 11744 9737 11878 16154 164343 18584 11638 18762 18895 189344 19478 21866 19647 20234 207215 20468 19576 20479 21699 21896

By comparing with DE the average value of MDGWO isimproved averagely by 3814 by checking against the cor-responding PSNR values The maximum value is increasedby 9789 for Baboon Image when 119896 = 2 The PSNR of theSmiling Girl with 119896 = 5 and Surfer Image with 119896 = 4 areslightly lower but the gap is not significant

Comparing between ABC and MDGWO the averagevalue of MDGWO is improved averagely by 1055 by check-ing against the corresponding PSNR values The maximumvalue is increased by 3836 for Surfer Image when 119896 = 2

From the perspective of STDwhich is shown in Table 5 itcan be observed that MDGWO shows obviously advantagesover MTEMO DE ABC and GWOThe smaller the STD isthe smaller the change of fitness functions over the course ofiterations will be that is the better stability of segmentation

Therefore the results show that MDGWO obtains excitingeffect in stability So MDGWOrsquos stability is better

Compared with GWO the average value of MDGWO isimproved averagely by 7352 compared to GWO by check-ing against the corresponding STD values The maximumvalue is increased by 9644 for Baboon Image when 119896 = 3and the minimum value is increased by 2492 for BaboonImage when 119896 = 3

By comparing with MTEMO the average value ofMDGWO is improved averagely by 4788 The maximumvalue is increased by 87 for Lena Image when 119896 = 2 and theminimum value is increased by 06 for Surfer Image when119896 = 3

Comparing between DE andMDGWO the average valueofMDGWO is improved averagely by 9560Themaximum

Computational Intelligence and Neuroscience 13

Table 5 STD metrics of MTEMO DE ABC GWO and MDGWO

Image 119896 MTEMO DE ABC GWO MDGWO

Camerman

2 01849 12592 01235 01697 004623 01649 17601 02122 02287 007584 02943 21995 03003 03627 006595 02999 26579 02784 04278 01964

Lena

2 00969 12902 00349 01536 001263 01665 17822 01300 03570 002644 02800 22104 01872 05965 009395 02515 25992 01827 05946 01570

Baboon

2 00108 12862 00358 02171 001023 00393 17678 00202 04376 001564 01727 22126 01610 02986 011845 02868 26239 02660 05377 02316

Butterfly

2 00903 12708 00750 02179 004653 02207 17429 02952 02712 020364 02482 22368 03906 04808 024155 02900 26571 04818 05096 02684

Maize

2 00356 13501 00218 03571 001883 01222 18612 00901 02225 002704 02305 23230 02605 03903 009275 02502 27461 03834 04584 01677

Sea Star

2 01073 13547 01088 01728 002903 01497 18741 01752 02028 003744 01596 23307 01817 05032 011195 02639 27550 02180 04550 01437

Smiling Girl

2 00377 12516 00318 01834 001113 00955 17311 00577 01712 002424 01966 21878 01094 02508 007815 01550 25989 02768 05273 01302

Surfer

2 00579 13213 00303 02681 002453 01002 18337 01646 03014 009964 03382 23317 01686 03162 014245 03690 27846 02580 03815 01706

value is increased by 9921 for Baboon Image when 119896 =2 The minimum value is increased by 8832 for ButterflyImage when 119896 = 3

Comparing with ABC the average value of MDGWOis improved averagely by 4590 The maximum value isincreased by 7970 for Lena Image when 119896 = 3 and theminimum value is increased by 1293 for Baboon Imagewhen 119896 = 5

As far as MEAN is concerned this parameter presentsthe average value of fitness function over the course ofiterations in Table 6 which reflects the algorithm stability tosome extent But its accuracy of evaluation is relatively lowwhich can only reflect the fuzzy stability of the algorithmThe experiment data is offered here just in response to theparameter provided in literature [20] In comparison withGWO MTEWO DE and ABC in Table 6 it can be safely

assumed that inmost casesMDGWOobtains higherMEANof fitness function Moreover the difference is extremelysmall when MDGWOrsquos MEAN is lower

From the analyses of Tables 3ndash6 together with the visualeffects of Figures 2 3 and 4 it can be observed thatMDGWO method obtains better segmentation effect andhas advantage in optimal process accuracy stability androbustnessThereforeMDGWO is aMT algorithmwith highaccuracy and high segmentation quality

6 Conclusion

This paper proposes a modified discrete grey wolf optimizerwhich is used to optimize the image histograms and realizethe multilevel image segmentation Based on the high effi-ciency of GWO in the course of optimization and stability

14 Computational Intelligence and Neuroscience

Table 6 MEANmetrics of MTEMO DE ABC GWO and MDGWO

Image 119896 MTEMO DE ABC GWO MDGWO

Camerman

2 17584 124212 177638 14634 174713 21976 173764 223059 21107 219194 26586 217520 268409 24927 274805 30506 262505 308328 30436 30548

Lena

2 17831 127730 178139 17809 183963 22120 176428 220832 22074 228564 25999 218784 260615 25318 264475 29787 257311 299664 29252 30381

Baboon

2 17625 127333 176760 17679 186193 22269 175005 221276 22129 229494 26688 219010 263912 26194 269005 30800 259681 303464 30067 30076

Butterfly

2 16681 125796 174205 17425 177233 21242 172545 222209 21585 224984 25179 220176 263794 25267 261905 28611 261795 306533 29492 29899

Maize

2 18631 133566 186316 18604 195423 23565 184245 232496 22941 239394 27529 229813 273931 26936 278425 31535 271709 312127 31023 30694

Sea Star

2 18754 134104 187295 18321 195873 23323 185516 232738 23245 239014 27582 230719 275057 27136 282105 31562 272551 314919 31167 31958

Smiling Girl

2 17334 123892 173129 17136 180353 21904 171339 218601 21253 219804 26040 216541 259904 25050 265975 30089 257130 300225 29870 30574

Surfer

2 18339 130786 183393 18283 188693 23231 181492 232889 23243 241354 27863 230548 278017 27275 274475 31823 274979 317335 31384 31325

this paper successfully applies the MDGWO to the field ofMT by improving the location selection mechanism of 120572 120573and 120575 during the hunting and using weight to optimize thefinal position of prey (best threshold)TheMDGWOmethodnot only obtains better segmentation quality but also showsobvious superiority over GWO MTEMO DE and ABC instability accuracy and multilevel thresholding

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work was supported in part by the National NaturalScience Foundation of China (no 61300239 no 71301081and no 61572261) the Postdoctoral Science Foundation (no

2014M551635 and no 1302085B) the Innovation Project ofGraduate Students Foundation of Jiangsu Province (KYLX150841) the Higher Education Revitalization Plan Foundationof Anhui Province (no 2013SQRL102ZD no 2015xdjy196no 2015jyxm728 no 2016jyxm0774 and no 2016jyxm0777)and Natural Science Fund for Colleges and Universities inJiangsu Province (no16KJB520034) A Project Funded by thePriority Academic Program Development of Jiangsu HigherEducation Institutions (PAPD) and Jiangsu CollaborativeInnovation Center on Atmospheric Environment and Equip-ment Technology (CICAEET)

References

[1] M Sonka V Hlavac and R Boyle Image Processing Analysisand Machine Vision Cengage Learning 2014

[2] S Masood M Sharif A Masood M Yasmin and M RazaldquoA survey on medical image segmentationrdquo Current MedicalImaging Reviews vol 11 no 1 pp 3ndash14 2015

Computational Intelligence and Neuroscience 15

[3] PGhamisiM S Couceiro FM LMartins and J A Benedikts-son ldquoMultilevel image segmentation based on fractional-orderdarwinian particle swarm optimizationrdquo IEEE Transactions onGeoscience and Remote Sensing vol 52 no 5 pp 2382ndash23942014

[4] M Waseem Khan ldquoA survey image segmentation techniquesrdquoInternational Journal of Future Computer and Communicationvol 3 no 2 pp 89ndash93 2014

[5] J Li X Li B Yang and X Sun ldquoSegmentation-based imagecopy-move forgery detection schemerdquo IEEE Transactions onInformation Forensics and Security vol 10 no 3 pp 507ndash5182015

[6] Z Pan J Lei Y Zhang X Sun and S Kwong ldquoFast motionestimation based on content property for low-complexityH265HEVC encoderrdquo IEEE Transactions on Broadcasting vol62 no 3 pp 675ndash684 2016

[7] X Chen S Feng and D Pan ldquoAn improved approach oflung image segmentation based on watershed algorithmrdquo inProceedings of the the 7th International Conference on InternetMultimedia Computing and Service pp 1ndash5 Zhangjiajie ChinaAugust 2015

[8] Y Zheng B Jeon D Xu Q M J Wu and H Zhang ldquoImagesegmentation by generalized hierarchical fuzzy C-means algo-rithmrdquo Journal of Intelligent and Fuzzy Systems vol 28 no 2pp 961ndash973 2015

[9] V Osuna-Enciso E Cuevas and H Sossa ldquoA comparison ofnature inspired algorithms for multi-threshold image segmen-tationrdquo Expert Systems with Applications vol 40 no 4 pp 1213ndash1219 2013

[10] T Kurban P Civicioglu R Kurban and E Besdok ldquoCompari-son of evolutionary and swarmbased computational techniquesfor multilevel color image thresholdingrdquo Applied Soft Comput-ing Journal vol 23 pp 128ndash143 2014

[11] J N Kapur P K Sahoo and A K C Wong ldquoA new methodfor gray-level picture thresholding using the entropy of thehistogramrdquo Computer Vision Graphics and Image Processingvol 29 no 3 pp 273ndash285 1985

[12] N Otsu ldquoA threshold selection method from gray-level his-togramsrdquo Automatica vol 11 no 285ndash296 pp 23ndash27 1975

[13] X Li Z Zhao and H D Cheng ldquoFuzzy entropy thresholdapproach to breast cancer detectionrdquo Information Sciences -Applications vol 4 no 1 pp 49ndash56 1995

[14] J Kittler and J Illingworth ldquoMinimum error thresholdingrdquoPattern Recognition vol 19 no 1 pp 41ndash47 1986

[15] Y Xue S Zhong T Ma and J Cao ldquoA hybrid evolution-ary algorithm for numerical optimization problemrdquo IntelligentAutomation amp Soft Computing vol 21 no 4 pp 473ndash490 2015

[16] P-Y Yin ldquoA fast scheme for optimal thresholding using geneticalgorithmsrdquo Signal Processing vol 72 no 2 pp 85ndash95 1999

[17] W Fujun L Junlan L Shiwei Z Xingyu Z Dawei and TYanling ldquoAn improved adaptive genetic algorithm for imagesegmentation and vision alignment used in microelectronicbondingrdquo IEEEASMETransactions onMechatronics vol 19 no3 pp 916ndash923 2014

[18] S Banerjee and N D Jana ldquoBi level kapurs entropy basedimage segmentation using particle swarm optimizationrdquo inProceedings of the 3rd International Conference on ComputerCommunication Control and InformationTechnology (C3IT rsquo15)pp 1ndash4 Hooghly India February 2015

[19] M-H Horng ldquoMultilevel thresholding selection based on theartificial bee colony algorithm for image segmentationrdquo ExpertSystems with Applications vol 38 no 11 pp 13785ndash13791 2011

[20] D Oliva E Cuevas G Pajares D Zaldivar and V OsunaldquoA multilevel thresholding algorithm using electromagnetismoptimizationrdquo Neurocomputing vol 139 pp 357ndash381 2014

[21] S Sarkar G R Patra and S Das ldquoA differential evolutionbased approach for multilevel image segmentation using mini-mum cross entropy thresholdingrdquo in Swarm Evolutionary andMemetic Computing pp 51ndash58 Springer Berlin Germany 2011

[22] Y Xue Y Zhuang T Ni S Ni and X Wen ldquoSelf-adaptivelearning based discrete differential evolution algorithm forsolving CJWTA problemrdquo Journal of Systems Engineering andElectronics vol 25 no 1 pp 59ndash68 2014

[23] S Agrawal R Panda S Bhuyan and B K Panigrahi ldquoTsallisentropy based optimal multilevel thresholding using cuckoosearch algorithmrdquo Swarm and Evolutionary Computation vol11 pp 16ndash30 2013

[24] PD Sathya andRKayalvizhi ldquoOptimalmultilevel thresholdingusing bacterial foraging algorithmrdquo Expert Systems with Appli-cations vol 38 no 12 pp 15549ndash15564 2011

[25] S Ayas H Dogan E Gedikli and M Ekinci ldquoMicroscopicimage segmentation based on firefly algorithm for detectionof tuberculosis bacteriardquo in Proceedings of the 23rd SignalProcessing and Communications Applications Conference (SIUrsquo15) pp 851ndash854 Malatya Turkey May 2015

[26] S Mirjalili S M Mirjalili and A Lewis ldquoGrey wolf optimizerrdquoAdvances in Engineering Software vol 69 pp 46ndash61 2014

[27] B Akay ldquoA study on particle swarm optimization and artificialbee colony algorithms for multilevel thresholdingrdquo Applied SoftComputing vol 13 no 6 pp 3066ndash3091 2013

[28] A K Bhandari A Kumar and G K Singh ldquoModified artificialbee colony based computationally efficient multilevel thresh-olding for satellite image segmentation using Kapurrsquos Otsu andTsallis functionsrdquo Expert Systems with Applications vol 42 no3 pp 1573ndash1601 2015

[29] P Ghamisi M S Couceiro J A Benediktsson and N M FFerreira ldquoAn efficientmethod for segmentation of images basedon fractional calculus and natural selectionrdquo Expert Systemswith Applications vol 39 no 16 pp 12407ndash12417 2012

[30] L Li L Sun W Kang J Guo C Han and S Li ldquoFuzzymultilevel image thresholding based on modified discrete greywolf optimizer and local information aggregationrdquo IEEE Accessvol 4 pp 6438ndash6450 2016

[31] H-S Wu F-M Zhang and L-S Wu ldquoNew swarm intelligencealgorithm-wolf pack algorithmrdquo Xi Tong Gong Cheng Yu DianZi Ji ShuSystems Engineering and Electronics vol 35 no 11 pp2430ndash2438 2013

[32] H Wu and F Zhang ldquoA uncultivated wolf pack algorithm forhigh-dimensional functions and its application in parametersoptimization of PID controllerrdquo in Proceedings of the IEEECongress on Evolutionary Computation (CEC rsquo14) pp 1477ndash1482Beijing China July 2014

[33] H-S Wu and F-M Zhang ldquoWolf pack algorithm for uncon-strained global optimizationrdquo Mathematical Problems in Engi-neering vol 2014 Article ID 465082 17 pages 2014

[34] Q Zhou and Y Zhou ldquoWolf colony search algorithm based onleader strategyrdquo Application Research of Computers vol 9 pp2629ndash2632 2013

[35] G M Komaki and V Kayvanfar ldquoGrey Wolf Optimizer algo-rithm for the two-stage assembly flow shop scheduling problemwith release timerdquo Journal of Computational Science vol 8 pp109ndash120 2015

16 Computational Intelligence and Neuroscience

[36] L I Wong M H Sulaiman M R Mohamed and M SHong ldquoGrey Wolf Optimizer for solving economic dispatchproblemsrdquo in Proceedings of the IEEE International Conferenceon Power and Energy (PECon rsquo14) pp 150ndash154 KuchingMalaysia December 2014

[37] A Chaman-Motlagh ldquoSuperdefect photonic crystal filter opti-mization using Grey Wolf Optimizerrdquo IEEE Photonics Technol-ogy Letters vol 27 no 22 pp 2355ndash2358 2015

[38] P Q Dzung N T Tien N Dinh Tuyen and H Lee ldquoSelectiveharmonic elimination for cascaded multilevel inverters usinggrey wolf optimizer algorithmrdquo in Proceedings of the 9thInternational Conference on Power Electronics and ECCE Asia(ICPE rsquo15-ECCE Asia) June 2015

[39] N Muangkote K Sunat and S Chiewchanwattana ldquoAnimproved grey wolf optimizer for training q-Gaussian RadialBasis Functional-link netsrdquo in Proceedings of the InternationalComputer Science and Engineering Conference (ICSEC rsquo14) pp209ndash214 Khon Kaen Thailand August 2014

[40] A Zhu C Xu Z Li J Wu and Z Liu ldquoHybridizing grey Wolfoptimization with differential evolution for global optimizationand test scheduling for 3D stacked SoCrdquo Journal of SystemsEngineering and Electronics vol 26 no 2 pp 317ndash328 2015

[41] P ArbelaezMMaire C Fowlkes and JMalik ldquoContour detec-tion and hierarchical image segmentationrdquo IEEE Transactionson Pattern Analysis and Machine Intelligence vol 33 no 5 pp898ndash916 2011

Submit your manuscripts athttpswwwhindawicom

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Human-ComputerInteraction

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Computational Intelligence and Neuroscience 5

Table 1 The corresponding relationships between MDGWO andimage segmentation

MDGWO Image segmentationPositions Threshold segmentation solutionAlpha Pos Optimal solutionAlpha score The largest fitness valueFitness Fitness function valueBest R Best fitness

been observed that the whole pack face internal fighting andproblems in case of losing the omega which is harmful to thegroup structure

In addition to the social hierarchy of wolves grouphunting is another interesting social behavior of grey wolvesThemain phases of greywolf hunting are as follows searchingfor the prey tracking chasing and approaching the preypursuing encircling and harassing the prey until it stopsmoving attacking toward the prey

In order to mathematically model the social hierarchy ofwolves in GWO [26] the fittest solution is considered as thealpha (120572) Consequently the second and third best solutionsare named beta (120573) and delta (120575) respectively The rest ofthe candidate solutions are assumed to be omega (120596) In theGWO algorithm the hunting (optimization) is guided by 120572120573 and 120575 The 120596 wolves follow these three wolves

In addition to the above four abstract models this paperproposes MDGWO based on the standard GWO settings forMT In the improved algorithm the corresponding relation-ships between grey wolf hunting and image segmentation areshown in Table 1

42 The Initialization of MDGWO The size of the wolf packis assumed as SN SN candidate solutions (the location ofthe wolves is the threshold values) are generated randomly inthe initialization phase Different from the GWO the imagethreshold is a set of discrete integers by rounding toward zero

997888rarr119883119894 = lfloorrand (SN 1) sdot (119906119887 minus 119897119887) + 119897119887rfloor (11)

where 119906119887 and 119897119887 are the upper limit and the lower limit ofparameters (namely boundaries of parameter)

After the initialization of candidate solutions MDGWOjudges whether the initial solution 997888rarr119883119894 is in the range of[119906119887 119897119887] If it is the fitness value will be calculated otherwisethe search agent will be put back in the search space (ieguaranteeing the initial solution in the range of [119906119887 119897119887])by (12) and then the fitness value will be recalculated byrounding toward zero

997888rarr119883119894 = lfloor(997888rarr119883119894 sdot (119906 + 119897)) + 119906119887 sdot 119906 + 119897119887 sdot 119897rfloor (12)

where 119906 = 997888rarr119883119894 gt 119906119887 119897 = 997888rarr119883119894 lt 119897119887

In the all fitness values calculated by (13) of candidatesolutions MDGWO chooses three optimal candidate solu-tions to assign to997888rarr119883120572997888rarr119883120573997888rarr119883120575 and records all the fitness valuesand candidate functions (namely locations of the wolves)

Fitness (997888rarr119883119894) = 1(1 + 119891 (997888rarr119883119894)) (119891 (997888rarr119883119894) ge 0)

1 + 100381610038161003816100381610038161003816119891 (997888rarr119883119894)100381610038161003816100381610038161003816 (119891 (997888rarr119883119894) ge 0) (13)

where997888rarr119883119894 is one of the candidate solutions which include a setof thresholds then 119891(997888rarr119883119894) is calculated by Kapurrsquos function asshown in (8)

43 Iterative Process After the initialization all the searchagents have to update their current locations for optimize thecandidate solutions over the course of iteration In the rangeof the maximum iteration (Max iter) all the update processand optimization process will be completed

431 Encircling Prey Grey wolves encircle prey before thehunt In the mathematical model the wolf pack has to updatethe position (namely the threshold value) constantly so thatthey can approach the prey In the algorithm all the agentposition updated by (15) over the course of encirclement

= 100381610038161003816100381610038161003816 sdot 997888997888rarr119883119901 (119905) minus (119905)100381610038161003816100381610038161003816 (14)

(119905 + 1) = 997888997888rarr119883119901 (119905) minus sdot (15)

where 119905 indicates the current iteration and are coefficientvectors 997888997888rarr119883119901 is the position vector of the prey and indicatesthe position vector of a grey wolf The vectors and arecalculated as follows

= 2 119890 sdot 997888rarr1199031 minus 119890 (16)

= 2997888rarr1199032 (17)

where components of 119890 are linearly decreased from 2 to 0 overthe course of iterations and997888rarr1199031 997888rarr1199032 are random vectors in [0 1]The detailed selection of the two vectors can be found in [26]

432 The Behavior of Hunting The hunt is usually guided bythe alphaThebeta and deltamight also participate in huntingoccasionally However in an abstract search space we haveno idea about the location of the optimum (prey) In order tomathematically simulate the hunting behavior of grey wolvesit is supposed that the alpha beta and delta have betterknowledge about the potential location of prey Thereforethe algorithm saves the first three best solutions obtainedso far and obliges the other search agents (including theomegas) to update their positions according to the positionof the best search agents The original GWO algorithm inliterature [26] calculates the updated parameter of searchagents by the first three best solutions and then updates thelocation of search agents (namely new candidate solutions)

6 Computational Intelligence and Neuroscience

if 10038161003816100381610038161003816A10038161003816100381610038161003816lt 1

(a)

if 10038161003816100381610038161003816A10038161003816100381610038161003816gt 1

(b)

Figure 1 Attacking prey of grey wolf

according to their average value As for the specific formulasand the detailed calculation please refer to literature [26]In order to approach the best solution more quickly theproposed algorithm in this paper improves the current bestsolution in solutions updating by weighting method Theupdate formulations are as shown in (20) and correlationcoefficients are calculated by (18) (19) where 1198601 1198602 1198603 arecalculated by (16)997888rarr119863120572 = 100381610038161003816100381610038161003816997888rarr1198621 sdot 997888rarr119883120572 minus 100381610038161003816100381610038161003816 997888rarr119863120573 = 100381610038161003816100381610038161003816997888rarr1198622 sdot 997888rarr119883120573 minus 100381610038161003816100381610038161003816 997888rarr119863120575 = 100381610038161003816100381610038161003816997888rarr1198623 sdot 997888rarr119883120575 minus 100381610038161003816100381610038161003816

(18)

997888rarr1198831 = 997888rarr119883120572 minus 997888rarr1198601 sdot 997888rarr119863120572997888rarr1198832 = 997888rarr119883120573 minus 997888rarr1198602 sdot 997888rarr119863120573997888rarr1198833 = 997888rarr119883120575 minus 997888rarr1198603 sdot 997888rarr119863120575(19)

(119905 + 1) = 1199081 sdot 997888rarr1198831 + 1199082 sdot 997888rarr1198832 + 1199083 sdot 997888rarr1198833 (20)

where 1199081 1199082 1199083 are the corresponding weights which arecalculated by

1199081 = 1198911119865 1199082 = 1198912119865 1199083 = 1198913119865

(21)

where 1198911 1198912 1198913 calculated by (13) are the correspondingfitness values of120572120573 120575119865 = 1198911+1198912+1198913This paper emphasizes

that different from GWO updating search agents MDGWOuses (20) and (21) to update the location of search agentsby weighting method for the first time it is also the majorcontribution to the improved GWO

433 Attacking Prey The grey wolves finish the hunt byattacking the prey when it stops moving In order to mathe-matically model approaching the prey we decrease the valueof 119890 Note that the fluctuation range of is also decreasedby 119890 In other words is a random value in the interval[minus119890 119890] where 119890 is decreased from 2 to 0 over the course ofiterations When random values of are in [minus1 1] the nextposition of a search agent can be in any position betweenits current position and the position of the prey that is thesearch agent will approach the best solution gradually asshown in Figure 1

At the same time for the purpose of mathematical modeldivergence we utilize with random values greater than 1or less than minus1 to oblige the search agent to diverge from theprey As shown in Figure 1(b) gt 1 forces the grey wolves todiverge from the prey to hopefully find a better prey

44 Pseudocode of MDGWO The application of MDGWOalgorithm in image segmentation mainly lies in optimizingKapurrsquo entropy to obtain the best threshold therefore thefitness function as shown in (13) will be calculated based onKapurrsquos entropy

Step 1 Read image 119869 if 119869 is a RGB image then it will beprocessed by three channel of 119869R 119869G 119869B and store the datain ℎR ℎG ℎB respectively if 119869 is a grey image then read thegrey value and store it in ℎgrStep 2 According to (3) calculate image grey values andprobability distribution histogram

Computational Intelligence and Neuroscience 7

Step 3 Initialize the population of grey wolves parameter 119890 and Max iter

Step 4 Initialize the population 997888rarr119883119894 (119894 = 1 2 SN)randomly 997888rarr119883119894 = rand (SN 1) sdot (119906119887 minus 119897119887) + 119897119887 (22)

Step 5 Use (11) to discretize 997888rarr119883119894 that is being roundedtoward zero Use (12) to adjust the singular data beyond theboundaries of search space

Step 6 Calculate objective functions of each search agent byusing (8) And calculate the fitness value of each search agenton the basis of objective functions

Step 7 According to the fitness values assigning first threebest search agents to 997888rarr119883120572 997888rarr119883120573 997888rarr119883120575 respectivelyStep 8 Updating encircling parameters based on997888rarr119883120572997888rarr119883120573997888rarr119883120575which include calculating 997888rarr1198601 997888rarr1198602 997888rarr1198603 by (16) 997888rarr1198621 997888rarr1198622 997888rarr1198623 by(17) and 997888rarr119863120572 997888rarr119863120573 997888rarr119863120575 by (18)Step 9 Update the position of search agents based on (19) and(20) for the next hunting

Step 10 Add one to circular point if 119902 ge Max iter ormeet thestop condition of the algorithm the iteration will be finishedand skip to Step 11 otherwise skip to Step 5

Step 11 Set the location of the wolf that has the best objectivefunction as the best threshold of segmentation

Step 12 Input best threshold and images before and aftersegmentation

5 Experiments and Discussion

51 Parameters Settings The proposed algorithm has beentested under a set of benchmark images Some of theseimages are widely used in the multilevel image segmenta-tion literature to test different methods (Cameraman LenaBaboon and Maize) Others are chosen on purpose fromthe Berkeley Segmentation Data Set and Benchmarks 500(BSD500 for short see [41]) as shown in Figure 2 Theexperiments were carried out on a Lenovo Laptop with anIntel Core i5 processor and 4GBmemoryThe algorithmwasdeveloped via the signal processing toolbox image processingtoolbox and global optimization toolbox of Matlab R2011bAccording to relevant literatures manymethods were provedto have certain advantages compared with previous meth-ods This paper chooses the best advantageous method ascomparison objective the earlier or inferior literatures willno longer be used for the analysis Based on quantities ofcontrast experiments this paper will verify the superiority ofMDGWO in image segmentation by comparison of imagedata chart and so forth In the following sections MDGWOwill be compared with the algorithm using electromagnetism

optimization (EMO) proposed in [20] the differential evo-lution (DE) [27] the Artifical Bee Colony (ABC) [10] andthe original grey wolf optimizer The EMO DE and ABC arethe latest intelligent optimization methods by using Kapurrsquosentropy so far The comparison with GWO is mainly used totest the advantages of MDWGO

In order to avoid the randomness of results we useappropriate statistical metrics to compare the effectiveness ofthese algorithms According to [19 20] and the experimentstest thresholds are th = 2 3 4 5 [1ndash3] and the stop criterionof each experiment is 150 iterations the detailed settings ofparameters are showed in Table 2

For verifying the stability we use (23) to calculate thestandard deviation (STD) at the end of each test Once theSTD value increases the algorithms becomes more instablecorrespondingly [29]

STD = radicMax itersum119894=1

(120579119894 minus 120576)2Max iter

(23)

In addition the peak signal to noise ratio (PSNR [20]) isused to compare the similarity between the segmented imageand original image according to the mean square error (MSE[26]) of each pixel

PSNR = 20 log10 ( 255MSE

) (dB) (24)

MSE = radicsumro119894=1sumco119895=1 (119868119886119900 (119894 119895) minus 119868119886th (119894 119895))

ro times co (25)

where 119868119886119900 is the original image 119868119886th is the segmented image and119886 depends on the type of image (grey image or RGB image)ro co are respectively the total number of rows and columnsin an image

Because Kapurrsquos entropy is based on histogram of theimage this paper provides test images and the correspondinghistograms From Figure 2 it can be seen that each imagehas the only distinctive histogram which can guarantee theuniversality and commonality of the algorithm More impor-tantly most of these histograms do not follow the bimodalcharacteristic therefore the difficulty level of optimizationincreases accordingly

52 The Image Segmentation Result Based on MDGWO withDifferent Thresholds In order to reflect the segmentationeffect Figures 3 and 4 illustrate the segmentation results oforiginal images in Figure 2when the threshold is 2 3 4 and 5respectively The experiments indicate that the segmentationresults turn out to be finer and there are alsomore segmentedareas when the number of thresholds is larger and vice versaIn extreme cases when the threshold is 2 the algorithmis reduced to be binary image segmentation (foreground-background segmentation) Certainly that how many areasare segmented is related to the applications and requirementsthis method only needs to set the corresponding number ofthresholds (th) Besides giving the MDGWO segmentationresults like [20] Figures 3 and 4 also mark the position

8 Computational Intelligence and Neuroscience

Table 2 Parameters settings of MDGWO

Parameters Population size Threshold Number of iterations Run time Lower bound Upper boundValue 50 2 3 4 5 150 35 1 256

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

000100020003000400050006000700080009

001

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 3000

0002000400060008

0010012001400160018

002

times10minus3

Histogram of left col ImageImage Histogram of left col

(a) Cameraman (b) Lena

(c) Baboon (d) Butterfly

(e) Maize (f) Starfish

(g) Smiling Girl (h) Surfing

Figure 2 The original images and their histograms

of the threshold in each histogram Compared with otherMT methods it is difficult to find the difference in termsof the segmentation effect Therefore Section 54 lists thethresholds PSNR STD and MEAN for comparisons ofMDGWO results and other techniques

53 The Comparison of MDGWO in Multilevel Image Thresh-olding with Different Objective Functions In Section 1 wesummarize the relevant objective functions The commonlyused optimization functions include maximization of theentropy andmaximization of the between-class variance (egOtsursquos method) In [27] the authors respectively analyze

these objective functions and compare Kapur and Otsusystematically The experiment results show that Kapurrsquosentropy gets the best effectiveness Therefore in order toverify MDGWOrsquos efficiency we compare the thresholds andPSNR between Otsu and Kapur in Table 3

As shown inTable 3 the threshold distribution ofKapur ismore dispersed and wider in most cases However the effectof image thresholding cannot be seen from the thresholddistribution directly Therefore we focus on analysis thePSNR between Otsu and Kapur In terms of PSNR the Kapurmethod produces higher PSNR values on most items inFigure 2 except for the Sea Star Imagewith 119896 = 3 5 and SurferImage with 119896 = 4

Computational Intelligence and Neuroscience 9

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005001

0015002

0025

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

000100020003000400050006000700080009

001

0 50 100 150 200 250 3000

000100020003000400050006000700080009

001

0 50 100 150 200 250 3000

000100020003000400050006000700080009

001

0 50 100 150 200 250 3000

000100020003000400050006000700080009

001

Image

Cam

eram

anLe

naBa

boon

Butte

rfly

th = 2 th = 3 th = 4 th = 5

Figure 3 The segmentation results of (a)ndash(d) in Figure 2 and their thresholds in histograms

10 Computational Intelligence and Neuroscience

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0002000400060008

0010012001400160018

002

0 50 100 150 200 250 3000

0002000400060008

0010012001400160018

002

0 50 100 150 200 250 3000

0002000400060008

0010012001400160018

002

0 50 100 150 200 250 30000002000400060008

0010012001400160018

002

times10minus3

times10minus3

times10minus3

times10minus3

Image th = 2 th = 3 th = 4 th = 5

Mai

zeSt

arfis

hSm

iling

Girl

Surfi

ng

Figure 4 The segmentation results of (e)ndash(h) in Figure 2 and their thresholds in histograms

Computational Intelligence and Neuroscience 11

Table 3 The comparison of MDGWOrsquos efficiency between Otsu and Kapur

Image 119896 Otsu thresholds PSNR Kapur thresholds PSNR

Cameraman

2 70 144 119475 44 106 1446293 58 119 156 129933 44 98 148 1993374 40 93 139 170 160180 39 83 119 156 2116845 35 81 121 149 174 163710 23 58 94 125 159 231191

Lena

2 92 151 131029 93 163 1471643 80 126 171 157626 70 121 172 1751444 75 114 145 180 164291 43 81 127 171 2017295 73 109 136 161 189 167206 41 73 103 141 178 218208

Baboon

2 97 149 124396 78 141 1603023 83 123 160 137731 46 103 151 1863404 70 105 136 167 149493 34 75 117 159 2051985 66 98 125 150 175 160012 29 64 100 134 170 220929

Butterfly

2 100 152 124400 87 150 1493253 81 118 159 142563 62 104 152 1855394 73 101 129 164 146987 49 88 128 168 2107115 69 95 121 149 177 164688 48 80 113 145 180 224539

Maize

2 92 168 136677 84 165 1404073 76 128 187 152676 59 113 171 1658534 65 104 150 200 167309 45 80 125 187 1898185 56 86 123 164 208 185649 39 74 108 147 198 208792

Sea Star

2 85 157 148445 81 160 1485953 69 120 178 176040 60 111 172 1745834 59 99 137 187 194039 46 89 131 184 1944875 51 85 117 150 193 214000 47 83 118 150 196 209681

Smiling Girl

2 60 123 131358 88 145 1800333 47 100 131 128470 44 91 145 1911484 28 74 111 136 156914 24 67 100 145 2007595 20 63 95 124 158 18 2260 44 83 115 152 203 217937

Surfer

2 92 162 125401 52 141 1643433 71 111 177 160569 52 103 168 1893434 47 81 118 179 208786 49 86 131 185 2072185 46 77 105 143 196 216071 24 53 88 126 183 218961

The average value of Kapur is improved averagely by2224 compared to Otsu by checking against the cor-responding PSNR values which are obtained from theMDGWO The maximum value is increased by 5342 forCameraman Image when 119896 = 3 Therefore the Kapurmethod is significantly better than the Otsu method and wealso mainly analyze the effectiveness of Kapurrsquos method inSection 54

54TheComparison ofQuality Assessment by PSNR STD andMEAN This paper adopts PSNR standard to evaluate thesegmentation quality in comparisonwith otherMTmethodsTables 4ndash6 illustrate the PSNR values under different thresh-olds ofMDGWOGWOEMODEABC and theMEANandSTD of objective functions As shown in Table 4 it can be

seen from the PSNR values that MDGWO gets the highestevaluation in most cases Thus it proves that MDGWO getsbetter results on image segmentation In addition when thenumber of thresholds increases it shows superior PSNRvalue In detail the MDGWO algorithm produces higherPSNR values on all items in Table 4 except for the SmilingGirl Image with 119896 = 5 and Surfer Image with 119896 = 4 on theresult of DE

As shown in Table 4 the average value of MDGWO isimproved averagely by 1316 compared toGWOby checkingagainst the corresponding PSNR valuesThemaximum valueis increased by 4505 for Butterfly Image when 119896 = 5

ComparingwithMTEMO the average value ofMDGWOis improved averagely by 1156 by checking against the cor-responding PSNR valuesThemaximumvalue is increased by3994 for Surfer Image when 119896 = 2

12 Computational Intelligence and Neuroscience

Table 4 PSNR metrics of MTEMO DE ABC GWO and MDGWO

Image 119896 MTEMO DE ABC GWO MDGWO

Cameraman

2 13626 12584 13920 14279 144633 18803 17584 14462 19696 199344 20586 20111 2081 20809 211685 20661 21282 2240 22404 23119

Lena

2 14672 8823 14590 14680 147163 17247 14386 17197 17416 175144 18251 16151 18559 19762 201735 20019 16720 20321 21299 21820

Baboon

2 16016 8103 16007 16024 160353 16016 12596 18592 18632 186344 18485 13178 18417 20480 205195 20507 13135 20224 22060 22092

Butterfly

2 11065 8702 14402 14762 149323 14176 13028 14504 17873 185534 16725 13028 16189 21021 210715 19026 14786 19286 21485 22453

Maize

2 13633 10549 13590 13950 140403 15229 13022 15295 16201 165854 16280 14270 16346 18713 189815 17211 15079 17046 20410 20879

Sea Star

2 14398 8610 14395 14809 148853 16987 14078 16981 17431 174584 18304 16191 18427 19421 194485 20165 16474 20330 20887 20968

Smiling Girl

2 13420 14986 13514 17989 180033 18254 11243 18069 18742 191144 18860 14556 18826 19823 200755 19840 22980 19769 21214 21793

Surfer

2 11744 9737 11878 16154 164343 18584 11638 18762 18895 189344 19478 21866 19647 20234 207215 20468 19576 20479 21699 21896

By comparing with DE the average value of MDGWO isimproved averagely by 3814 by checking against the cor-responding PSNR values The maximum value is increasedby 9789 for Baboon Image when 119896 = 2 The PSNR of theSmiling Girl with 119896 = 5 and Surfer Image with 119896 = 4 areslightly lower but the gap is not significant

Comparing between ABC and MDGWO the averagevalue of MDGWO is improved averagely by 1055 by check-ing against the corresponding PSNR values The maximumvalue is increased by 3836 for Surfer Image when 119896 = 2

From the perspective of STDwhich is shown in Table 5 itcan be observed that MDGWO shows obviously advantagesover MTEMO DE ABC and GWOThe smaller the STD isthe smaller the change of fitness functions over the course ofiterations will be that is the better stability of segmentation

Therefore the results show that MDGWO obtains excitingeffect in stability So MDGWOrsquos stability is better

Compared with GWO the average value of MDGWO isimproved averagely by 7352 compared to GWO by check-ing against the corresponding STD values The maximumvalue is increased by 9644 for Baboon Image when 119896 = 3and the minimum value is increased by 2492 for BaboonImage when 119896 = 3

By comparing with MTEMO the average value ofMDGWO is improved averagely by 4788 The maximumvalue is increased by 87 for Lena Image when 119896 = 2 and theminimum value is increased by 06 for Surfer Image when119896 = 3

Comparing between DE andMDGWO the average valueofMDGWO is improved averagely by 9560Themaximum

Computational Intelligence and Neuroscience 13

Table 5 STD metrics of MTEMO DE ABC GWO and MDGWO

Image 119896 MTEMO DE ABC GWO MDGWO

Camerman

2 01849 12592 01235 01697 004623 01649 17601 02122 02287 007584 02943 21995 03003 03627 006595 02999 26579 02784 04278 01964

Lena

2 00969 12902 00349 01536 001263 01665 17822 01300 03570 002644 02800 22104 01872 05965 009395 02515 25992 01827 05946 01570

Baboon

2 00108 12862 00358 02171 001023 00393 17678 00202 04376 001564 01727 22126 01610 02986 011845 02868 26239 02660 05377 02316

Butterfly

2 00903 12708 00750 02179 004653 02207 17429 02952 02712 020364 02482 22368 03906 04808 024155 02900 26571 04818 05096 02684

Maize

2 00356 13501 00218 03571 001883 01222 18612 00901 02225 002704 02305 23230 02605 03903 009275 02502 27461 03834 04584 01677

Sea Star

2 01073 13547 01088 01728 002903 01497 18741 01752 02028 003744 01596 23307 01817 05032 011195 02639 27550 02180 04550 01437

Smiling Girl

2 00377 12516 00318 01834 001113 00955 17311 00577 01712 002424 01966 21878 01094 02508 007815 01550 25989 02768 05273 01302

Surfer

2 00579 13213 00303 02681 002453 01002 18337 01646 03014 009964 03382 23317 01686 03162 014245 03690 27846 02580 03815 01706

value is increased by 9921 for Baboon Image when 119896 =2 The minimum value is increased by 8832 for ButterflyImage when 119896 = 3

Comparing with ABC the average value of MDGWOis improved averagely by 4590 The maximum value isincreased by 7970 for Lena Image when 119896 = 3 and theminimum value is increased by 1293 for Baboon Imagewhen 119896 = 5

As far as MEAN is concerned this parameter presentsthe average value of fitness function over the course ofiterations in Table 6 which reflects the algorithm stability tosome extent But its accuracy of evaluation is relatively lowwhich can only reflect the fuzzy stability of the algorithmThe experiment data is offered here just in response to theparameter provided in literature [20] In comparison withGWO MTEWO DE and ABC in Table 6 it can be safely

assumed that inmost casesMDGWOobtains higherMEANof fitness function Moreover the difference is extremelysmall when MDGWOrsquos MEAN is lower

From the analyses of Tables 3ndash6 together with the visualeffects of Figures 2 3 and 4 it can be observed thatMDGWO method obtains better segmentation effect andhas advantage in optimal process accuracy stability androbustnessThereforeMDGWO is aMT algorithmwith highaccuracy and high segmentation quality

6 Conclusion

This paper proposes a modified discrete grey wolf optimizerwhich is used to optimize the image histograms and realizethe multilevel image segmentation Based on the high effi-ciency of GWO in the course of optimization and stability

14 Computational Intelligence and Neuroscience

Table 6 MEANmetrics of MTEMO DE ABC GWO and MDGWO

Image 119896 MTEMO DE ABC GWO MDGWO

Camerman

2 17584 124212 177638 14634 174713 21976 173764 223059 21107 219194 26586 217520 268409 24927 274805 30506 262505 308328 30436 30548

Lena

2 17831 127730 178139 17809 183963 22120 176428 220832 22074 228564 25999 218784 260615 25318 264475 29787 257311 299664 29252 30381

Baboon

2 17625 127333 176760 17679 186193 22269 175005 221276 22129 229494 26688 219010 263912 26194 269005 30800 259681 303464 30067 30076

Butterfly

2 16681 125796 174205 17425 177233 21242 172545 222209 21585 224984 25179 220176 263794 25267 261905 28611 261795 306533 29492 29899

Maize

2 18631 133566 186316 18604 195423 23565 184245 232496 22941 239394 27529 229813 273931 26936 278425 31535 271709 312127 31023 30694

Sea Star

2 18754 134104 187295 18321 195873 23323 185516 232738 23245 239014 27582 230719 275057 27136 282105 31562 272551 314919 31167 31958

Smiling Girl

2 17334 123892 173129 17136 180353 21904 171339 218601 21253 219804 26040 216541 259904 25050 265975 30089 257130 300225 29870 30574

Surfer

2 18339 130786 183393 18283 188693 23231 181492 232889 23243 241354 27863 230548 278017 27275 274475 31823 274979 317335 31384 31325

this paper successfully applies the MDGWO to the field ofMT by improving the location selection mechanism of 120572 120573and 120575 during the hunting and using weight to optimize thefinal position of prey (best threshold)TheMDGWOmethodnot only obtains better segmentation quality but also showsobvious superiority over GWO MTEMO DE and ABC instability accuracy and multilevel thresholding

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work was supported in part by the National NaturalScience Foundation of China (no 61300239 no 71301081and no 61572261) the Postdoctoral Science Foundation (no

2014M551635 and no 1302085B) the Innovation Project ofGraduate Students Foundation of Jiangsu Province (KYLX150841) the Higher Education Revitalization Plan Foundationof Anhui Province (no 2013SQRL102ZD no 2015xdjy196no 2015jyxm728 no 2016jyxm0774 and no 2016jyxm0777)and Natural Science Fund for Colleges and Universities inJiangsu Province (no16KJB520034) A Project Funded by thePriority Academic Program Development of Jiangsu HigherEducation Institutions (PAPD) and Jiangsu CollaborativeInnovation Center on Atmospheric Environment and Equip-ment Technology (CICAEET)

References

[1] M Sonka V Hlavac and R Boyle Image Processing Analysisand Machine Vision Cengage Learning 2014

[2] S Masood M Sharif A Masood M Yasmin and M RazaldquoA survey on medical image segmentationrdquo Current MedicalImaging Reviews vol 11 no 1 pp 3ndash14 2015

Computational Intelligence and Neuroscience 15

[3] PGhamisiM S Couceiro FM LMartins and J A Benedikts-son ldquoMultilevel image segmentation based on fractional-orderdarwinian particle swarm optimizationrdquo IEEE Transactions onGeoscience and Remote Sensing vol 52 no 5 pp 2382ndash23942014

[4] M Waseem Khan ldquoA survey image segmentation techniquesrdquoInternational Journal of Future Computer and Communicationvol 3 no 2 pp 89ndash93 2014

[5] J Li X Li B Yang and X Sun ldquoSegmentation-based imagecopy-move forgery detection schemerdquo IEEE Transactions onInformation Forensics and Security vol 10 no 3 pp 507ndash5182015

[6] Z Pan J Lei Y Zhang X Sun and S Kwong ldquoFast motionestimation based on content property for low-complexityH265HEVC encoderrdquo IEEE Transactions on Broadcasting vol62 no 3 pp 675ndash684 2016

[7] X Chen S Feng and D Pan ldquoAn improved approach oflung image segmentation based on watershed algorithmrdquo inProceedings of the the 7th International Conference on InternetMultimedia Computing and Service pp 1ndash5 Zhangjiajie ChinaAugust 2015

[8] Y Zheng B Jeon D Xu Q M J Wu and H Zhang ldquoImagesegmentation by generalized hierarchical fuzzy C-means algo-rithmrdquo Journal of Intelligent and Fuzzy Systems vol 28 no 2pp 961ndash973 2015

[9] V Osuna-Enciso E Cuevas and H Sossa ldquoA comparison ofnature inspired algorithms for multi-threshold image segmen-tationrdquo Expert Systems with Applications vol 40 no 4 pp 1213ndash1219 2013

[10] T Kurban P Civicioglu R Kurban and E Besdok ldquoCompari-son of evolutionary and swarmbased computational techniquesfor multilevel color image thresholdingrdquo Applied Soft Comput-ing Journal vol 23 pp 128ndash143 2014

[11] J N Kapur P K Sahoo and A K C Wong ldquoA new methodfor gray-level picture thresholding using the entropy of thehistogramrdquo Computer Vision Graphics and Image Processingvol 29 no 3 pp 273ndash285 1985

[12] N Otsu ldquoA threshold selection method from gray-level his-togramsrdquo Automatica vol 11 no 285ndash296 pp 23ndash27 1975

[13] X Li Z Zhao and H D Cheng ldquoFuzzy entropy thresholdapproach to breast cancer detectionrdquo Information Sciences -Applications vol 4 no 1 pp 49ndash56 1995

[14] J Kittler and J Illingworth ldquoMinimum error thresholdingrdquoPattern Recognition vol 19 no 1 pp 41ndash47 1986

[15] Y Xue S Zhong T Ma and J Cao ldquoA hybrid evolution-ary algorithm for numerical optimization problemrdquo IntelligentAutomation amp Soft Computing vol 21 no 4 pp 473ndash490 2015

[16] P-Y Yin ldquoA fast scheme for optimal thresholding using geneticalgorithmsrdquo Signal Processing vol 72 no 2 pp 85ndash95 1999

[17] W Fujun L Junlan L Shiwei Z Xingyu Z Dawei and TYanling ldquoAn improved adaptive genetic algorithm for imagesegmentation and vision alignment used in microelectronicbondingrdquo IEEEASMETransactions onMechatronics vol 19 no3 pp 916ndash923 2014

[18] S Banerjee and N D Jana ldquoBi level kapurs entropy basedimage segmentation using particle swarm optimizationrdquo inProceedings of the 3rd International Conference on ComputerCommunication Control and InformationTechnology (C3IT rsquo15)pp 1ndash4 Hooghly India February 2015

[19] M-H Horng ldquoMultilevel thresholding selection based on theartificial bee colony algorithm for image segmentationrdquo ExpertSystems with Applications vol 38 no 11 pp 13785ndash13791 2011

[20] D Oliva E Cuevas G Pajares D Zaldivar and V OsunaldquoA multilevel thresholding algorithm using electromagnetismoptimizationrdquo Neurocomputing vol 139 pp 357ndash381 2014

[21] S Sarkar G R Patra and S Das ldquoA differential evolutionbased approach for multilevel image segmentation using mini-mum cross entropy thresholdingrdquo in Swarm Evolutionary andMemetic Computing pp 51ndash58 Springer Berlin Germany 2011

[22] Y Xue Y Zhuang T Ni S Ni and X Wen ldquoSelf-adaptivelearning based discrete differential evolution algorithm forsolving CJWTA problemrdquo Journal of Systems Engineering andElectronics vol 25 no 1 pp 59ndash68 2014

[23] S Agrawal R Panda S Bhuyan and B K Panigrahi ldquoTsallisentropy based optimal multilevel thresholding using cuckoosearch algorithmrdquo Swarm and Evolutionary Computation vol11 pp 16ndash30 2013

[24] PD Sathya andRKayalvizhi ldquoOptimalmultilevel thresholdingusing bacterial foraging algorithmrdquo Expert Systems with Appli-cations vol 38 no 12 pp 15549ndash15564 2011

[25] S Ayas H Dogan E Gedikli and M Ekinci ldquoMicroscopicimage segmentation based on firefly algorithm for detectionof tuberculosis bacteriardquo in Proceedings of the 23rd SignalProcessing and Communications Applications Conference (SIUrsquo15) pp 851ndash854 Malatya Turkey May 2015

[26] S Mirjalili S M Mirjalili and A Lewis ldquoGrey wolf optimizerrdquoAdvances in Engineering Software vol 69 pp 46ndash61 2014

[27] B Akay ldquoA study on particle swarm optimization and artificialbee colony algorithms for multilevel thresholdingrdquo Applied SoftComputing vol 13 no 6 pp 3066ndash3091 2013

[28] A K Bhandari A Kumar and G K Singh ldquoModified artificialbee colony based computationally efficient multilevel thresh-olding for satellite image segmentation using Kapurrsquos Otsu andTsallis functionsrdquo Expert Systems with Applications vol 42 no3 pp 1573ndash1601 2015

[29] P Ghamisi M S Couceiro J A Benediktsson and N M FFerreira ldquoAn efficientmethod for segmentation of images basedon fractional calculus and natural selectionrdquo Expert Systemswith Applications vol 39 no 16 pp 12407ndash12417 2012

[30] L Li L Sun W Kang J Guo C Han and S Li ldquoFuzzymultilevel image thresholding based on modified discrete greywolf optimizer and local information aggregationrdquo IEEE Accessvol 4 pp 6438ndash6450 2016

[31] H-S Wu F-M Zhang and L-S Wu ldquoNew swarm intelligencealgorithm-wolf pack algorithmrdquo Xi Tong Gong Cheng Yu DianZi Ji ShuSystems Engineering and Electronics vol 35 no 11 pp2430ndash2438 2013

[32] H Wu and F Zhang ldquoA uncultivated wolf pack algorithm forhigh-dimensional functions and its application in parametersoptimization of PID controllerrdquo in Proceedings of the IEEECongress on Evolutionary Computation (CEC rsquo14) pp 1477ndash1482Beijing China July 2014

[33] H-S Wu and F-M Zhang ldquoWolf pack algorithm for uncon-strained global optimizationrdquo Mathematical Problems in Engi-neering vol 2014 Article ID 465082 17 pages 2014

[34] Q Zhou and Y Zhou ldquoWolf colony search algorithm based onleader strategyrdquo Application Research of Computers vol 9 pp2629ndash2632 2013

[35] G M Komaki and V Kayvanfar ldquoGrey Wolf Optimizer algo-rithm for the two-stage assembly flow shop scheduling problemwith release timerdquo Journal of Computational Science vol 8 pp109ndash120 2015

16 Computational Intelligence and Neuroscience

[36] L I Wong M H Sulaiman M R Mohamed and M SHong ldquoGrey Wolf Optimizer for solving economic dispatchproblemsrdquo in Proceedings of the IEEE International Conferenceon Power and Energy (PECon rsquo14) pp 150ndash154 KuchingMalaysia December 2014

[37] A Chaman-Motlagh ldquoSuperdefect photonic crystal filter opti-mization using Grey Wolf Optimizerrdquo IEEE Photonics Technol-ogy Letters vol 27 no 22 pp 2355ndash2358 2015

[38] P Q Dzung N T Tien N Dinh Tuyen and H Lee ldquoSelectiveharmonic elimination for cascaded multilevel inverters usinggrey wolf optimizer algorithmrdquo in Proceedings of the 9thInternational Conference on Power Electronics and ECCE Asia(ICPE rsquo15-ECCE Asia) June 2015

[39] N Muangkote K Sunat and S Chiewchanwattana ldquoAnimproved grey wolf optimizer for training q-Gaussian RadialBasis Functional-link netsrdquo in Proceedings of the InternationalComputer Science and Engineering Conference (ICSEC rsquo14) pp209ndash214 Khon Kaen Thailand August 2014

[40] A Zhu C Xu Z Li J Wu and Z Liu ldquoHybridizing grey Wolfoptimization with differential evolution for global optimizationand test scheduling for 3D stacked SoCrdquo Journal of SystemsEngineering and Electronics vol 26 no 2 pp 317ndash328 2015

[41] P ArbelaezMMaire C Fowlkes and JMalik ldquoContour detec-tion and hierarchical image segmentationrdquo IEEE Transactionson Pattern Analysis and Machine Intelligence vol 33 no 5 pp898ndash916 2011

Submit your manuscripts athttpswwwhindawicom

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Distributed Sensor Networks

International Journal of

Advances in

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Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

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ArtificialNeural Systems

Advances in

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RoboticsJournal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

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6 Computational Intelligence and Neuroscience

if 10038161003816100381610038161003816A10038161003816100381610038161003816lt 1

(a)

if 10038161003816100381610038161003816A10038161003816100381610038161003816gt 1

(b)

Figure 1 Attacking prey of grey wolf

according to their average value As for the specific formulasand the detailed calculation please refer to literature [26]In order to approach the best solution more quickly theproposed algorithm in this paper improves the current bestsolution in solutions updating by weighting method Theupdate formulations are as shown in (20) and correlationcoefficients are calculated by (18) (19) where 1198601 1198602 1198603 arecalculated by (16)997888rarr119863120572 = 100381610038161003816100381610038161003816997888rarr1198621 sdot 997888rarr119883120572 minus 100381610038161003816100381610038161003816 997888rarr119863120573 = 100381610038161003816100381610038161003816997888rarr1198622 sdot 997888rarr119883120573 minus 100381610038161003816100381610038161003816 997888rarr119863120575 = 100381610038161003816100381610038161003816997888rarr1198623 sdot 997888rarr119883120575 minus 100381610038161003816100381610038161003816

(18)

997888rarr1198831 = 997888rarr119883120572 minus 997888rarr1198601 sdot 997888rarr119863120572997888rarr1198832 = 997888rarr119883120573 minus 997888rarr1198602 sdot 997888rarr119863120573997888rarr1198833 = 997888rarr119883120575 minus 997888rarr1198603 sdot 997888rarr119863120575(19)

(119905 + 1) = 1199081 sdot 997888rarr1198831 + 1199082 sdot 997888rarr1198832 + 1199083 sdot 997888rarr1198833 (20)

where 1199081 1199082 1199083 are the corresponding weights which arecalculated by

1199081 = 1198911119865 1199082 = 1198912119865 1199083 = 1198913119865

(21)

where 1198911 1198912 1198913 calculated by (13) are the correspondingfitness values of120572120573 120575119865 = 1198911+1198912+1198913This paper emphasizes

that different from GWO updating search agents MDGWOuses (20) and (21) to update the location of search agentsby weighting method for the first time it is also the majorcontribution to the improved GWO

433 Attacking Prey The grey wolves finish the hunt byattacking the prey when it stops moving In order to mathe-matically model approaching the prey we decrease the valueof 119890 Note that the fluctuation range of is also decreasedby 119890 In other words is a random value in the interval[minus119890 119890] where 119890 is decreased from 2 to 0 over the course ofiterations When random values of are in [minus1 1] the nextposition of a search agent can be in any position betweenits current position and the position of the prey that is thesearch agent will approach the best solution gradually asshown in Figure 1

At the same time for the purpose of mathematical modeldivergence we utilize with random values greater than 1or less than minus1 to oblige the search agent to diverge from theprey As shown in Figure 1(b) gt 1 forces the grey wolves todiverge from the prey to hopefully find a better prey

44 Pseudocode of MDGWO The application of MDGWOalgorithm in image segmentation mainly lies in optimizingKapurrsquo entropy to obtain the best threshold therefore thefitness function as shown in (13) will be calculated based onKapurrsquos entropy

Step 1 Read image 119869 if 119869 is a RGB image then it will beprocessed by three channel of 119869R 119869G 119869B and store the datain ℎR ℎG ℎB respectively if 119869 is a grey image then read thegrey value and store it in ℎgrStep 2 According to (3) calculate image grey values andprobability distribution histogram

Computational Intelligence and Neuroscience 7

Step 3 Initialize the population of grey wolves parameter 119890 and Max iter

Step 4 Initialize the population 997888rarr119883119894 (119894 = 1 2 SN)randomly 997888rarr119883119894 = rand (SN 1) sdot (119906119887 minus 119897119887) + 119897119887 (22)

Step 5 Use (11) to discretize 997888rarr119883119894 that is being roundedtoward zero Use (12) to adjust the singular data beyond theboundaries of search space

Step 6 Calculate objective functions of each search agent byusing (8) And calculate the fitness value of each search agenton the basis of objective functions

Step 7 According to the fitness values assigning first threebest search agents to 997888rarr119883120572 997888rarr119883120573 997888rarr119883120575 respectivelyStep 8 Updating encircling parameters based on997888rarr119883120572997888rarr119883120573997888rarr119883120575which include calculating 997888rarr1198601 997888rarr1198602 997888rarr1198603 by (16) 997888rarr1198621 997888rarr1198622 997888rarr1198623 by(17) and 997888rarr119863120572 997888rarr119863120573 997888rarr119863120575 by (18)Step 9 Update the position of search agents based on (19) and(20) for the next hunting

Step 10 Add one to circular point if 119902 ge Max iter ormeet thestop condition of the algorithm the iteration will be finishedand skip to Step 11 otherwise skip to Step 5

Step 11 Set the location of the wolf that has the best objectivefunction as the best threshold of segmentation

Step 12 Input best threshold and images before and aftersegmentation

5 Experiments and Discussion

51 Parameters Settings The proposed algorithm has beentested under a set of benchmark images Some of theseimages are widely used in the multilevel image segmenta-tion literature to test different methods (Cameraman LenaBaboon and Maize) Others are chosen on purpose fromthe Berkeley Segmentation Data Set and Benchmarks 500(BSD500 for short see [41]) as shown in Figure 2 Theexperiments were carried out on a Lenovo Laptop with anIntel Core i5 processor and 4GBmemoryThe algorithmwasdeveloped via the signal processing toolbox image processingtoolbox and global optimization toolbox of Matlab R2011bAccording to relevant literatures manymethods were provedto have certain advantages compared with previous meth-ods This paper chooses the best advantageous method ascomparison objective the earlier or inferior literatures willno longer be used for the analysis Based on quantities ofcontrast experiments this paper will verify the superiority ofMDGWO in image segmentation by comparison of imagedata chart and so forth In the following sections MDGWOwill be compared with the algorithm using electromagnetism

optimization (EMO) proposed in [20] the differential evo-lution (DE) [27] the Artifical Bee Colony (ABC) [10] andthe original grey wolf optimizer The EMO DE and ABC arethe latest intelligent optimization methods by using Kapurrsquosentropy so far The comparison with GWO is mainly used totest the advantages of MDWGO

In order to avoid the randomness of results we useappropriate statistical metrics to compare the effectiveness ofthese algorithms According to [19 20] and the experimentstest thresholds are th = 2 3 4 5 [1ndash3] and the stop criterionof each experiment is 150 iterations the detailed settings ofparameters are showed in Table 2

For verifying the stability we use (23) to calculate thestandard deviation (STD) at the end of each test Once theSTD value increases the algorithms becomes more instablecorrespondingly [29]

STD = radicMax itersum119894=1

(120579119894 minus 120576)2Max iter

(23)

In addition the peak signal to noise ratio (PSNR [20]) isused to compare the similarity between the segmented imageand original image according to the mean square error (MSE[26]) of each pixel

PSNR = 20 log10 ( 255MSE

) (dB) (24)

MSE = radicsumro119894=1sumco119895=1 (119868119886119900 (119894 119895) minus 119868119886th (119894 119895))

ro times co (25)

where 119868119886119900 is the original image 119868119886th is the segmented image and119886 depends on the type of image (grey image or RGB image)ro co are respectively the total number of rows and columnsin an image

Because Kapurrsquos entropy is based on histogram of theimage this paper provides test images and the correspondinghistograms From Figure 2 it can be seen that each imagehas the only distinctive histogram which can guarantee theuniversality and commonality of the algorithm More impor-tantly most of these histograms do not follow the bimodalcharacteristic therefore the difficulty level of optimizationincreases accordingly

52 The Image Segmentation Result Based on MDGWO withDifferent Thresholds In order to reflect the segmentationeffect Figures 3 and 4 illustrate the segmentation results oforiginal images in Figure 2when the threshold is 2 3 4 and 5respectively The experiments indicate that the segmentationresults turn out to be finer and there are alsomore segmentedareas when the number of thresholds is larger and vice versaIn extreme cases when the threshold is 2 the algorithmis reduced to be binary image segmentation (foreground-background segmentation) Certainly that how many areasare segmented is related to the applications and requirementsthis method only needs to set the corresponding number ofthresholds (th) Besides giving the MDGWO segmentationresults like [20] Figures 3 and 4 also mark the position

8 Computational Intelligence and Neuroscience

Table 2 Parameters settings of MDGWO

Parameters Population size Threshold Number of iterations Run time Lower bound Upper boundValue 50 2 3 4 5 150 35 1 256

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

000100020003000400050006000700080009

001

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 3000

0002000400060008

0010012001400160018

002

times10minus3

Histogram of left col ImageImage Histogram of left col

(a) Cameraman (b) Lena

(c) Baboon (d) Butterfly

(e) Maize (f) Starfish

(g) Smiling Girl (h) Surfing

Figure 2 The original images and their histograms

of the threshold in each histogram Compared with otherMT methods it is difficult to find the difference in termsof the segmentation effect Therefore Section 54 lists thethresholds PSNR STD and MEAN for comparisons ofMDGWO results and other techniques

53 The Comparison of MDGWO in Multilevel Image Thresh-olding with Different Objective Functions In Section 1 wesummarize the relevant objective functions The commonlyused optimization functions include maximization of theentropy andmaximization of the between-class variance (egOtsursquos method) In [27] the authors respectively analyze

these objective functions and compare Kapur and Otsusystematically The experiment results show that Kapurrsquosentropy gets the best effectiveness Therefore in order toverify MDGWOrsquos efficiency we compare the thresholds andPSNR between Otsu and Kapur in Table 3

As shown inTable 3 the threshold distribution ofKapur ismore dispersed and wider in most cases However the effectof image thresholding cannot be seen from the thresholddistribution directly Therefore we focus on analysis thePSNR between Otsu and Kapur In terms of PSNR the Kapurmethod produces higher PSNR values on most items inFigure 2 except for the Sea Star Imagewith 119896 = 3 5 and SurferImage with 119896 = 4

Computational Intelligence and Neuroscience 9

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005001

0015002

0025

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

000100020003000400050006000700080009

001

0 50 100 150 200 250 3000

000100020003000400050006000700080009

001

0 50 100 150 200 250 3000

000100020003000400050006000700080009

001

0 50 100 150 200 250 3000

000100020003000400050006000700080009

001

Image

Cam

eram

anLe

naBa

boon

Butte

rfly

th = 2 th = 3 th = 4 th = 5

Figure 3 The segmentation results of (a)ndash(d) in Figure 2 and their thresholds in histograms

10 Computational Intelligence and Neuroscience

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0002000400060008

0010012001400160018

002

0 50 100 150 200 250 3000

0002000400060008

0010012001400160018

002

0 50 100 150 200 250 3000

0002000400060008

0010012001400160018

002

0 50 100 150 200 250 30000002000400060008

0010012001400160018

002

times10minus3

times10minus3

times10minus3

times10minus3

Image th = 2 th = 3 th = 4 th = 5

Mai

zeSt

arfis

hSm

iling

Girl

Surfi

ng

Figure 4 The segmentation results of (e)ndash(h) in Figure 2 and their thresholds in histograms

Computational Intelligence and Neuroscience 11

Table 3 The comparison of MDGWOrsquos efficiency between Otsu and Kapur

Image 119896 Otsu thresholds PSNR Kapur thresholds PSNR

Cameraman

2 70 144 119475 44 106 1446293 58 119 156 129933 44 98 148 1993374 40 93 139 170 160180 39 83 119 156 2116845 35 81 121 149 174 163710 23 58 94 125 159 231191

Lena

2 92 151 131029 93 163 1471643 80 126 171 157626 70 121 172 1751444 75 114 145 180 164291 43 81 127 171 2017295 73 109 136 161 189 167206 41 73 103 141 178 218208

Baboon

2 97 149 124396 78 141 1603023 83 123 160 137731 46 103 151 1863404 70 105 136 167 149493 34 75 117 159 2051985 66 98 125 150 175 160012 29 64 100 134 170 220929

Butterfly

2 100 152 124400 87 150 1493253 81 118 159 142563 62 104 152 1855394 73 101 129 164 146987 49 88 128 168 2107115 69 95 121 149 177 164688 48 80 113 145 180 224539

Maize

2 92 168 136677 84 165 1404073 76 128 187 152676 59 113 171 1658534 65 104 150 200 167309 45 80 125 187 1898185 56 86 123 164 208 185649 39 74 108 147 198 208792

Sea Star

2 85 157 148445 81 160 1485953 69 120 178 176040 60 111 172 1745834 59 99 137 187 194039 46 89 131 184 1944875 51 85 117 150 193 214000 47 83 118 150 196 209681

Smiling Girl

2 60 123 131358 88 145 1800333 47 100 131 128470 44 91 145 1911484 28 74 111 136 156914 24 67 100 145 2007595 20 63 95 124 158 18 2260 44 83 115 152 203 217937

Surfer

2 92 162 125401 52 141 1643433 71 111 177 160569 52 103 168 1893434 47 81 118 179 208786 49 86 131 185 2072185 46 77 105 143 196 216071 24 53 88 126 183 218961

The average value of Kapur is improved averagely by2224 compared to Otsu by checking against the cor-responding PSNR values which are obtained from theMDGWO The maximum value is increased by 5342 forCameraman Image when 119896 = 3 Therefore the Kapurmethod is significantly better than the Otsu method and wealso mainly analyze the effectiveness of Kapurrsquos method inSection 54

54TheComparison ofQuality Assessment by PSNR STD andMEAN This paper adopts PSNR standard to evaluate thesegmentation quality in comparisonwith otherMTmethodsTables 4ndash6 illustrate the PSNR values under different thresh-olds ofMDGWOGWOEMODEABC and theMEANandSTD of objective functions As shown in Table 4 it can be

seen from the PSNR values that MDGWO gets the highestevaluation in most cases Thus it proves that MDGWO getsbetter results on image segmentation In addition when thenumber of thresholds increases it shows superior PSNRvalue In detail the MDGWO algorithm produces higherPSNR values on all items in Table 4 except for the SmilingGirl Image with 119896 = 5 and Surfer Image with 119896 = 4 on theresult of DE

As shown in Table 4 the average value of MDGWO isimproved averagely by 1316 compared toGWOby checkingagainst the corresponding PSNR valuesThemaximum valueis increased by 4505 for Butterfly Image when 119896 = 5

ComparingwithMTEMO the average value ofMDGWOis improved averagely by 1156 by checking against the cor-responding PSNR valuesThemaximumvalue is increased by3994 for Surfer Image when 119896 = 2

12 Computational Intelligence and Neuroscience

Table 4 PSNR metrics of MTEMO DE ABC GWO and MDGWO

Image 119896 MTEMO DE ABC GWO MDGWO

Cameraman

2 13626 12584 13920 14279 144633 18803 17584 14462 19696 199344 20586 20111 2081 20809 211685 20661 21282 2240 22404 23119

Lena

2 14672 8823 14590 14680 147163 17247 14386 17197 17416 175144 18251 16151 18559 19762 201735 20019 16720 20321 21299 21820

Baboon

2 16016 8103 16007 16024 160353 16016 12596 18592 18632 186344 18485 13178 18417 20480 205195 20507 13135 20224 22060 22092

Butterfly

2 11065 8702 14402 14762 149323 14176 13028 14504 17873 185534 16725 13028 16189 21021 210715 19026 14786 19286 21485 22453

Maize

2 13633 10549 13590 13950 140403 15229 13022 15295 16201 165854 16280 14270 16346 18713 189815 17211 15079 17046 20410 20879

Sea Star

2 14398 8610 14395 14809 148853 16987 14078 16981 17431 174584 18304 16191 18427 19421 194485 20165 16474 20330 20887 20968

Smiling Girl

2 13420 14986 13514 17989 180033 18254 11243 18069 18742 191144 18860 14556 18826 19823 200755 19840 22980 19769 21214 21793

Surfer

2 11744 9737 11878 16154 164343 18584 11638 18762 18895 189344 19478 21866 19647 20234 207215 20468 19576 20479 21699 21896

By comparing with DE the average value of MDGWO isimproved averagely by 3814 by checking against the cor-responding PSNR values The maximum value is increasedby 9789 for Baboon Image when 119896 = 2 The PSNR of theSmiling Girl with 119896 = 5 and Surfer Image with 119896 = 4 areslightly lower but the gap is not significant

Comparing between ABC and MDGWO the averagevalue of MDGWO is improved averagely by 1055 by check-ing against the corresponding PSNR values The maximumvalue is increased by 3836 for Surfer Image when 119896 = 2

From the perspective of STDwhich is shown in Table 5 itcan be observed that MDGWO shows obviously advantagesover MTEMO DE ABC and GWOThe smaller the STD isthe smaller the change of fitness functions over the course ofiterations will be that is the better stability of segmentation

Therefore the results show that MDGWO obtains excitingeffect in stability So MDGWOrsquos stability is better

Compared with GWO the average value of MDGWO isimproved averagely by 7352 compared to GWO by check-ing against the corresponding STD values The maximumvalue is increased by 9644 for Baboon Image when 119896 = 3and the minimum value is increased by 2492 for BaboonImage when 119896 = 3

By comparing with MTEMO the average value ofMDGWO is improved averagely by 4788 The maximumvalue is increased by 87 for Lena Image when 119896 = 2 and theminimum value is increased by 06 for Surfer Image when119896 = 3

Comparing between DE andMDGWO the average valueofMDGWO is improved averagely by 9560Themaximum

Computational Intelligence and Neuroscience 13

Table 5 STD metrics of MTEMO DE ABC GWO and MDGWO

Image 119896 MTEMO DE ABC GWO MDGWO

Camerman

2 01849 12592 01235 01697 004623 01649 17601 02122 02287 007584 02943 21995 03003 03627 006595 02999 26579 02784 04278 01964

Lena

2 00969 12902 00349 01536 001263 01665 17822 01300 03570 002644 02800 22104 01872 05965 009395 02515 25992 01827 05946 01570

Baboon

2 00108 12862 00358 02171 001023 00393 17678 00202 04376 001564 01727 22126 01610 02986 011845 02868 26239 02660 05377 02316

Butterfly

2 00903 12708 00750 02179 004653 02207 17429 02952 02712 020364 02482 22368 03906 04808 024155 02900 26571 04818 05096 02684

Maize

2 00356 13501 00218 03571 001883 01222 18612 00901 02225 002704 02305 23230 02605 03903 009275 02502 27461 03834 04584 01677

Sea Star

2 01073 13547 01088 01728 002903 01497 18741 01752 02028 003744 01596 23307 01817 05032 011195 02639 27550 02180 04550 01437

Smiling Girl

2 00377 12516 00318 01834 001113 00955 17311 00577 01712 002424 01966 21878 01094 02508 007815 01550 25989 02768 05273 01302

Surfer

2 00579 13213 00303 02681 002453 01002 18337 01646 03014 009964 03382 23317 01686 03162 014245 03690 27846 02580 03815 01706

value is increased by 9921 for Baboon Image when 119896 =2 The minimum value is increased by 8832 for ButterflyImage when 119896 = 3

Comparing with ABC the average value of MDGWOis improved averagely by 4590 The maximum value isincreased by 7970 for Lena Image when 119896 = 3 and theminimum value is increased by 1293 for Baboon Imagewhen 119896 = 5

As far as MEAN is concerned this parameter presentsthe average value of fitness function over the course ofiterations in Table 6 which reflects the algorithm stability tosome extent But its accuracy of evaluation is relatively lowwhich can only reflect the fuzzy stability of the algorithmThe experiment data is offered here just in response to theparameter provided in literature [20] In comparison withGWO MTEWO DE and ABC in Table 6 it can be safely

assumed that inmost casesMDGWOobtains higherMEANof fitness function Moreover the difference is extremelysmall when MDGWOrsquos MEAN is lower

From the analyses of Tables 3ndash6 together with the visualeffects of Figures 2 3 and 4 it can be observed thatMDGWO method obtains better segmentation effect andhas advantage in optimal process accuracy stability androbustnessThereforeMDGWO is aMT algorithmwith highaccuracy and high segmentation quality

6 Conclusion

This paper proposes a modified discrete grey wolf optimizerwhich is used to optimize the image histograms and realizethe multilevel image segmentation Based on the high effi-ciency of GWO in the course of optimization and stability

14 Computational Intelligence and Neuroscience

Table 6 MEANmetrics of MTEMO DE ABC GWO and MDGWO

Image 119896 MTEMO DE ABC GWO MDGWO

Camerman

2 17584 124212 177638 14634 174713 21976 173764 223059 21107 219194 26586 217520 268409 24927 274805 30506 262505 308328 30436 30548

Lena

2 17831 127730 178139 17809 183963 22120 176428 220832 22074 228564 25999 218784 260615 25318 264475 29787 257311 299664 29252 30381

Baboon

2 17625 127333 176760 17679 186193 22269 175005 221276 22129 229494 26688 219010 263912 26194 269005 30800 259681 303464 30067 30076

Butterfly

2 16681 125796 174205 17425 177233 21242 172545 222209 21585 224984 25179 220176 263794 25267 261905 28611 261795 306533 29492 29899

Maize

2 18631 133566 186316 18604 195423 23565 184245 232496 22941 239394 27529 229813 273931 26936 278425 31535 271709 312127 31023 30694

Sea Star

2 18754 134104 187295 18321 195873 23323 185516 232738 23245 239014 27582 230719 275057 27136 282105 31562 272551 314919 31167 31958

Smiling Girl

2 17334 123892 173129 17136 180353 21904 171339 218601 21253 219804 26040 216541 259904 25050 265975 30089 257130 300225 29870 30574

Surfer

2 18339 130786 183393 18283 188693 23231 181492 232889 23243 241354 27863 230548 278017 27275 274475 31823 274979 317335 31384 31325

this paper successfully applies the MDGWO to the field ofMT by improving the location selection mechanism of 120572 120573and 120575 during the hunting and using weight to optimize thefinal position of prey (best threshold)TheMDGWOmethodnot only obtains better segmentation quality but also showsobvious superiority over GWO MTEMO DE and ABC instability accuracy and multilevel thresholding

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work was supported in part by the National NaturalScience Foundation of China (no 61300239 no 71301081and no 61572261) the Postdoctoral Science Foundation (no

2014M551635 and no 1302085B) the Innovation Project ofGraduate Students Foundation of Jiangsu Province (KYLX150841) the Higher Education Revitalization Plan Foundationof Anhui Province (no 2013SQRL102ZD no 2015xdjy196no 2015jyxm728 no 2016jyxm0774 and no 2016jyxm0777)and Natural Science Fund for Colleges and Universities inJiangsu Province (no16KJB520034) A Project Funded by thePriority Academic Program Development of Jiangsu HigherEducation Institutions (PAPD) and Jiangsu CollaborativeInnovation Center on Atmospheric Environment and Equip-ment Technology (CICAEET)

References

[1] M Sonka V Hlavac and R Boyle Image Processing Analysisand Machine Vision Cengage Learning 2014

[2] S Masood M Sharif A Masood M Yasmin and M RazaldquoA survey on medical image segmentationrdquo Current MedicalImaging Reviews vol 11 no 1 pp 3ndash14 2015

Computational Intelligence and Neuroscience 15

[3] PGhamisiM S Couceiro FM LMartins and J A Benedikts-son ldquoMultilevel image segmentation based on fractional-orderdarwinian particle swarm optimizationrdquo IEEE Transactions onGeoscience and Remote Sensing vol 52 no 5 pp 2382ndash23942014

[4] M Waseem Khan ldquoA survey image segmentation techniquesrdquoInternational Journal of Future Computer and Communicationvol 3 no 2 pp 89ndash93 2014

[5] J Li X Li B Yang and X Sun ldquoSegmentation-based imagecopy-move forgery detection schemerdquo IEEE Transactions onInformation Forensics and Security vol 10 no 3 pp 507ndash5182015

[6] Z Pan J Lei Y Zhang X Sun and S Kwong ldquoFast motionestimation based on content property for low-complexityH265HEVC encoderrdquo IEEE Transactions on Broadcasting vol62 no 3 pp 675ndash684 2016

[7] X Chen S Feng and D Pan ldquoAn improved approach oflung image segmentation based on watershed algorithmrdquo inProceedings of the the 7th International Conference on InternetMultimedia Computing and Service pp 1ndash5 Zhangjiajie ChinaAugust 2015

[8] Y Zheng B Jeon D Xu Q M J Wu and H Zhang ldquoImagesegmentation by generalized hierarchical fuzzy C-means algo-rithmrdquo Journal of Intelligent and Fuzzy Systems vol 28 no 2pp 961ndash973 2015

[9] V Osuna-Enciso E Cuevas and H Sossa ldquoA comparison ofnature inspired algorithms for multi-threshold image segmen-tationrdquo Expert Systems with Applications vol 40 no 4 pp 1213ndash1219 2013

[10] T Kurban P Civicioglu R Kurban and E Besdok ldquoCompari-son of evolutionary and swarmbased computational techniquesfor multilevel color image thresholdingrdquo Applied Soft Comput-ing Journal vol 23 pp 128ndash143 2014

[11] J N Kapur P K Sahoo and A K C Wong ldquoA new methodfor gray-level picture thresholding using the entropy of thehistogramrdquo Computer Vision Graphics and Image Processingvol 29 no 3 pp 273ndash285 1985

[12] N Otsu ldquoA threshold selection method from gray-level his-togramsrdquo Automatica vol 11 no 285ndash296 pp 23ndash27 1975

[13] X Li Z Zhao and H D Cheng ldquoFuzzy entropy thresholdapproach to breast cancer detectionrdquo Information Sciences -Applications vol 4 no 1 pp 49ndash56 1995

[14] J Kittler and J Illingworth ldquoMinimum error thresholdingrdquoPattern Recognition vol 19 no 1 pp 41ndash47 1986

[15] Y Xue S Zhong T Ma and J Cao ldquoA hybrid evolution-ary algorithm for numerical optimization problemrdquo IntelligentAutomation amp Soft Computing vol 21 no 4 pp 473ndash490 2015

[16] P-Y Yin ldquoA fast scheme for optimal thresholding using geneticalgorithmsrdquo Signal Processing vol 72 no 2 pp 85ndash95 1999

[17] W Fujun L Junlan L Shiwei Z Xingyu Z Dawei and TYanling ldquoAn improved adaptive genetic algorithm for imagesegmentation and vision alignment used in microelectronicbondingrdquo IEEEASMETransactions onMechatronics vol 19 no3 pp 916ndash923 2014

[18] S Banerjee and N D Jana ldquoBi level kapurs entropy basedimage segmentation using particle swarm optimizationrdquo inProceedings of the 3rd International Conference on ComputerCommunication Control and InformationTechnology (C3IT rsquo15)pp 1ndash4 Hooghly India February 2015

[19] M-H Horng ldquoMultilevel thresholding selection based on theartificial bee colony algorithm for image segmentationrdquo ExpertSystems with Applications vol 38 no 11 pp 13785ndash13791 2011

[20] D Oliva E Cuevas G Pajares D Zaldivar and V OsunaldquoA multilevel thresholding algorithm using electromagnetismoptimizationrdquo Neurocomputing vol 139 pp 357ndash381 2014

[21] S Sarkar G R Patra and S Das ldquoA differential evolutionbased approach for multilevel image segmentation using mini-mum cross entropy thresholdingrdquo in Swarm Evolutionary andMemetic Computing pp 51ndash58 Springer Berlin Germany 2011

[22] Y Xue Y Zhuang T Ni S Ni and X Wen ldquoSelf-adaptivelearning based discrete differential evolution algorithm forsolving CJWTA problemrdquo Journal of Systems Engineering andElectronics vol 25 no 1 pp 59ndash68 2014

[23] S Agrawal R Panda S Bhuyan and B K Panigrahi ldquoTsallisentropy based optimal multilevel thresholding using cuckoosearch algorithmrdquo Swarm and Evolutionary Computation vol11 pp 16ndash30 2013

[24] PD Sathya andRKayalvizhi ldquoOptimalmultilevel thresholdingusing bacterial foraging algorithmrdquo Expert Systems with Appli-cations vol 38 no 12 pp 15549ndash15564 2011

[25] S Ayas H Dogan E Gedikli and M Ekinci ldquoMicroscopicimage segmentation based on firefly algorithm for detectionof tuberculosis bacteriardquo in Proceedings of the 23rd SignalProcessing and Communications Applications Conference (SIUrsquo15) pp 851ndash854 Malatya Turkey May 2015

[26] S Mirjalili S M Mirjalili and A Lewis ldquoGrey wolf optimizerrdquoAdvances in Engineering Software vol 69 pp 46ndash61 2014

[27] B Akay ldquoA study on particle swarm optimization and artificialbee colony algorithms for multilevel thresholdingrdquo Applied SoftComputing vol 13 no 6 pp 3066ndash3091 2013

[28] A K Bhandari A Kumar and G K Singh ldquoModified artificialbee colony based computationally efficient multilevel thresh-olding for satellite image segmentation using Kapurrsquos Otsu andTsallis functionsrdquo Expert Systems with Applications vol 42 no3 pp 1573ndash1601 2015

[29] P Ghamisi M S Couceiro J A Benediktsson and N M FFerreira ldquoAn efficientmethod for segmentation of images basedon fractional calculus and natural selectionrdquo Expert Systemswith Applications vol 39 no 16 pp 12407ndash12417 2012

[30] L Li L Sun W Kang J Guo C Han and S Li ldquoFuzzymultilevel image thresholding based on modified discrete greywolf optimizer and local information aggregationrdquo IEEE Accessvol 4 pp 6438ndash6450 2016

[31] H-S Wu F-M Zhang and L-S Wu ldquoNew swarm intelligencealgorithm-wolf pack algorithmrdquo Xi Tong Gong Cheng Yu DianZi Ji ShuSystems Engineering and Electronics vol 35 no 11 pp2430ndash2438 2013

[32] H Wu and F Zhang ldquoA uncultivated wolf pack algorithm forhigh-dimensional functions and its application in parametersoptimization of PID controllerrdquo in Proceedings of the IEEECongress on Evolutionary Computation (CEC rsquo14) pp 1477ndash1482Beijing China July 2014

[33] H-S Wu and F-M Zhang ldquoWolf pack algorithm for uncon-strained global optimizationrdquo Mathematical Problems in Engi-neering vol 2014 Article ID 465082 17 pages 2014

[34] Q Zhou and Y Zhou ldquoWolf colony search algorithm based onleader strategyrdquo Application Research of Computers vol 9 pp2629ndash2632 2013

[35] G M Komaki and V Kayvanfar ldquoGrey Wolf Optimizer algo-rithm for the two-stage assembly flow shop scheduling problemwith release timerdquo Journal of Computational Science vol 8 pp109ndash120 2015

16 Computational Intelligence and Neuroscience

[36] L I Wong M H Sulaiman M R Mohamed and M SHong ldquoGrey Wolf Optimizer for solving economic dispatchproblemsrdquo in Proceedings of the IEEE International Conferenceon Power and Energy (PECon rsquo14) pp 150ndash154 KuchingMalaysia December 2014

[37] A Chaman-Motlagh ldquoSuperdefect photonic crystal filter opti-mization using Grey Wolf Optimizerrdquo IEEE Photonics Technol-ogy Letters vol 27 no 22 pp 2355ndash2358 2015

[38] P Q Dzung N T Tien N Dinh Tuyen and H Lee ldquoSelectiveharmonic elimination for cascaded multilevel inverters usinggrey wolf optimizer algorithmrdquo in Proceedings of the 9thInternational Conference on Power Electronics and ECCE Asia(ICPE rsquo15-ECCE Asia) June 2015

[39] N Muangkote K Sunat and S Chiewchanwattana ldquoAnimproved grey wolf optimizer for training q-Gaussian RadialBasis Functional-link netsrdquo in Proceedings of the InternationalComputer Science and Engineering Conference (ICSEC rsquo14) pp209ndash214 Khon Kaen Thailand August 2014

[40] A Zhu C Xu Z Li J Wu and Z Liu ldquoHybridizing grey Wolfoptimization with differential evolution for global optimizationand test scheduling for 3D stacked SoCrdquo Journal of SystemsEngineering and Electronics vol 26 no 2 pp 317ndash328 2015

[41] P ArbelaezMMaire C Fowlkes and JMalik ldquoContour detec-tion and hierarchical image segmentationrdquo IEEE Transactionson Pattern Analysis and Machine Intelligence vol 33 no 5 pp898ndash916 2011

Submit your manuscripts athttpswwwhindawicom

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Distributed Sensor Networks

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Advances in

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Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

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Applied Computational Intelligence and Soft Computing

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Artificial Intelligence

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Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Electrical and Computer Engineering

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Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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httpwwwhindawicom Volume 2014

Advances in

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International Journal of

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ArtificialNeural Systems

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RoboticsJournal of

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Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

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Computational Intelligence and Neuroscience 7

Step 3 Initialize the population of grey wolves parameter 119890 and Max iter

Step 4 Initialize the population 997888rarr119883119894 (119894 = 1 2 SN)randomly 997888rarr119883119894 = rand (SN 1) sdot (119906119887 minus 119897119887) + 119897119887 (22)

Step 5 Use (11) to discretize 997888rarr119883119894 that is being roundedtoward zero Use (12) to adjust the singular data beyond theboundaries of search space

Step 6 Calculate objective functions of each search agent byusing (8) And calculate the fitness value of each search agenton the basis of objective functions

Step 7 According to the fitness values assigning first threebest search agents to 997888rarr119883120572 997888rarr119883120573 997888rarr119883120575 respectivelyStep 8 Updating encircling parameters based on997888rarr119883120572997888rarr119883120573997888rarr119883120575which include calculating 997888rarr1198601 997888rarr1198602 997888rarr1198603 by (16) 997888rarr1198621 997888rarr1198622 997888rarr1198623 by(17) and 997888rarr119863120572 997888rarr119863120573 997888rarr119863120575 by (18)Step 9 Update the position of search agents based on (19) and(20) for the next hunting

Step 10 Add one to circular point if 119902 ge Max iter ormeet thestop condition of the algorithm the iteration will be finishedand skip to Step 11 otherwise skip to Step 5

Step 11 Set the location of the wolf that has the best objectivefunction as the best threshold of segmentation

Step 12 Input best threshold and images before and aftersegmentation

5 Experiments and Discussion

51 Parameters Settings The proposed algorithm has beentested under a set of benchmark images Some of theseimages are widely used in the multilevel image segmenta-tion literature to test different methods (Cameraman LenaBaboon and Maize) Others are chosen on purpose fromthe Berkeley Segmentation Data Set and Benchmarks 500(BSD500 for short see [41]) as shown in Figure 2 Theexperiments were carried out on a Lenovo Laptop with anIntel Core i5 processor and 4GBmemoryThe algorithmwasdeveloped via the signal processing toolbox image processingtoolbox and global optimization toolbox of Matlab R2011bAccording to relevant literatures manymethods were provedto have certain advantages compared with previous meth-ods This paper chooses the best advantageous method ascomparison objective the earlier or inferior literatures willno longer be used for the analysis Based on quantities ofcontrast experiments this paper will verify the superiority ofMDGWO in image segmentation by comparison of imagedata chart and so forth In the following sections MDGWOwill be compared with the algorithm using electromagnetism

optimization (EMO) proposed in [20] the differential evo-lution (DE) [27] the Artifical Bee Colony (ABC) [10] andthe original grey wolf optimizer The EMO DE and ABC arethe latest intelligent optimization methods by using Kapurrsquosentropy so far The comparison with GWO is mainly used totest the advantages of MDWGO

In order to avoid the randomness of results we useappropriate statistical metrics to compare the effectiveness ofthese algorithms According to [19 20] and the experimentstest thresholds are th = 2 3 4 5 [1ndash3] and the stop criterionof each experiment is 150 iterations the detailed settings ofparameters are showed in Table 2

For verifying the stability we use (23) to calculate thestandard deviation (STD) at the end of each test Once theSTD value increases the algorithms becomes more instablecorrespondingly [29]

STD = radicMax itersum119894=1

(120579119894 minus 120576)2Max iter

(23)

In addition the peak signal to noise ratio (PSNR [20]) isused to compare the similarity between the segmented imageand original image according to the mean square error (MSE[26]) of each pixel

PSNR = 20 log10 ( 255MSE

) (dB) (24)

MSE = radicsumro119894=1sumco119895=1 (119868119886119900 (119894 119895) minus 119868119886th (119894 119895))

ro times co (25)

where 119868119886119900 is the original image 119868119886th is the segmented image and119886 depends on the type of image (grey image or RGB image)ro co are respectively the total number of rows and columnsin an image

Because Kapurrsquos entropy is based on histogram of theimage this paper provides test images and the correspondinghistograms From Figure 2 it can be seen that each imagehas the only distinctive histogram which can guarantee theuniversality and commonality of the algorithm More impor-tantly most of these histograms do not follow the bimodalcharacteristic therefore the difficulty level of optimizationincreases accordingly

52 The Image Segmentation Result Based on MDGWO withDifferent Thresholds In order to reflect the segmentationeffect Figures 3 and 4 illustrate the segmentation results oforiginal images in Figure 2when the threshold is 2 3 4 and 5respectively The experiments indicate that the segmentationresults turn out to be finer and there are alsomore segmentedareas when the number of thresholds is larger and vice versaIn extreme cases when the threshold is 2 the algorithmis reduced to be binary image segmentation (foreground-background segmentation) Certainly that how many areasare segmented is related to the applications and requirementsthis method only needs to set the corresponding number ofthresholds (th) Besides giving the MDGWO segmentationresults like [20] Figures 3 and 4 also mark the position

8 Computational Intelligence and Neuroscience

Table 2 Parameters settings of MDGWO

Parameters Population size Threshold Number of iterations Run time Lower bound Upper boundValue 50 2 3 4 5 150 35 1 256

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

000100020003000400050006000700080009

001

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 3000

0002000400060008

0010012001400160018

002

times10minus3

Histogram of left col ImageImage Histogram of left col

(a) Cameraman (b) Lena

(c) Baboon (d) Butterfly

(e) Maize (f) Starfish

(g) Smiling Girl (h) Surfing

Figure 2 The original images and their histograms

of the threshold in each histogram Compared with otherMT methods it is difficult to find the difference in termsof the segmentation effect Therefore Section 54 lists thethresholds PSNR STD and MEAN for comparisons ofMDGWO results and other techniques

53 The Comparison of MDGWO in Multilevel Image Thresh-olding with Different Objective Functions In Section 1 wesummarize the relevant objective functions The commonlyused optimization functions include maximization of theentropy andmaximization of the between-class variance (egOtsursquos method) In [27] the authors respectively analyze

these objective functions and compare Kapur and Otsusystematically The experiment results show that Kapurrsquosentropy gets the best effectiveness Therefore in order toverify MDGWOrsquos efficiency we compare the thresholds andPSNR between Otsu and Kapur in Table 3

As shown inTable 3 the threshold distribution ofKapur ismore dispersed and wider in most cases However the effectof image thresholding cannot be seen from the thresholddistribution directly Therefore we focus on analysis thePSNR between Otsu and Kapur In terms of PSNR the Kapurmethod produces higher PSNR values on most items inFigure 2 except for the Sea Star Imagewith 119896 = 3 5 and SurferImage with 119896 = 4

Computational Intelligence and Neuroscience 9

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005001

0015002

0025

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

000100020003000400050006000700080009

001

0 50 100 150 200 250 3000

000100020003000400050006000700080009

001

0 50 100 150 200 250 3000

000100020003000400050006000700080009

001

0 50 100 150 200 250 3000

000100020003000400050006000700080009

001

Image

Cam

eram

anLe

naBa

boon

Butte

rfly

th = 2 th = 3 th = 4 th = 5

Figure 3 The segmentation results of (a)ndash(d) in Figure 2 and their thresholds in histograms

10 Computational Intelligence and Neuroscience

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0002000400060008

0010012001400160018

002

0 50 100 150 200 250 3000

0002000400060008

0010012001400160018

002

0 50 100 150 200 250 3000

0002000400060008

0010012001400160018

002

0 50 100 150 200 250 30000002000400060008

0010012001400160018

002

times10minus3

times10minus3

times10minus3

times10minus3

Image th = 2 th = 3 th = 4 th = 5

Mai

zeSt

arfis

hSm

iling

Girl

Surfi

ng

Figure 4 The segmentation results of (e)ndash(h) in Figure 2 and their thresholds in histograms

Computational Intelligence and Neuroscience 11

Table 3 The comparison of MDGWOrsquos efficiency between Otsu and Kapur

Image 119896 Otsu thresholds PSNR Kapur thresholds PSNR

Cameraman

2 70 144 119475 44 106 1446293 58 119 156 129933 44 98 148 1993374 40 93 139 170 160180 39 83 119 156 2116845 35 81 121 149 174 163710 23 58 94 125 159 231191

Lena

2 92 151 131029 93 163 1471643 80 126 171 157626 70 121 172 1751444 75 114 145 180 164291 43 81 127 171 2017295 73 109 136 161 189 167206 41 73 103 141 178 218208

Baboon

2 97 149 124396 78 141 1603023 83 123 160 137731 46 103 151 1863404 70 105 136 167 149493 34 75 117 159 2051985 66 98 125 150 175 160012 29 64 100 134 170 220929

Butterfly

2 100 152 124400 87 150 1493253 81 118 159 142563 62 104 152 1855394 73 101 129 164 146987 49 88 128 168 2107115 69 95 121 149 177 164688 48 80 113 145 180 224539

Maize

2 92 168 136677 84 165 1404073 76 128 187 152676 59 113 171 1658534 65 104 150 200 167309 45 80 125 187 1898185 56 86 123 164 208 185649 39 74 108 147 198 208792

Sea Star

2 85 157 148445 81 160 1485953 69 120 178 176040 60 111 172 1745834 59 99 137 187 194039 46 89 131 184 1944875 51 85 117 150 193 214000 47 83 118 150 196 209681

Smiling Girl

2 60 123 131358 88 145 1800333 47 100 131 128470 44 91 145 1911484 28 74 111 136 156914 24 67 100 145 2007595 20 63 95 124 158 18 2260 44 83 115 152 203 217937

Surfer

2 92 162 125401 52 141 1643433 71 111 177 160569 52 103 168 1893434 47 81 118 179 208786 49 86 131 185 2072185 46 77 105 143 196 216071 24 53 88 126 183 218961

The average value of Kapur is improved averagely by2224 compared to Otsu by checking against the cor-responding PSNR values which are obtained from theMDGWO The maximum value is increased by 5342 forCameraman Image when 119896 = 3 Therefore the Kapurmethod is significantly better than the Otsu method and wealso mainly analyze the effectiveness of Kapurrsquos method inSection 54

54TheComparison ofQuality Assessment by PSNR STD andMEAN This paper adopts PSNR standard to evaluate thesegmentation quality in comparisonwith otherMTmethodsTables 4ndash6 illustrate the PSNR values under different thresh-olds ofMDGWOGWOEMODEABC and theMEANandSTD of objective functions As shown in Table 4 it can be

seen from the PSNR values that MDGWO gets the highestevaluation in most cases Thus it proves that MDGWO getsbetter results on image segmentation In addition when thenumber of thresholds increases it shows superior PSNRvalue In detail the MDGWO algorithm produces higherPSNR values on all items in Table 4 except for the SmilingGirl Image with 119896 = 5 and Surfer Image with 119896 = 4 on theresult of DE

As shown in Table 4 the average value of MDGWO isimproved averagely by 1316 compared toGWOby checkingagainst the corresponding PSNR valuesThemaximum valueis increased by 4505 for Butterfly Image when 119896 = 5

ComparingwithMTEMO the average value ofMDGWOis improved averagely by 1156 by checking against the cor-responding PSNR valuesThemaximumvalue is increased by3994 for Surfer Image when 119896 = 2

12 Computational Intelligence and Neuroscience

Table 4 PSNR metrics of MTEMO DE ABC GWO and MDGWO

Image 119896 MTEMO DE ABC GWO MDGWO

Cameraman

2 13626 12584 13920 14279 144633 18803 17584 14462 19696 199344 20586 20111 2081 20809 211685 20661 21282 2240 22404 23119

Lena

2 14672 8823 14590 14680 147163 17247 14386 17197 17416 175144 18251 16151 18559 19762 201735 20019 16720 20321 21299 21820

Baboon

2 16016 8103 16007 16024 160353 16016 12596 18592 18632 186344 18485 13178 18417 20480 205195 20507 13135 20224 22060 22092

Butterfly

2 11065 8702 14402 14762 149323 14176 13028 14504 17873 185534 16725 13028 16189 21021 210715 19026 14786 19286 21485 22453

Maize

2 13633 10549 13590 13950 140403 15229 13022 15295 16201 165854 16280 14270 16346 18713 189815 17211 15079 17046 20410 20879

Sea Star

2 14398 8610 14395 14809 148853 16987 14078 16981 17431 174584 18304 16191 18427 19421 194485 20165 16474 20330 20887 20968

Smiling Girl

2 13420 14986 13514 17989 180033 18254 11243 18069 18742 191144 18860 14556 18826 19823 200755 19840 22980 19769 21214 21793

Surfer

2 11744 9737 11878 16154 164343 18584 11638 18762 18895 189344 19478 21866 19647 20234 207215 20468 19576 20479 21699 21896

By comparing with DE the average value of MDGWO isimproved averagely by 3814 by checking against the cor-responding PSNR values The maximum value is increasedby 9789 for Baboon Image when 119896 = 2 The PSNR of theSmiling Girl with 119896 = 5 and Surfer Image with 119896 = 4 areslightly lower but the gap is not significant

Comparing between ABC and MDGWO the averagevalue of MDGWO is improved averagely by 1055 by check-ing against the corresponding PSNR values The maximumvalue is increased by 3836 for Surfer Image when 119896 = 2

From the perspective of STDwhich is shown in Table 5 itcan be observed that MDGWO shows obviously advantagesover MTEMO DE ABC and GWOThe smaller the STD isthe smaller the change of fitness functions over the course ofiterations will be that is the better stability of segmentation

Therefore the results show that MDGWO obtains excitingeffect in stability So MDGWOrsquos stability is better

Compared with GWO the average value of MDGWO isimproved averagely by 7352 compared to GWO by check-ing against the corresponding STD values The maximumvalue is increased by 9644 for Baboon Image when 119896 = 3and the minimum value is increased by 2492 for BaboonImage when 119896 = 3

By comparing with MTEMO the average value ofMDGWO is improved averagely by 4788 The maximumvalue is increased by 87 for Lena Image when 119896 = 2 and theminimum value is increased by 06 for Surfer Image when119896 = 3

Comparing between DE andMDGWO the average valueofMDGWO is improved averagely by 9560Themaximum

Computational Intelligence and Neuroscience 13

Table 5 STD metrics of MTEMO DE ABC GWO and MDGWO

Image 119896 MTEMO DE ABC GWO MDGWO

Camerman

2 01849 12592 01235 01697 004623 01649 17601 02122 02287 007584 02943 21995 03003 03627 006595 02999 26579 02784 04278 01964

Lena

2 00969 12902 00349 01536 001263 01665 17822 01300 03570 002644 02800 22104 01872 05965 009395 02515 25992 01827 05946 01570

Baboon

2 00108 12862 00358 02171 001023 00393 17678 00202 04376 001564 01727 22126 01610 02986 011845 02868 26239 02660 05377 02316

Butterfly

2 00903 12708 00750 02179 004653 02207 17429 02952 02712 020364 02482 22368 03906 04808 024155 02900 26571 04818 05096 02684

Maize

2 00356 13501 00218 03571 001883 01222 18612 00901 02225 002704 02305 23230 02605 03903 009275 02502 27461 03834 04584 01677

Sea Star

2 01073 13547 01088 01728 002903 01497 18741 01752 02028 003744 01596 23307 01817 05032 011195 02639 27550 02180 04550 01437

Smiling Girl

2 00377 12516 00318 01834 001113 00955 17311 00577 01712 002424 01966 21878 01094 02508 007815 01550 25989 02768 05273 01302

Surfer

2 00579 13213 00303 02681 002453 01002 18337 01646 03014 009964 03382 23317 01686 03162 014245 03690 27846 02580 03815 01706

value is increased by 9921 for Baboon Image when 119896 =2 The minimum value is increased by 8832 for ButterflyImage when 119896 = 3

Comparing with ABC the average value of MDGWOis improved averagely by 4590 The maximum value isincreased by 7970 for Lena Image when 119896 = 3 and theminimum value is increased by 1293 for Baboon Imagewhen 119896 = 5

As far as MEAN is concerned this parameter presentsthe average value of fitness function over the course ofiterations in Table 6 which reflects the algorithm stability tosome extent But its accuracy of evaluation is relatively lowwhich can only reflect the fuzzy stability of the algorithmThe experiment data is offered here just in response to theparameter provided in literature [20] In comparison withGWO MTEWO DE and ABC in Table 6 it can be safely

assumed that inmost casesMDGWOobtains higherMEANof fitness function Moreover the difference is extremelysmall when MDGWOrsquos MEAN is lower

From the analyses of Tables 3ndash6 together with the visualeffects of Figures 2 3 and 4 it can be observed thatMDGWO method obtains better segmentation effect andhas advantage in optimal process accuracy stability androbustnessThereforeMDGWO is aMT algorithmwith highaccuracy and high segmentation quality

6 Conclusion

This paper proposes a modified discrete grey wolf optimizerwhich is used to optimize the image histograms and realizethe multilevel image segmentation Based on the high effi-ciency of GWO in the course of optimization and stability

14 Computational Intelligence and Neuroscience

Table 6 MEANmetrics of MTEMO DE ABC GWO and MDGWO

Image 119896 MTEMO DE ABC GWO MDGWO

Camerman

2 17584 124212 177638 14634 174713 21976 173764 223059 21107 219194 26586 217520 268409 24927 274805 30506 262505 308328 30436 30548

Lena

2 17831 127730 178139 17809 183963 22120 176428 220832 22074 228564 25999 218784 260615 25318 264475 29787 257311 299664 29252 30381

Baboon

2 17625 127333 176760 17679 186193 22269 175005 221276 22129 229494 26688 219010 263912 26194 269005 30800 259681 303464 30067 30076

Butterfly

2 16681 125796 174205 17425 177233 21242 172545 222209 21585 224984 25179 220176 263794 25267 261905 28611 261795 306533 29492 29899

Maize

2 18631 133566 186316 18604 195423 23565 184245 232496 22941 239394 27529 229813 273931 26936 278425 31535 271709 312127 31023 30694

Sea Star

2 18754 134104 187295 18321 195873 23323 185516 232738 23245 239014 27582 230719 275057 27136 282105 31562 272551 314919 31167 31958

Smiling Girl

2 17334 123892 173129 17136 180353 21904 171339 218601 21253 219804 26040 216541 259904 25050 265975 30089 257130 300225 29870 30574

Surfer

2 18339 130786 183393 18283 188693 23231 181492 232889 23243 241354 27863 230548 278017 27275 274475 31823 274979 317335 31384 31325

this paper successfully applies the MDGWO to the field ofMT by improving the location selection mechanism of 120572 120573and 120575 during the hunting and using weight to optimize thefinal position of prey (best threshold)TheMDGWOmethodnot only obtains better segmentation quality but also showsobvious superiority over GWO MTEMO DE and ABC instability accuracy and multilevel thresholding

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work was supported in part by the National NaturalScience Foundation of China (no 61300239 no 71301081and no 61572261) the Postdoctoral Science Foundation (no

2014M551635 and no 1302085B) the Innovation Project ofGraduate Students Foundation of Jiangsu Province (KYLX150841) the Higher Education Revitalization Plan Foundationof Anhui Province (no 2013SQRL102ZD no 2015xdjy196no 2015jyxm728 no 2016jyxm0774 and no 2016jyxm0777)and Natural Science Fund for Colleges and Universities inJiangsu Province (no16KJB520034) A Project Funded by thePriority Academic Program Development of Jiangsu HigherEducation Institutions (PAPD) and Jiangsu CollaborativeInnovation Center on Atmospheric Environment and Equip-ment Technology (CICAEET)

References

[1] M Sonka V Hlavac and R Boyle Image Processing Analysisand Machine Vision Cengage Learning 2014

[2] S Masood M Sharif A Masood M Yasmin and M RazaldquoA survey on medical image segmentationrdquo Current MedicalImaging Reviews vol 11 no 1 pp 3ndash14 2015

Computational Intelligence and Neuroscience 15

[3] PGhamisiM S Couceiro FM LMartins and J A Benedikts-son ldquoMultilevel image segmentation based on fractional-orderdarwinian particle swarm optimizationrdquo IEEE Transactions onGeoscience and Remote Sensing vol 52 no 5 pp 2382ndash23942014

[4] M Waseem Khan ldquoA survey image segmentation techniquesrdquoInternational Journal of Future Computer and Communicationvol 3 no 2 pp 89ndash93 2014

[5] J Li X Li B Yang and X Sun ldquoSegmentation-based imagecopy-move forgery detection schemerdquo IEEE Transactions onInformation Forensics and Security vol 10 no 3 pp 507ndash5182015

[6] Z Pan J Lei Y Zhang X Sun and S Kwong ldquoFast motionestimation based on content property for low-complexityH265HEVC encoderrdquo IEEE Transactions on Broadcasting vol62 no 3 pp 675ndash684 2016

[7] X Chen S Feng and D Pan ldquoAn improved approach oflung image segmentation based on watershed algorithmrdquo inProceedings of the the 7th International Conference on InternetMultimedia Computing and Service pp 1ndash5 Zhangjiajie ChinaAugust 2015

[8] Y Zheng B Jeon D Xu Q M J Wu and H Zhang ldquoImagesegmentation by generalized hierarchical fuzzy C-means algo-rithmrdquo Journal of Intelligent and Fuzzy Systems vol 28 no 2pp 961ndash973 2015

[9] V Osuna-Enciso E Cuevas and H Sossa ldquoA comparison ofnature inspired algorithms for multi-threshold image segmen-tationrdquo Expert Systems with Applications vol 40 no 4 pp 1213ndash1219 2013

[10] T Kurban P Civicioglu R Kurban and E Besdok ldquoCompari-son of evolutionary and swarmbased computational techniquesfor multilevel color image thresholdingrdquo Applied Soft Comput-ing Journal vol 23 pp 128ndash143 2014

[11] J N Kapur P K Sahoo and A K C Wong ldquoA new methodfor gray-level picture thresholding using the entropy of thehistogramrdquo Computer Vision Graphics and Image Processingvol 29 no 3 pp 273ndash285 1985

[12] N Otsu ldquoA threshold selection method from gray-level his-togramsrdquo Automatica vol 11 no 285ndash296 pp 23ndash27 1975

[13] X Li Z Zhao and H D Cheng ldquoFuzzy entropy thresholdapproach to breast cancer detectionrdquo Information Sciences -Applications vol 4 no 1 pp 49ndash56 1995

[14] J Kittler and J Illingworth ldquoMinimum error thresholdingrdquoPattern Recognition vol 19 no 1 pp 41ndash47 1986

[15] Y Xue S Zhong T Ma and J Cao ldquoA hybrid evolution-ary algorithm for numerical optimization problemrdquo IntelligentAutomation amp Soft Computing vol 21 no 4 pp 473ndash490 2015

[16] P-Y Yin ldquoA fast scheme for optimal thresholding using geneticalgorithmsrdquo Signal Processing vol 72 no 2 pp 85ndash95 1999

[17] W Fujun L Junlan L Shiwei Z Xingyu Z Dawei and TYanling ldquoAn improved adaptive genetic algorithm for imagesegmentation and vision alignment used in microelectronicbondingrdquo IEEEASMETransactions onMechatronics vol 19 no3 pp 916ndash923 2014

[18] S Banerjee and N D Jana ldquoBi level kapurs entropy basedimage segmentation using particle swarm optimizationrdquo inProceedings of the 3rd International Conference on ComputerCommunication Control and InformationTechnology (C3IT rsquo15)pp 1ndash4 Hooghly India February 2015

[19] M-H Horng ldquoMultilevel thresholding selection based on theartificial bee colony algorithm for image segmentationrdquo ExpertSystems with Applications vol 38 no 11 pp 13785ndash13791 2011

[20] D Oliva E Cuevas G Pajares D Zaldivar and V OsunaldquoA multilevel thresholding algorithm using electromagnetismoptimizationrdquo Neurocomputing vol 139 pp 357ndash381 2014

[21] S Sarkar G R Patra and S Das ldquoA differential evolutionbased approach for multilevel image segmentation using mini-mum cross entropy thresholdingrdquo in Swarm Evolutionary andMemetic Computing pp 51ndash58 Springer Berlin Germany 2011

[22] Y Xue Y Zhuang T Ni S Ni and X Wen ldquoSelf-adaptivelearning based discrete differential evolution algorithm forsolving CJWTA problemrdquo Journal of Systems Engineering andElectronics vol 25 no 1 pp 59ndash68 2014

[23] S Agrawal R Panda S Bhuyan and B K Panigrahi ldquoTsallisentropy based optimal multilevel thresholding using cuckoosearch algorithmrdquo Swarm and Evolutionary Computation vol11 pp 16ndash30 2013

[24] PD Sathya andRKayalvizhi ldquoOptimalmultilevel thresholdingusing bacterial foraging algorithmrdquo Expert Systems with Appli-cations vol 38 no 12 pp 15549ndash15564 2011

[25] S Ayas H Dogan E Gedikli and M Ekinci ldquoMicroscopicimage segmentation based on firefly algorithm for detectionof tuberculosis bacteriardquo in Proceedings of the 23rd SignalProcessing and Communications Applications Conference (SIUrsquo15) pp 851ndash854 Malatya Turkey May 2015

[26] S Mirjalili S M Mirjalili and A Lewis ldquoGrey wolf optimizerrdquoAdvances in Engineering Software vol 69 pp 46ndash61 2014

[27] B Akay ldquoA study on particle swarm optimization and artificialbee colony algorithms for multilevel thresholdingrdquo Applied SoftComputing vol 13 no 6 pp 3066ndash3091 2013

[28] A K Bhandari A Kumar and G K Singh ldquoModified artificialbee colony based computationally efficient multilevel thresh-olding for satellite image segmentation using Kapurrsquos Otsu andTsallis functionsrdquo Expert Systems with Applications vol 42 no3 pp 1573ndash1601 2015

[29] P Ghamisi M S Couceiro J A Benediktsson and N M FFerreira ldquoAn efficientmethod for segmentation of images basedon fractional calculus and natural selectionrdquo Expert Systemswith Applications vol 39 no 16 pp 12407ndash12417 2012

[30] L Li L Sun W Kang J Guo C Han and S Li ldquoFuzzymultilevel image thresholding based on modified discrete greywolf optimizer and local information aggregationrdquo IEEE Accessvol 4 pp 6438ndash6450 2016

[31] H-S Wu F-M Zhang and L-S Wu ldquoNew swarm intelligencealgorithm-wolf pack algorithmrdquo Xi Tong Gong Cheng Yu DianZi Ji ShuSystems Engineering and Electronics vol 35 no 11 pp2430ndash2438 2013

[32] H Wu and F Zhang ldquoA uncultivated wolf pack algorithm forhigh-dimensional functions and its application in parametersoptimization of PID controllerrdquo in Proceedings of the IEEECongress on Evolutionary Computation (CEC rsquo14) pp 1477ndash1482Beijing China July 2014

[33] H-S Wu and F-M Zhang ldquoWolf pack algorithm for uncon-strained global optimizationrdquo Mathematical Problems in Engi-neering vol 2014 Article ID 465082 17 pages 2014

[34] Q Zhou and Y Zhou ldquoWolf colony search algorithm based onleader strategyrdquo Application Research of Computers vol 9 pp2629ndash2632 2013

[35] G M Komaki and V Kayvanfar ldquoGrey Wolf Optimizer algo-rithm for the two-stage assembly flow shop scheduling problemwith release timerdquo Journal of Computational Science vol 8 pp109ndash120 2015

16 Computational Intelligence and Neuroscience

[36] L I Wong M H Sulaiman M R Mohamed and M SHong ldquoGrey Wolf Optimizer for solving economic dispatchproblemsrdquo in Proceedings of the IEEE International Conferenceon Power and Energy (PECon rsquo14) pp 150ndash154 KuchingMalaysia December 2014

[37] A Chaman-Motlagh ldquoSuperdefect photonic crystal filter opti-mization using Grey Wolf Optimizerrdquo IEEE Photonics Technol-ogy Letters vol 27 no 22 pp 2355ndash2358 2015

[38] P Q Dzung N T Tien N Dinh Tuyen and H Lee ldquoSelectiveharmonic elimination for cascaded multilevel inverters usinggrey wolf optimizer algorithmrdquo in Proceedings of the 9thInternational Conference on Power Electronics and ECCE Asia(ICPE rsquo15-ECCE Asia) June 2015

[39] N Muangkote K Sunat and S Chiewchanwattana ldquoAnimproved grey wolf optimizer for training q-Gaussian RadialBasis Functional-link netsrdquo in Proceedings of the InternationalComputer Science and Engineering Conference (ICSEC rsquo14) pp209ndash214 Khon Kaen Thailand August 2014

[40] A Zhu C Xu Z Li J Wu and Z Liu ldquoHybridizing grey Wolfoptimization with differential evolution for global optimizationand test scheduling for 3D stacked SoCrdquo Journal of SystemsEngineering and Electronics vol 26 no 2 pp 317ndash328 2015

[41] P ArbelaezMMaire C Fowlkes and JMalik ldquoContour detec-tion and hierarchical image segmentationrdquo IEEE Transactionson Pattern Analysis and Machine Intelligence vol 33 no 5 pp898ndash916 2011

Submit your manuscripts athttpswwwhindawicom

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ReconfigurableComputing

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Applied Computational Intelligence and Soft Computing

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Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Electrical and Computer Engineering

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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httpwwwhindawicom Volume 2014

Advances in

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International Journal of

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ArtificialNeural Systems

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RoboticsJournal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

8 Computational Intelligence and Neuroscience

Table 2 Parameters settings of MDGWO

Parameters Population size Threshold Number of iterations Run time Lower bound Upper boundValue 50 2 3 4 5 150 35 1 256

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

000100020003000400050006000700080009

001

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 3000

0002000400060008

0010012001400160018

002

times10minus3

Histogram of left col ImageImage Histogram of left col

(a) Cameraman (b) Lena

(c) Baboon (d) Butterfly

(e) Maize (f) Starfish

(g) Smiling Girl (h) Surfing

Figure 2 The original images and their histograms

of the threshold in each histogram Compared with otherMT methods it is difficult to find the difference in termsof the segmentation effect Therefore Section 54 lists thethresholds PSNR STD and MEAN for comparisons ofMDGWO results and other techniques

53 The Comparison of MDGWO in Multilevel Image Thresh-olding with Different Objective Functions In Section 1 wesummarize the relevant objective functions The commonlyused optimization functions include maximization of theentropy andmaximization of the between-class variance (egOtsursquos method) In [27] the authors respectively analyze

these objective functions and compare Kapur and Otsusystematically The experiment results show that Kapurrsquosentropy gets the best effectiveness Therefore in order toverify MDGWOrsquos efficiency we compare the thresholds andPSNR between Otsu and Kapur in Table 3

As shown inTable 3 the threshold distribution ofKapur ismore dispersed and wider in most cases However the effectof image thresholding cannot be seen from the thresholddistribution directly Therefore we focus on analysis thePSNR between Otsu and Kapur In terms of PSNR the Kapurmethod produces higher PSNR values on most items inFigure 2 except for the Sea Star Imagewith 119896 = 3 5 and SurferImage with 119896 = 4

Computational Intelligence and Neuroscience 9

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005001

0015002

0025

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

000100020003000400050006000700080009

001

0 50 100 150 200 250 3000

000100020003000400050006000700080009

001

0 50 100 150 200 250 3000

000100020003000400050006000700080009

001

0 50 100 150 200 250 3000

000100020003000400050006000700080009

001

Image

Cam

eram

anLe

naBa

boon

Butte

rfly

th = 2 th = 3 th = 4 th = 5

Figure 3 The segmentation results of (a)ndash(d) in Figure 2 and their thresholds in histograms

10 Computational Intelligence and Neuroscience

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0002000400060008

0010012001400160018

002

0 50 100 150 200 250 3000

0002000400060008

0010012001400160018

002

0 50 100 150 200 250 3000

0002000400060008

0010012001400160018

002

0 50 100 150 200 250 30000002000400060008

0010012001400160018

002

times10minus3

times10minus3

times10minus3

times10minus3

Image th = 2 th = 3 th = 4 th = 5

Mai

zeSt

arfis

hSm

iling

Girl

Surfi

ng

Figure 4 The segmentation results of (e)ndash(h) in Figure 2 and their thresholds in histograms

Computational Intelligence and Neuroscience 11

Table 3 The comparison of MDGWOrsquos efficiency between Otsu and Kapur

Image 119896 Otsu thresholds PSNR Kapur thresholds PSNR

Cameraman

2 70 144 119475 44 106 1446293 58 119 156 129933 44 98 148 1993374 40 93 139 170 160180 39 83 119 156 2116845 35 81 121 149 174 163710 23 58 94 125 159 231191

Lena

2 92 151 131029 93 163 1471643 80 126 171 157626 70 121 172 1751444 75 114 145 180 164291 43 81 127 171 2017295 73 109 136 161 189 167206 41 73 103 141 178 218208

Baboon

2 97 149 124396 78 141 1603023 83 123 160 137731 46 103 151 1863404 70 105 136 167 149493 34 75 117 159 2051985 66 98 125 150 175 160012 29 64 100 134 170 220929

Butterfly

2 100 152 124400 87 150 1493253 81 118 159 142563 62 104 152 1855394 73 101 129 164 146987 49 88 128 168 2107115 69 95 121 149 177 164688 48 80 113 145 180 224539

Maize

2 92 168 136677 84 165 1404073 76 128 187 152676 59 113 171 1658534 65 104 150 200 167309 45 80 125 187 1898185 56 86 123 164 208 185649 39 74 108 147 198 208792

Sea Star

2 85 157 148445 81 160 1485953 69 120 178 176040 60 111 172 1745834 59 99 137 187 194039 46 89 131 184 1944875 51 85 117 150 193 214000 47 83 118 150 196 209681

Smiling Girl

2 60 123 131358 88 145 1800333 47 100 131 128470 44 91 145 1911484 28 74 111 136 156914 24 67 100 145 2007595 20 63 95 124 158 18 2260 44 83 115 152 203 217937

Surfer

2 92 162 125401 52 141 1643433 71 111 177 160569 52 103 168 1893434 47 81 118 179 208786 49 86 131 185 2072185 46 77 105 143 196 216071 24 53 88 126 183 218961

The average value of Kapur is improved averagely by2224 compared to Otsu by checking against the cor-responding PSNR values which are obtained from theMDGWO The maximum value is increased by 5342 forCameraman Image when 119896 = 3 Therefore the Kapurmethod is significantly better than the Otsu method and wealso mainly analyze the effectiveness of Kapurrsquos method inSection 54

54TheComparison ofQuality Assessment by PSNR STD andMEAN This paper adopts PSNR standard to evaluate thesegmentation quality in comparisonwith otherMTmethodsTables 4ndash6 illustrate the PSNR values under different thresh-olds ofMDGWOGWOEMODEABC and theMEANandSTD of objective functions As shown in Table 4 it can be

seen from the PSNR values that MDGWO gets the highestevaluation in most cases Thus it proves that MDGWO getsbetter results on image segmentation In addition when thenumber of thresholds increases it shows superior PSNRvalue In detail the MDGWO algorithm produces higherPSNR values on all items in Table 4 except for the SmilingGirl Image with 119896 = 5 and Surfer Image with 119896 = 4 on theresult of DE

As shown in Table 4 the average value of MDGWO isimproved averagely by 1316 compared toGWOby checkingagainst the corresponding PSNR valuesThemaximum valueis increased by 4505 for Butterfly Image when 119896 = 5

ComparingwithMTEMO the average value ofMDGWOis improved averagely by 1156 by checking against the cor-responding PSNR valuesThemaximumvalue is increased by3994 for Surfer Image when 119896 = 2

12 Computational Intelligence and Neuroscience

Table 4 PSNR metrics of MTEMO DE ABC GWO and MDGWO

Image 119896 MTEMO DE ABC GWO MDGWO

Cameraman

2 13626 12584 13920 14279 144633 18803 17584 14462 19696 199344 20586 20111 2081 20809 211685 20661 21282 2240 22404 23119

Lena

2 14672 8823 14590 14680 147163 17247 14386 17197 17416 175144 18251 16151 18559 19762 201735 20019 16720 20321 21299 21820

Baboon

2 16016 8103 16007 16024 160353 16016 12596 18592 18632 186344 18485 13178 18417 20480 205195 20507 13135 20224 22060 22092

Butterfly

2 11065 8702 14402 14762 149323 14176 13028 14504 17873 185534 16725 13028 16189 21021 210715 19026 14786 19286 21485 22453

Maize

2 13633 10549 13590 13950 140403 15229 13022 15295 16201 165854 16280 14270 16346 18713 189815 17211 15079 17046 20410 20879

Sea Star

2 14398 8610 14395 14809 148853 16987 14078 16981 17431 174584 18304 16191 18427 19421 194485 20165 16474 20330 20887 20968

Smiling Girl

2 13420 14986 13514 17989 180033 18254 11243 18069 18742 191144 18860 14556 18826 19823 200755 19840 22980 19769 21214 21793

Surfer

2 11744 9737 11878 16154 164343 18584 11638 18762 18895 189344 19478 21866 19647 20234 207215 20468 19576 20479 21699 21896

By comparing with DE the average value of MDGWO isimproved averagely by 3814 by checking against the cor-responding PSNR values The maximum value is increasedby 9789 for Baboon Image when 119896 = 2 The PSNR of theSmiling Girl with 119896 = 5 and Surfer Image with 119896 = 4 areslightly lower but the gap is not significant

Comparing between ABC and MDGWO the averagevalue of MDGWO is improved averagely by 1055 by check-ing against the corresponding PSNR values The maximumvalue is increased by 3836 for Surfer Image when 119896 = 2

From the perspective of STDwhich is shown in Table 5 itcan be observed that MDGWO shows obviously advantagesover MTEMO DE ABC and GWOThe smaller the STD isthe smaller the change of fitness functions over the course ofiterations will be that is the better stability of segmentation

Therefore the results show that MDGWO obtains excitingeffect in stability So MDGWOrsquos stability is better

Compared with GWO the average value of MDGWO isimproved averagely by 7352 compared to GWO by check-ing against the corresponding STD values The maximumvalue is increased by 9644 for Baboon Image when 119896 = 3and the minimum value is increased by 2492 for BaboonImage when 119896 = 3

By comparing with MTEMO the average value ofMDGWO is improved averagely by 4788 The maximumvalue is increased by 87 for Lena Image when 119896 = 2 and theminimum value is increased by 06 for Surfer Image when119896 = 3

Comparing between DE andMDGWO the average valueofMDGWO is improved averagely by 9560Themaximum

Computational Intelligence and Neuroscience 13

Table 5 STD metrics of MTEMO DE ABC GWO and MDGWO

Image 119896 MTEMO DE ABC GWO MDGWO

Camerman

2 01849 12592 01235 01697 004623 01649 17601 02122 02287 007584 02943 21995 03003 03627 006595 02999 26579 02784 04278 01964

Lena

2 00969 12902 00349 01536 001263 01665 17822 01300 03570 002644 02800 22104 01872 05965 009395 02515 25992 01827 05946 01570

Baboon

2 00108 12862 00358 02171 001023 00393 17678 00202 04376 001564 01727 22126 01610 02986 011845 02868 26239 02660 05377 02316

Butterfly

2 00903 12708 00750 02179 004653 02207 17429 02952 02712 020364 02482 22368 03906 04808 024155 02900 26571 04818 05096 02684

Maize

2 00356 13501 00218 03571 001883 01222 18612 00901 02225 002704 02305 23230 02605 03903 009275 02502 27461 03834 04584 01677

Sea Star

2 01073 13547 01088 01728 002903 01497 18741 01752 02028 003744 01596 23307 01817 05032 011195 02639 27550 02180 04550 01437

Smiling Girl

2 00377 12516 00318 01834 001113 00955 17311 00577 01712 002424 01966 21878 01094 02508 007815 01550 25989 02768 05273 01302

Surfer

2 00579 13213 00303 02681 002453 01002 18337 01646 03014 009964 03382 23317 01686 03162 014245 03690 27846 02580 03815 01706

value is increased by 9921 for Baboon Image when 119896 =2 The minimum value is increased by 8832 for ButterflyImage when 119896 = 3

Comparing with ABC the average value of MDGWOis improved averagely by 4590 The maximum value isincreased by 7970 for Lena Image when 119896 = 3 and theminimum value is increased by 1293 for Baboon Imagewhen 119896 = 5

As far as MEAN is concerned this parameter presentsthe average value of fitness function over the course ofiterations in Table 6 which reflects the algorithm stability tosome extent But its accuracy of evaluation is relatively lowwhich can only reflect the fuzzy stability of the algorithmThe experiment data is offered here just in response to theparameter provided in literature [20] In comparison withGWO MTEWO DE and ABC in Table 6 it can be safely

assumed that inmost casesMDGWOobtains higherMEANof fitness function Moreover the difference is extremelysmall when MDGWOrsquos MEAN is lower

From the analyses of Tables 3ndash6 together with the visualeffects of Figures 2 3 and 4 it can be observed thatMDGWO method obtains better segmentation effect andhas advantage in optimal process accuracy stability androbustnessThereforeMDGWO is aMT algorithmwith highaccuracy and high segmentation quality

6 Conclusion

This paper proposes a modified discrete grey wolf optimizerwhich is used to optimize the image histograms and realizethe multilevel image segmentation Based on the high effi-ciency of GWO in the course of optimization and stability

14 Computational Intelligence and Neuroscience

Table 6 MEANmetrics of MTEMO DE ABC GWO and MDGWO

Image 119896 MTEMO DE ABC GWO MDGWO

Camerman

2 17584 124212 177638 14634 174713 21976 173764 223059 21107 219194 26586 217520 268409 24927 274805 30506 262505 308328 30436 30548

Lena

2 17831 127730 178139 17809 183963 22120 176428 220832 22074 228564 25999 218784 260615 25318 264475 29787 257311 299664 29252 30381

Baboon

2 17625 127333 176760 17679 186193 22269 175005 221276 22129 229494 26688 219010 263912 26194 269005 30800 259681 303464 30067 30076

Butterfly

2 16681 125796 174205 17425 177233 21242 172545 222209 21585 224984 25179 220176 263794 25267 261905 28611 261795 306533 29492 29899

Maize

2 18631 133566 186316 18604 195423 23565 184245 232496 22941 239394 27529 229813 273931 26936 278425 31535 271709 312127 31023 30694

Sea Star

2 18754 134104 187295 18321 195873 23323 185516 232738 23245 239014 27582 230719 275057 27136 282105 31562 272551 314919 31167 31958

Smiling Girl

2 17334 123892 173129 17136 180353 21904 171339 218601 21253 219804 26040 216541 259904 25050 265975 30089 257130 300225 29870 30574

Surfer

2 18339 130786 183393 18283 188693 23231 181492 232889 23243 241354 27863 230548 278017 27275 274475 31823 274979 317335 31384 31325

this paper successfully applies the MDGWO to the field ofMT by improving the location selection mechanism of 120572 120573and 120575 during the hunting and using weight to optimize thefinal position of prey (best threshold)TheMDGWOmethodnot only obtains better segmentation quality but also showsobvious superiority over GWO MTEMO DE and ABC instability accuracy and multilevel thresholding

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work was supported in part by the National NaturalScience Foundation of China (no 61300239 no 71301081and no 61572261) the Postdoctoral Science Foundation (no

2014M551635 and no 1302085B) the Innovation Project ofGraduate Students Foundation of Jiangsu Province (KYLX150841) the Higher Education Revitalization Plan Foundationof Anhui Province (no 2013SQRL102ZD no 2015xdjy196no 2015jyxm728 no 2016jyxm0774 and no 2016jyxm0777)and Natural Science Fund for Colleges and Universities inJiangsu Province (no16KJB520034) A Project Funded by thePriority Academic Program Development of Jiangsu HigherEducation Institutions (PAPD) and Jiangsu CollaborativeInnovation Center on Atmospheric Environment and Equip-ment Technology (CICAEET)

References

[1] M Sonka V Hlavac and R Boyle Image Processing Analysisand Machine Vision Cengage Learning 2014

[2] S Masood M Sharif A Masood M Yasmin and M RazaldquoA survey on medical image segmentationrdquo Current MedicalImaging Reviews vol 11 no 1 pp 3ndash14 2015

Computational Intelligence and Neuroscience 15

[3] PGhamisiM S Couceiro FM LMartins and J A Benedikts-son ldquoMultilevel image segmentation based on fractional-orderdarwinian particle swarm optimizationrdquo IEEE Transactions onGeoscience and Remote Sensing vol 52 no 5 pp 2382ndash23942014

[4] M Waseem Khan ldquoA survey image segmentation techniquesrdquoInternational Journal of Future Computer and Communicationvol 3 no 2 pp 89ndash93 2014

[5] J Li X Li B Yang and X Sun ldquoSegmentation-based imagecopy-move forgery detection schemerdquo IEEE Transactions onInformation Forensics and Security vol 10 no 3 pp 507ndash5182015

[6] Z Pan J Lei Y Zhang X Sun and S Kwong ldquoFast motionestimation based on content property for low-complexityH265HEVC encoderrdquo IEEE Transactions on Broadcasting vol62 no 3 pp 675ndash684 2016

[7] X Chen S Feng and D Pan ldquoAn improved approach oflung image segmentation based on watershed algorithmrdquo inProceedings of the the 7th International Conference on InternetMultimedia Computing and Service pp 1ndash5 Zhangjiajie ChinaAugust 2015

[8] Y Zheng B Jeon D Xu Q M J Wu and H Zhang ldquoImagesegmentation by generalized hierarchical fuzzy C-means algo-rithmrdquo Journal of Intelligent and Fuzzy Systems vol 28 no 2pp 961ndash973 2015

[9] V Osuna-Enciso E Cuevas and H Sossa ldquoA comparison ofnature inspired algorithms for multi-threshold image segmen-tationrdquo Expert Systems with Applications vol 40 no 4 pp 1213ndash1219 2013

[10] T Kurban P Civicioglu R Kurban and E Besdok ldquoCompari-son of evolutionary and swarmbased computational techniquesfor multilevel color image thresholdingrdquo Applied Soft Comput-ing Journal vol 23 pp 128ndash143 2014

[11] J N Kapur P K Sahoo and A K C Wong ldquoA new methodfor gray-level picture thresholding using the entropy of thehistogramrdquo Computer Vision Graphics and Image Processingvol 29 no 3 pp 273ndash285 1985

[12] N Otsu ldquoA threshold selection method from gray-level his-togramsrdquo Automatica vol 11 no 285ndash296 pp 23ndash27 1975

[13] X Li Z Zhao and H D Cheng ldquoFuzzy entropy thresholdapproach to breast cancer detectionrdquo Information Sciences -Applications vol 4 no 1 pp 49ndash56 1995

[14] J Kittler and J Illingworth ldquoMinimum error thresholdingrdquoPattern Recognition vol 19 no 1 pp 41ndash47 1986

[15] Y Xue S Zhong T Ma and J Cao ldquoA hybrid evolution-ary algorithm for numerical optimization problemrdquo IntelligentAutomation amp Soft Computing vol 21 no 4 pp 473ndash490 2015

[16] P-Y Yin ldquoA fast scheme for optimal thresholding using geneticalgorithmsrdquo Signal Processing vol 72 no 2 pp 85ndash95 1999

[17] W Fujun L Junlan L Shiwei Z Xingyu Z Dawei and TYanling ldquoAn improved adaptive genetic algorithm for imagesegmentation and vision alignment used in microelectronicbondingrdquo IEEEASMETransactions onMechatronics vol 19 no3 pp 916ndash923 2014

[18] S Banerjee and N D Jana ldquoBi level kapurs entropy basedimage segmentation using particle swarm optimizationrdquo inProceedings of the 3rd International Conference on ComputerCommunication Control and InformationTechnology (C3IT rsquo15)pp 1ndash4 Hooghly India February 2015

[19] M-H Horng ldquoMultilevel thresholding selection based on theartificial bee colony algorithm for image segmentationrdquo ExpertSystems with Applications vol 38 no 11 pp 13785ndash13791 2011

[20] D Oliva E Cuevas G Pajares D Zaldivar and V OsunaldquoA multilevel thresholding algorithm using electromagnetismoptimizationrdquo Neurocomputing vol 139 pp 357ndash381 2014

[21] S Sarkar G R Patra and S Das ldquoA differential evolutionbased approach for multilevel image segmentation using mini-mum cross entropy thresholdingrdquo in Swarm Evolutionary andMemetic Computing pp 51ndash58 Springer Berlin Germany 2011

[22] Y Xue Y Zhuang T Ni S Ni and X Wen ldquoSelf-adaptivelearning based discrete differential evolution algorithm forsolving CJWTA problemrdquo Journal of Systems Engineering andElectronics vol 25 no 1 pp 59ndash68 2014

[23] S Agrawal R Panda S Bhuyan and B K Panigrahi ldquoTsallisentropy based optimal multilevel thresholding using cuckoosearch algorithmrdquo Swarm and Evolutionary Computation vol11 pp 16ndash30 2013

[24] PD Sathya andRKayalvizhi ldquoOptimalmultilevel thresholdingusing bacterial foraging algorithmrdquo Expert Systems with Appli-cations vol 38 no 12 pp 15549ndash15564 2011

[25] S Ayas H Dogan E Gedikli and M Ekinci ldquoMicroscopicimage segmentation based on firefly algorithm for detectionof tuberculosis bacteriardquo in Proceedings of the 23rd SignalProcessing and Communications Applications Conference (SIUrsquo15) pp 851ndash854 Malatya Turkey May 2015

[26] S Mirjalili S M Mirjalili and A Lewis ldquoGrey wolf optimizerrdquoAdvances in Engineering Software vol 69 pp 46ndash61 2014

[27] B Akay ldquoA study on particle swarm optimization and artificialbee colony algorithms for multilevel thresholdingrdquo Applied SoftComputing vol 13 no 6 pp 3066ndash3091 2013

[28] A K Bhandari A Kumar and G K Singh ldquoModified artificialbee colony based computationally efficient multilevel thresh-olding for satellite image segmentation using Kapurrsquos Otsu andTsallis functionsrdquo Expert Systems with Applications vol 42 no3 pp 1573ndash1601 2015

[29] P Ghamisi M S Couceiro J A Benediktsson and N M FFerreira ldquoAn efficientmethod for segmentation of images basedon fractional calculus and natural selectionrdquo Expert Systemswith Applications vol 39 no 16 pp 12407ndash12417 2012

[30] L Li L Sun W Kang J Guo C Han and S Li ldquoFuzzymultilevel image thresholding based on modified discrete greywolf optimizer and local information aggregationrdquo IEEE Accessvol 4 pp 6438ndash6450 2016

[31] H-S Wu F-M Zhang and L-S Wu ldquoNew swarm intelligencealgorithm-wolf pack algorithmrdquo Xi Tong Gong Cheng Yu DianZi Ji ShuSystems Engineering and Electronics vol 35 no 11 pp2430ndash2438 2013

[32] H Wu and F Zhang ldquoA uncultivated wolf pack algorithm forhigh-dimensional functions and its application in parametersoptimization of PID controllerrdquo in Proceedings of the IEEECongress on Evolutionary Computation (CEC rsquo14) pp 1477ndash1482Beijing China July 2014

[33] H-S Wu and F-M Zhang ldquoWolf pack algorithm for uncon-strained global optimizationrdquo Mathematical Problems in Engi-neering vol 2014 Article ID 465082 17 pages 2014

[34] Q Zhou and Y Zhou ldquoWolf colony search algorithm based onleader strategyrdquo Application Research of Computers vol 9 pp2629ndash2632 2013

[35] G M Komaki and V Kayvanfar ldquoGrey Wolf Optimizer algo-rithm for the two-stage assembly flow shop scheduling problemwith release timerdquo Journal of Computational Science vol 8 pp109ndash120 2015

16 Computational Intelligence and Neuroscience

[36] L I Wong M H Sulaiman M R Mohamed and M SHong ldquoGrey Wolf Optimizer for solving economic dispatchproblemsrdquo in Proceedings of the IEEE International Conferenceon Power and Energy (PECon rsquo14) pp 150ndash154 KuchingMalaysia December 2014

[37] A Chaman-Motlagh ldquoSuperdefect photonic crystal filter opti-mization using Grey Wolf Optimizerrdquo IEEE Photonics Technol-ogy Letters vol 27 no 22 pp 2355ndash2358 2015

[38] P Q Dzung N T Tien N Dinh Tuyen and H Lee ldquoSelectiveharmonic elimination for cascaded multilevel inverters usinggrey wolf optimizer algorithmrdquo in Proceedings of the 9thInternational Conference on Power Electronics and ECCE Asia(ICPE rsquo15-ECCE Asia) June 2015

[39] N Muangkote K Sunat and S Chiewchanwattana ldquoAnimproved grey wolf optimizer for training q-Gaussian RadialBasis Functional-link netsrdquo in Proceedings of the InternationalComputer Science and Engineering Conference (ICSEC rsquo14) pp209ndash214 Khon Kaen Thailand August 2014

[40] A Zhu C Xu Z Li J Wu and Z Liu ldquoHybridizing grey Wolfoptimization with differential evolution for global optimizationand test scheduling for 3D stacked SoCrdquo Journal of SystemsEngineering and Electronics vol 26 no 2 pp 317ndash328 2015

[41] P ArbelaezMMaire C Fowlkes and JMalik ldquoContour detec-tion and hierarchical image segmentationrdquo IEEE Transactionson Pattern Analysis and Machine Intelligence vol 33 no 5 pp898ndash916 2011

Submit your manuscripts athttpswwwhindawicom

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International Journal of

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Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

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Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

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Computational Intelligence and Neuroscience 9

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005001

0015002

0025

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

0002000400060008

0010012

0 50 100 150 200 250 3000

000100020003000400050006000700080009

001

0 50 100 150 200 250 3000

000100020003000400050006000700080009

001

0 50 100 150 200 250 3000

000100020003000400050006000700080009

001

0 50 100 150 200 250 3000

000100020003000400050006000700080009

001

Image

Cam

eram

anLe

naBa

boon

Butte

rfly

th = 2 th = 3 th = 4 th = 5

Figure 3 The segmentation results of (a)ndash(d) in Figure 2 and their thresholds in histograms

10 Computational Intelligence and Neuroscience

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0002000400060008

0010012001400160018

002

0 50 100 150 200 250 3000

0002000400060008

0010012001400160018

002

0 50 100 150 200 250 3000

0002000400060008

0010012001400160018

002

0 50 100 150 200 250 30000002000400060008

0010012001400160018

002

times10minus3

times10minus3

times10minus3

times10minus3

Image th = 2 th = 3 th = 4 th = 5

Mai

zeSt

arfis

hSm

iling

Girl

Surfi

ng

Figure 4 The segmentation results of (e)ndash(h) in Figure 2 and their thresholds in histograms

Computational Intelligence and Neuroscience 11

Table 3 The comparison of MDGWOrsquos efficiency between Otsu and Kapur

Image 119896 Otsu thresholds PSNR Kapur thresholds PSNR

Cameraman

2 70 144 119475 44 106 1446293 58 119 156 129933 44 98 148 1993374 40 93 139 170 160180 39 83 119 156 2116845 35 81 121 149 174 163710 23 58 94 125 159 231191

Lena

2 92 151 131029 93 163 1471643 80 126 171 157626 70 121 172 1751444 75 114 145 180 164291 43 81 127 171 2017295 73 109 136 161 189 167206 41 73 103 141 178 218208

Baboon

2 97 149 124396 78 141 1603023 83 123 160 137731 46 103 151 1863404 70 105 136 167 149493 34 75 117 159 2051985 66 98 125 150 175 160012 29 64 100 134 170 220929

Butterfly

2 100 152 124400 87 150 1493253 81 118 159 142563 62 104 152 1855394 73 101 129 164 146987 49 88 128 168 2107115 69 95 121 149 177 164688 48 80 113 145 180 224539

Maize

2 92 168 136677 84 165 1404073 76 128 187 152676 59 113 171 1658534 65 104 150 200 167309 45 80 125 187 1898185 56 86 123 164 208 185649 39 74 108 147 198 208792

Sea Star

2 85 157 148445 81 160 1485953 69 120 178 176040 60 111 172 1745834 59 99 137 187 194039 46 89 131 184 1944875 51 85 117 150 193 214000 47 83 118 150 196 209681

Smiling Girl

2 60 123 131358 88 145 1800333 47 100 131 128470 44 91 145 1911484 28 74 111 136 156914 24 67 100 145 2007595 20 63 95 124 158 18 2260 44 83 115 152 203 217937

Surfer

2 92 162 125401 52 141 1643433 71 111 177 160569 52 103 168 1893434 47 81 118 179 208786 49 86 131 185 2072185 46 77 105 143 196 216071 24 53 88 126 183 218961

The average value of Kapur is improved averagely by2224 compared to Otsu by checking against the cor-responding PSNR values which are obtained from theMDGWO The maximum value is increased by 5342 forCameraman Image when 119896 = 3 Therefore the Kapurmethod is significantly better than the Otsu method and wealso mainly analyze the effectiveness of Kapurrsquos method inSection 54

54TheComparison ofQuality Assessment by PSNR STD andMEAN This paper adopts PSNR standard to evaluate thesegmentation quality in comparisonwith otherMTmethodsTables 4ndash6 illustrate the PSNR values under different thresh-olds ofMDGWOGWOEMODEABC and theMEANandSTD of objective functions As shown in Table 4 it can be

seen from the PSNR values that MDGWO gets the highestevaluation in most cases Thus it proves that MDGWO getsbetter results on image segmentation In addition when thenumber of thresholds increases it shows superior PSNRvalue In detail the MDGWO algorithm produces higherPSNR values on all items in Table 4 except for the SmilingGirl Image with 119896 = 5 and Surfer Image with 119896 = 4 on theresult of DE

As shown in Table 4 the average value of MDGWO isimproved averagely by 1316 compared toGWOby checkingagainst the corresponding PSNR valuesThemaximum valueis increased by 4505 for Butterfly Image when 119896 = 5

ComparingwithMTEMO the average value ofMDGWOis improved averagely by 1156 by checking against the cor-responding PSNR valuesThemaximumvalue is increased by3994 for Surfer Image when 119896 = 2

12 Computational Intelligence and Neuroscience

Table 4 PSNR metrics of MTEMO DE ABC GWO and MDGWO

Image 119896 MTEMO DE ABC GWO MDGWO

Cameraman

2 13626 12584 13920 14279 144633 18803 17584 14462 19696 199344 20586 20111 2081 20809 211685 20661 21282 2240 22404 23119

Lena

2 14672 8823 14590 14680 147163 17247 14386 17197 17416 175144 18251 16151 18559 19762 201735 20019 16720 20321 21299 21820

Baboon

2 16016 8103 16007 16024 160353 16016 12596 18592 18632 186344 18485 13178 18417 20480 205195 20507 13135 20224 22060 22092

Butterfly

2 11065 8702 14402 14762 149323 14176 13028 14504 17873 185534 16725 13028 16189 21021 210715 19026 14786 19286 21485 22453

Maize

2 13633 10549 13590 13950 140403 15229 13022 15295 16201 165854 16280 14270 16346 18713 189815 17211 15079 17046 20410 20879

Sea Star

2 14398 8610 14395 14809 148853 16987 14078 16981 17431 174584 18304 16191 18427 19421 194485 20165 16474 20330 20887 20968

Smiling Girl

2 13420 14986 13514 17989 180033 18254 11243 18069 18742 191144 18860 14556 18826 19823 200755 19840 22980 19769 21214 21793

Surfer

2 11744 9737 11878 16154 164343 18584 11638 18762 18895 189344 19478 21866 19647 20234 207215 20468 19576 20479 21699 21896

By comparing with DE the average value of MDGWO isimproved averagely by 3814 by checking against the cor-responding PSNR values The maximum value is increasedby 9789 for Baboon Image when 119896 = 2 The PSNR of theSmiling Girl with 119896 = 5 and Surfer Image with 119896 = 4 areslightly lower but the gap is not significant

Comparing between ABC and MDGWO the averagevalue of MDGWO is improved averagely by 1055 by check-ing against the corresponding PSNR values The maximumvalue is increased by 3836 for Surfer Image when 119896 = 2

From the perspective of STDwhich is shown in Table 5 itcan be observed that MDGWO shows obviously advantagesover MTEMO DE ABC and GWOThe smaller the STD isthe smaller the change of fitness functions over the course ofiterations will be that is the better stability of segmentation

Therefore the results show that MDGWO obtains excitingeffect in stability So MDGWOrsquos stability is better

Compared with GWO the average value of MDGWO isimproved averagely by 7352 compared to GWO by check-ing against the corresponding STD values The maximumvalue is increased by 9644 for Baboon Image when 119896 = 3and the minimum value is increased by 2492 for BaboonImage when 119896 = 3

By comparing with MTEMO the average value ofMDGWO is improved averagely by 4788 The maximumvalue is increased by 87 for Lena Image when 119896 = 2 and theminimum value is increased by 06 for Surfer Image when119896 = 3

Comparing between DE andMDGWO the average valueofMDGWO is improved averagely by 9560Themaximum

Computational Intelligence and Neuroscience 13

Table 5 STD metrics of MTEMO DE ABC GWO and MDGWO

Image 119896 MTEMO DE ABC GWO MDGWO

Camerman

2 01849 12592 01235 01697 004623 01649 17601 02122 02287 007584 02943 21995 03003 03627 006595 02999 26579 02784 04278 01964

Lena

2 00969 12902 00349 01536 001263 01665 17822 01300 03570 002644 02800 22104 01872 05965 009395 02515 25992 01827 05946 01570

Baboon

2 00108 12862 00358 02171 001023 00393 17678 00202 04376 001564 01727 22126 01610 02986 011845 02868 26239 02660 05377 02316

Butterfly

2 00903 12708 00750 02179 004653 02207 17429 02952 02712 020364 02482 22368 03906 04808 024155 02900 26571 04818 05096 02684

Maize

2 00356 13501 00218 03571 001883 01222 18612 00901 02225 002704 02305 23230 02605 03903 009275 02502 27461 03834 04584 01677

Sea Star

2 01073 13547 01088 01728 002903 01497 18741 01752 02028 003744 01596 23307 01817 05032 011195 02639 27550 02180 04550 01437

Smiling Girl

2 00377 12516 00318 01834 001113 00955 17311 00577 01712 002424 01966 21878 01094 02508 007815 01550 25989 02768 05273 01302

Surfer

2 00579 13213 00303 02681 002453 01002 18337 01646 03014 009964 03382 23317 01686 03162 014245 03690 27846 02580 03815 01706

value is increased by 9921 for Baboon Image when 119896 =2 The minimum value is increased by 8832 for ButterflyImage when 119896 = 3

Comparing with ABC the average value of MDGWOis improved averagely by 4590 The maximum value isincreased by 7970 for Lena Image when 119896 = 3 and theminimum value is increased by 1293 for Baboon Imagewhen 119896 = 5

As far as MEAN is concerned this parameter presentsthe average value of fitness function over the course ofiterations in Table 6 which reflects the algorithm stability tosome extent But its accuracy of evaluation is relatively lowwhich can only reflect the fuzzy stability of the algorithmThe experiment data is offered here just in response to theparameter provided in literature [20] In comparison withGWO MTEWO DE and ABC in Table 6 it can be safely

assumed that inmost casesMDGWOobtains higherMEANof fitness function Moreover the difference is extremelysmall when MDGWOrsquos MEAN is lower

From the analyses of Tables 3ndash6 together with the visualeffects of Figures 2 3 and 4 it can be observed thatMDGWO method obtains better segmentation effect andhas advantage in optimal process accuracy stability androbustnessThereforeMDGWO is aMT algorithmwith highaccuracy and high segmentation quality

6 Conclusion

This paper proposes a modified discrete grey wolf optimizerwhich is used to optimize the image histograms and realizethe multilevel image segmentation Based on the high effi-ciency of GWO in the course of optimization and stability

14 Computational Intelligence and Neuroscience

Table 6 MEANmetrics of MTEMO DE ABC GWO and MDGWO

Image 119896 MTEMO DE ABC GWO MDGWO

Camerman

2 17584 124212 177638 14634 174713 21976 173764 223059 21107 219194 26586 217520 268409 24927 274805 30506 262505 308328 30436 30548

Lena

2 17831 127730 178139 17809 183963 22120 176428 220832 22074 228564 25999 218784 260615 25318 264475 29787 257311 299664 29252 30381

Baboon

2 17625 127333 176760 17679 186193 22269 175005 221276 22129 229494 26688 219010 263912 26194 269005 30800 259681 303464 30067 30076

Butterfly

2 16681 125796 174205 17425 177233 21242 172545 222209 21585 224984 25179 220176 263794 25267 261905 28611 261795 306533 29492 29899

Maize

2 18631 133566 186316 18604 195423 23565 184245 232496 22941 239394 27529 229813 273931 26936 278425 31535 271709 312127 31023 30694

Sea Star

2 18754 134104 187295 18321 195873 23323 185516 232738 23245 239014 27582 230719 275057 27136 282105 31562 272551 314919 31167 31958

Smiling Girl

2 17334 123892 173129 17136 180353 21904 171339 218601 21253 219804 26040 216541 259904 25050 265975 30089 257130 300225 29870 30574

Surfer

2 18339 130786 183393 18283 188693 23231 181492 232889 23243 241354 27863 230548 278017 27275 274475 31823 274979 317335 31384 31325

this paper successfully applies the MDGWO to the field ofMT by improving the location selection mechanism of 120572 120573and 120575 during the hunting and using weight to optimize thefinal position of prey (best threshold)TheMDGWOmethodnot only obtains better segmentation quality but also showsobvious superiority over GWO MTEMO DE and ABC instability accuracy and multilevel thresholding

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work was supported in part by the National NaturalScience Foundation of China (no 61300239 no 71301081and no 61572261) the Postdoctoral Science Foundation (no

2014M551635 and no 1302085B) the Innovation Project ofGraduate Students Foundation of Jiangsu Province (KYLX150841) the Higher Education Revitalization Plan Foundationof Anhui Province (no 2013SQRL102ZD no 2015xdjy196no 2015jyxm728 no 2016jyxm0774 and no 2016jyxm0777)and Natural Science Fund for Colleges and Universities inJiangsu Province (no16KJB520034) A Project Funded by thePriority Academic Program Development of Jiangsu HigherEducation Institutions (PAPD) and Jiangsu CollaborativeInnovation Center on Atmospheric Environment and Equip-ment Technology (CICAEET)

References

[1] M Sonka V Hlavac and R Boyle Image Processing Analysisand Machine Vision Cengage Learning 2014

[2] S Masood M Sharif A Masood M Yasmin and M RazaldquoA survey on medical image segmentationrdquo Current MedicalImaging Reviews vol 11 no 1 pp 3ndash14 2015

Computational Intelligence and Neuroscience 15

[3] PGhamisiM S Couceiro FM LMartins and J A Benedikts-son ldquoMultilevel image segmentation based on fractional-orderdarwinian particle swarm optimizationrdquo IEEE Transactions onGeoscience and Remote Sensing vol 52 no 5 pp 2382ndash23942014

[4] M Waseem Khan ldquoA survey image segmentation techniquesrdquoInternational Journal of Future Computer and Communicationvol 3 no 2 pp 89ndash93 2014

[5] J Li X Li B Yang and X Sun ldquoSegmentation-based imagecopy-move forgery detection schemerdquo IEEE Transactions onInformation Forensics and Security vol 10 no 3 pp 507ndash5182015

[6] Z Pan J Lei Y Zhang X Sun and S Kwong ldquoFast motionestimation based on content property for low-complexityH265HEVC encoderrdquo IEEE Transactions on Broadcasting vol62 no 3 pp 675ndash684 2016

[7] X Chen S Feng and D Pan ldquoAn improved approach oflung image segmentation based on watershed algorithmrdquo inProceedings of the the 7th International Conference on InternetMultimedia Computing and Service pp 1ndash5 Zhangjiajie ChinaAugust 2015

[8] Y Zheng B Jeon D Xu Q M J Wu and H Zhang ldquoImagesegmentation by generalized hierarchical fuzzy C-means algo-rithmrdquo Journal of Intelligent and Fuzzy Systems vol 28 no 2pp 961ndash973 2015

[9] V Osuna-Enciso E Cuevas and H Sossa ldquoA comparison ofnature inspired algorithms for multi-threshold image segmen-tationrdquo Expert Systems with Applications vol 40 no 4 pp 1213ndash1219 2013

[10] T Kurban P Civicioglu R Kurban and E Besdok ldquoCompari-son of evolutionary and swarmbased computational techniquesfor multilevel color image thresholdingrdquo Applied Soft Comput-ing Journal vol 23 pp 128ndash143 2014

[11] J N Kapur P K Sahoo and A K C Wong ldquoA new methodfor gray-level picture thresholding using the entropy of thehistogramrdquo Computer Vision Graphics and Image Processingvol 29 no 3 pp 273ndash285 1985

[12] N Otsu ldquoA threshold selection method from gray-level his-togramsrdquo Automatica vol 11 no 285ndash296 pp 23ndash27 1975

[13] X Li Z Zhao and H D Cheng ldquoFuzzy entropy thresholdapproach to breast cancer detectionrdquo Information Sciences -Applications vol 4 no 1 pp 49ndash56 1995

[14] J Kittler and J Illingworth ldquoMinimum error thresholdingrdquoPattern Recognition vol 19 no 1 pp 41ndash47 1986

[15] Y Xue S Zhong T Ma and J Cao ldquoA hybrid evolution-ary algorithm for numerical optimization problemrdquo IntelligentAutomation amp Soft Computing vol 21 no 4 pp 473ndash490 2015

[16] P-Y Yin ldquoA fast scheme for optimal thresholding using geneticalgorithmsrdquo Signal Processing vol 72 no 2 pp 85ndash95 1999

[17] W Fujun L Junlan L Shiwei Z Xingyu Z Dawei and TYanling ldquoAn improved adaptive genetic algorithm for imagesegmentation and vision alignment used in microelectronicbondingrdquo IEEEASMETransactions onMechatronics vol 19 no3 pp 916ndash923 2014

[18] S Banerjee and N D Jana ldquoBi level kapurs entropy basedimage segmentation using particle swarm optimizationrdquo inProceedings of the 3rd International Conference on ComputerCommunication Control and InformationTechnology (C3IT rsquo15)pp 1ndash4 Hooghly India February 2015

[19] M-H Horng ldquoMultilevel thresholding selection based on theartificial bee colony algorithm for image segmentationrdquo ExpertSystems with Applications vol 38 no 11 pp 13785ndash13791 2011

[20] D Oliva E Cuevas G Pajares D Zaldivar and V OsunaldquoA multilevel thresholding algorithm using electromagnetismoptimizationrdquo Neurocomputing vol 139 pp 357ndash381 2014

[21] S Sarkar G R Patra and S Das ldquoA differential evolutionbased approach for multilevel image segmentation using mini-mum cross entropy thresholdingrdquo in Swarm Evolutionary andMemetic Computing pp 51ndash58 Springer Berlin Germany 2011

[22] Y Xue Y Zhuang T Ni S Ni and X Wen ldquoSelf-adaptivelearning based discrete differential evolution algorithm forsolving CJWTA problemrdquo Journal of Systems Engineering andElectronics vol 25 no 1 pp 59ndash68 2014

[23] S Agrawal R Panda S Bhuyan and B K Panigrahi ldquoTsallisentropy based optimal multilevel thresholding using cuckoosearch algorithmrdquo Swarm and Evolutionary Computation vol11 pp 16ndash30 2013

[24] PD Sathya andRKayalvizhi ldquoOptimalmultilevel thresholdingusing bacterial foraging algorithmrdquo Expert Systems with Appli-cations vol 38 no 12 pp 15549ndash15564 2011

[25] S Ayas H Dogan E Gedikli and M Ekinci ldquoMicroscopicimage segmentation based on firefly algorithm for detectionof tuberculosis bacteriardquo in Proceedings of the 23rd SignalProcessing and Communications Applications Conference (SIUrsquo15) pp 851ndash854 Malatya Turkey May 2015

[26] S Mirjalili S M Mirjalili and A Lewis ldquoGrey wolf optimizerrdquoAdvances in Engineering Software vol 69 pp 46ndash61 2014

[27] B Akay ldquoA study on particle swarm optimization and artificialbee colony algorithms for multilevel thresholdingrdquo Applied SoftComputing vol 13 no 6 pp 3066ndash3091 2013

[28] A K Bhandari A Kumar and G K Singh ldquoModified artificialbee colony based computationally efficient multilevel thresh-olding for satellite image segmentation using Kapurrsquos Otsu andTsallis functionsrdquo Expert Systems with Applications vol 42 no3 pp 1573ndash1601 2015

[29] P Ghamisi M S Couceiro J A Benediktsson and N M FFerreira ldquoAn efficientmethod for segmentation of images basedon fractional calculus and natural selectionrdquo Expert Systemswith Applications vol 39 no 16 pp 12407ndash12417 2012

[30] L Li L Sun W Kang J Guo C Han and S Li ldquoFuzzymultilevel image thresholding based on modified discrete greywolf optimizer and local information aggregationrdquo IEEE Accessvol 4 pp 6438ndash6450 2016

[31] H-S Wu F-M Zhang and L-S Wu ldquoNew swarm intelligencealgorithm-wolf pack algorithmrdquo Xi Tong Gong Cheng Yu DianZi Ji ShuSystems Engineering and Electronics vol 35 no 11 pp2430ndash2438 2013

[32] H Wu and F Zhang ldquoA uncultivated wolf pack algorithm forhigh-dimensional functions and its application in parametersoptimization of PID controllerrdquo in Proceedings of the IEEECongress on Evolutionary Computation (CEC rsquo14) pp 1477ndash1482Beijing China July 2014

[33] H-S Wu and F-M Zhang ldquoWolf pack algorithm for uncon-strained global optimizationrdquo Mathematical Problems in Engi-neering vol 2014 Article ID 465082 17 pages 2014

[34] Q Zhou and Y Zhou ldquoWolf colony search algorithm based onleader strategyrdquo Application Research of Computers vol 9 pp2629ndash2632 2013

[35] G M Komaki and V Kayvanfar ldquoGrey Wolf Optimizer algo-rithm for the two-stage assembly flow shop scheduling problemwith release timerdquo Journal of Computational Science vol 8 pp109ndash120 2015

16 Computational Intelligence and Neuroscience

[36] L I Wong M H Sulaiman M R Mohamed and M SHong ldquoGrey Wolf Optimizer for solving economic dispatchproblemsrdquo in Proceedings of the IEEE International Conferenceon Power and Energy (PECon rsquo14) pp 150ndash154 KuchingMalaysia December 2014

[37] A Chaman-Motlagh ldquoSuperdefect photonic crystal filter opti-mization using Grey Wolf Optimizerrdquo IEEE Photonics Technol-ogy Letters vol 27 no 22 pp 2355ndash2358 2015

[38] P Q Dzung N T Tien N Dinh Tuyen and H Lee ldquoSelectiveharmonic elimination for cascaded multilevel inverters usinggrey wolf optimizer algorithmrdquo in Proceedings of the 9thInternational Conference on Power Electronics and ECCE Asia(ICPE rsquo15-ECCE Asia) June 2015

[39] N Muangkote K Sunat and S Chiewchanwattana ldquoAnimproved grey wolf optimizer for training q-Gaussian RadialBasis Functional-link netsrdquo in Proceedings of the InternationalComputer Science and Engineering Conference (ICSEC rsquo14) pp209ndash214 Khon Kaen Thailand August 2014

[40] A Zhu C Xu Z Li J Wu and Z Liu ldquoHybridizing grey Wolfoptimization with differential evolution for global optimizationand test scheduling for 3D stacked SoCrdquo Journal of SystemsEngineering and Electronics vol 26 no 2 pp 317ndash328 2015

[41] P ArbelaezMMaire C Fowlkes and JMalik ldquoContour detec-tion and hierarchical image segmentationrdquo IEEE Transactionson Pattern Analysis and Machine Intelligence vol 33 no 5 pp898ndash916 2011

Submit your manuscripts athttpswwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

10 Computational Intelligence and Neuroscience

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 3000

0002000400060008

00100120014

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 300012345678

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0005

001

0015

002

0025

0 50 100 150 200 250 3000

0002000400060008

0010012001400160018

002

0 50 100 150 200 250 3000

0002000400060008

0010012001400160018

002

0 50 100 150 200 250 3000

0002000400060008

0010012001400160018

002

0 50 100 150 200 250 30000002000400060008

0010012001400160018

002

times10minus3

times10minus3

times10minus3

times10minus3

Image th = 2 th = 3 th = 4 th = 5

Mai

zeSt

arfis

hSm

iling

Girl

Surfi

ng

Figure 4 The segmentation results of (e)ndash(h) in Figure 2 and their thresholds in histograms

Computational Intelligence and Neuroscience 11

Table 3 The comparison of MDGWOrsquos efficiency between Otsu and Kapur

Image 119896 Otsu thresholds PSNR Kapur thresholds PSNR

Cameraman

2 70 144 119475 44 106 1446293 58 119 156 129933 44 98 148 1993374 40 93 139 170 160180 39 83 119 156 2116845 35 81 121 149 174 163710 23 58 94 125 159 231191

Lena

2 92 151 131029 93 163 1471643 80 126 171 157626 70 121 172 1751444 75 114 145 180 164291 43 81 127 171 2017295 73 109 136 161 189 167206 41 73 103 141 178 218208

Baboon

2 97 149 124396 78 141 1603023 83 123 160 137731 46 103 151 1863404 70 105 136 167 149493 34 75 117 159 2051985 66 98 125 150 175 160012 29 64 100 134 170 220929

Butterfly

2 100 152 124400 87 150 1493253 81 118 159 142563 62 104 152 1855394 73 101 129 164 146987 49 88 128 168 2107115 69 95 121 149 177 164688 48 80 113 145 180 224539

Maize

2 92 168 136677 84 165 1404073 76 128 187 152676 59 113 171 1658534 65 104 150 200 167309 45 80 125 187 1898185 56 86 123 164 208 185649 39 74 108 147 198 208792

Sea Star

2 85 157 148445 81 160 1485953 69 120 178 176040 60 111 172 1745834 59 99 137 187 194039 46 89 131 184 1944875 51 85 117 150 193 214000 47 83 118 150 196 209681

Smiling Girl

2 60 123 131358 88 145 1800333 47 100 131 128470 44 91 145 1911484 28 74 111 136 156914 24 67 100 145 2007595 20 63 95 124 158 18 2260 44 83 115 152 203 217937

Surfer

2 92 162 125401 52 141 1643433 71 111 177 160569 52 103 168 1893434 47 81 118 179 208786 49 86 131 185 2072185 46 77 105 143 196 216071 24 53 88 126 183 218961

The average value of Kapur is improved averagely by2224 compared to Otsu by checking against the cor-responding PSNR values which are obtained from theMDGWO The maximum value is increased by 5342 forCameraman Image when 119896 = 3 Therefore the Kapurmethod is significantly better than the Otsu method and wealso mainly analyze the effectiveness of Kapurrsquos method inSection 54

54TheComparison ofQuality Assessment by PSNR STD andMEAN This paper adopts PSNR standard to evaluate thesegmentation quality in comparisonwith otherMTmethodsTables 4ndash6 illustrate the PSNR values under different thresh-olds ofMDGWOGWOEMODEABC and theMEANandSTD of objective functions As shown in Table 4 it can be

seen from the PSNR values that MDGWO gets the highestevaluation in most cases Thus it proves that MDGWO getsbetter results on image segmentation In addition when thenumber of thresholds increases it shows superior PSNRvalue In detail the MDGWO algorithm produces higherPSNR values on all items in Table 4 except for the SmilingGirl Image with 119896 = 5 and Surfer Image with 119896 = 4 on theresult of DE

As shown in Table 4 the average value of MDGWO isimproved averagely by 1316 compared toGWOby checkingagainst the corresponding PSNR valuesThemaximum valueis increased by 4505 for Butterfly Image when 119896 = 5

ComparingwithMTEMO the average value ofMDGWOis improved averagely by 1156 by checking against the cor-responding PSNR valuesThemaximumvalue is increased by3994 for Surfer Image when 119896 = 2

12 Computational Intelligence and Neuroscience

Table 4 PSNR metrics of MTEMO DE ABC GWO and MDGWO

Image 119896 MTEMO DE ABC GWO MDGWO

Cameraman

2 13626 12584 13920 14279 144633 18803 17584 14462 19696 199344 20586 20111 2081 20809 211685 20661 21282 2240 22404 23119

Lena

2 14672 8823 14590 14680 147163 17247 14386 17197 17416 175144 18251 16151 18559 19762 201735 20019 16720 20321 21299 21820

Baboon

2 16016 8103 16007 16024 160353 16016 12596 18592 18632 186344 18485 13178 18417 20480 205195 20507 13135 20224 22060 22092

Butterfly

2 11065 8702 14402 14762 149323 14176 13028 14504 17873 185534 16725 13028 16189 21021 210715 19026 14786 19286 21485 22453

Maize

2 13633 10549 13590 13950 140403 15229 13022 15295 16201 165854 16280 14270 16346 18713 189815 17211 15079 17046 20410 20879

Sea Star

2 14398 8610 14395 14809 148853 16987 14078 16981 17431 174584 18304 16191 18427 19421 194485 20165 16474 20330 20887 20968

Smiling Girl

2 13420 14986 13514 17989 180033 18254 11243 18069 18742 191144 18860 14556 18826 19823 200755 19840 22980 19769 21214 21793

Surfer

2 11744 9737 11878 16154 164343 18584 11638 18762 18895 189344 19478 21866 19647 20234 207215 20468 19576 20479 21699 21896

By comparing with DE the average value of MDGWO isimproved averagely by 3814 by checking against the cor-responding PSNR values The maximum value is increasedby 9789 for Baboon Image when 119896 = 2 The PSNR of theSmiling Girl with 119896 = 5 and Surfer Image with 119896 = 4 areslightly lower but the gap is not significant

Comparing between ABC and MDGWO the averagevalue of MDGWO is improved averagely by 1055 by check-ing against the corresponding PSNR values The maximumvalue is increased by 3836 for Surfer Image when 119896 = 2

From the perspective of STDwhich is shown in Table 5 itcan be observed that MDGWO shows obviously advantagesover MTEMO DE ABC and GWOThe smaller the STD isthe smaller the change of fitness functions over the course ofiterations will be that is the better stability of segmentation

Therefore the results show that MDGWO obtains excitingeffect in stability So MDGWOrsquos stability is better

Compared with GWO the average value of MDGWO isimproved averagely by 7352 compared to GWO by check-ing against the corresponding STD values The maximumvalue is increased by 9644 for Baboon Image when 119896 = 3and the minimum value is increased by 2492 for BaboonImage when 119896 = 3

By comparing with MTEMO the average value ofMDGWO is improved averagely by 4788 The maximumvalue is increased by 87 for Lena Image when 119896 = 2 and theminimum value is increased by 06 for Surfer Image when119896 = 3

Comparing between DE andMDGWO the average valueofMDGWO is improved averagely by 9560Themaximum

Computational Intelligence and Neuroscience 13

Table 5 STD metrics of MTEMO DE ABC GWO and MDGWO

Image 119896 MTEMO DE ABC GWO MDGWO

Camerman

2 01849 12592 01235 01697 004623 01649 17601 02122 02287 007584 02943 21995 03003 03627 006595 02999 26579 02784 04278 01964

Lena

2 00969 12902 00349 01536 001263 01665 17822 01300 03570 002644 02800 22104 01872 05965 009395 02515 25992 01827 05946 01570

Baboon

2 00108 12862 00358 02171 001023 00393 17678 00202 04376 001564 01727 22126 01610 02986 011845 02868 26239 02660 05377 02316

Butterfly

2 00903 12708 00750 02179 004653 02207 17429 02952 02712 020364 02482 22368 03906 04808 024155 02900 26571 04818 05096 02684

Maize

2 00356 13501 00218 03571 001883 01222 18612 00901 02225 002704 02305 23230 02605 03903 009275 02502 27461 03834 04584 01677

Sea Star

2 01073 13547 01088 01728 002903 01497 18741 01752 02028 003744 01596 23307 01817 05032 011195 02639 27550 02180 04550 01437

Smiling Girl

2 00377 12516 00318 01834 001113 00955 17311 00577 01712 002424 01966 21878 01094 02508 007815 01550 25989 02768 05273 01302

Surfer

2 00579 13213 00303 02681 002453 01002 18337 01646 03014 009964 03382 23317 01686 03162 014245 03690 27846 02580 03815 01706

value is increased by 9921 for Baboon Image when 119896 =2 The minimum value is increased by 8832 for ButterflyImage when 119896 = 3

Comparing with ABC the average value of MDGWOis improved averagely by 4590 The maximum value isincreased by 7970 for Lena Image when 119896 = 3 and theminimum value is increased by 1293 for Baboon Imagewhen 119896 = 5

As far as MEAN is concerned this parameter presentsthe average value of fitness function over the course ofiterations in Table 6 which reflects the algorithm stability tosome extent But its accuracy of evaluation is relatively lowwhich can only reflect the fuzzy stability of the algorithmThe experiment data is offered here just in response to theparameter provided in literature [20] In comparison withGWO MTEWO DE and ABC in Table 6 it can be safely

assumed that inmost casesMDGWOobtains higherMEANof fitness function Moreover the difference is extremelysmall when MDGWOrsquos MEAN is lower

From the analyses of Tables 3ndash6 together with the visualeffects of Figures 2 3 and 4 it can be observed thatMDGWO method obtains better segmentation effect andhas advantage in optimal process accuracy stability androbustnessThereforeMDGWO is aMT algorithmwith highaccuracy and high segmentation quality

6 Conclusion

This paper proposes a modified discrete grey wolf optimizerwhich is used to optimize the image histograms and realizethe multilevel image segmentation Based on the high effi-ciency of GWO in the course of optimization and stability

14 Computational Intelligence and Neuroscience

Table 6 MEANmetrics of MTEMO DE ABC GWO and MDGWO

Image 119896 MTEMO DE ABC GWO MDGWO

Camerman

2 17584 124212 177638 14634 174713 21976 173764 223059 21107 219194 26586 217520 268409 24927 274805 30506 262505 308328 30436 30548

Lena

2 17831 127730 178139 17809 183963 22120 176428 220832 22074 228564 25999 218784 260615 25318 264475 29787 257311 299664 29252 30381

Baboon

2 17625 127333 176760 17679 186193 22269 175005 221276 22129 229494 26688 219010 263912 26194 269005 30800 259681 303464 30067 30076

Butterfly

2 16681 125796 174205 17425 177233 21242 172545 222209 21585 224984 25179 220176 263794 25267 261905 28611 261795 306533 29492 29899

Maize

2 18631 133566 186316 18604 195423 23565 184245 232496 22941 239394 27529 229813 273931 26936 278425 31535 271709 312127 31023 30694

Sea Star

2 18754 134104 187295 18321 195873 23323 185516 232738 23245 239014 27582 230719 275057 27136 282105 31562 272551 314919 31167 31958

Smiling Girl

2 17334 123892 173129 17136 180353 21904 171339 218601 21253 219804 26040 216541 259904 25050 265975 30089 257130 300225 29870 30574

Surfer

2 18339 130786 183393 18283 188693 23231 181492 232889 23243 241354 27863 230548 278017 27275 274475 31823 274979 317335 31384 31325

this paper successfully applies the MDGWO to the field ofMT by improving the location selection mechanism of 120572 120573and 120575 during the hunting and using weight to optimize thefinal position of prey (best threshold)TheMDGWOmethodnot only obtains better segmentation quality but also showsobvious superiority over GWO MTEMO DE and ABC instability accuracy and multilevel thresholding

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work was supported in part by the National NaturalScience Foundation of China (no 61300239 no 71301081and no 61572261) the Postdoctoral Science Foundation (no

2014M551635 and no 1302085B) the Innovation Project ofGraduate Students Foundation of Jiangsu Province (KYLX150841) the Higher Education Revitalization Plan Foundationof Anhui Province (no 2013SQRL102ZD no 2015xdjy196no 2015jyxm728 no 2016jyxm0774 and no 2016jyxm0777)and Natural Science Fund for Colleges and Universities inJiangsu Province (no16KJB520034) A Project Funded by thePriority Academic Program Development of Jiangsu HigherEducation Institutions (PAPD) and Jiangsu CollaborativeInnovation Center on Atmospheric Environment and Equip-ment Technology (CICAEET)

References

[1] M Sonka V Hlavac and R Boyle Image Processing Analysisand Machine Vision Cengage Learning 2014

[2] S Masood M Sharif A Masood M Yasmin and M RazaldquoA survey on medical image segmentationrdquo Current MedicalImaging Reviews vol 11 no 1 pp 3ndash14 2015

Computational Intelligence and Neuroscience 15

[3] PGhamisiM S Couceiro FM LMartins and J A Benedikts-son ldquoMultilevel image segmentation based on fractional-orderdarwinian particle swarm optimizationrdquo IEEE Transactions onGeoscience and Remote Sensing vol 52 no 5 pp 2382ndash23942014

[4] M Waseem Khan ldquoA survey image segmentation techniquesrdquoInternational Journal of Future Computer and Communicationvol 3 no 2 pp 89ndash93 2014

[5] J Li X Li B Yang and X Sun ldquoSegmentation-based imagecopy-move forgery detection schemerdquo IEEE Transactions onInformation Forensics and Security vol 10 no 3 pp 507ndash5182015

[6] Z Pan J Lei Y Zhang X Sun and S Kwong ldquoFast motionestimation based on content property for low-complexityH265HEVC encoderrdquo IEEE Transactions on Broadcasting vol62 no 3 pp 675ndash684 2016

[7] X Chen S Feng and D Pan ldquoAn improved approach oflung image segmentation based on watershed algorithmrdquo inProceedings of the the 7th International Conference on InternetMultimedia Computing and Service pp 1ndash5 Zhangjiajie ChinaAugust 2015

[8] Y Zheng B Jeon D Xu Q M J Wu and H Zhang ldquoImagesegmentation by generalized hierarchical fuzzy C-means algo-rithmrdquo Journal of Intelligent and Fuzzy Systems vol 28 no 2pp 961ndash973 2015

[9] V Osuna-Enciso E Cuevas and H Sossa ldquoA comparison ofnature inspired algorithms for multi-threshold image segmen-tationrdquo Expert Systems with Applications vol 40 no 4 pp 1213ndash1219 2013

[10] T Kurban P Civicioglu R Kurban and E Besdok ldquoCompari-son of evolutionary and swarmbased computational techniquesfor multilevel color image thresholdingrdquo Applied Soft Comput-ing Journal vol 23 pp 128ndash143 2014

[11] J N Kapur P K Sahoo and A K C Wong ldquoA new methodfor gray-level picture thresholding using the entropy of thehistogramrdquo Computer Vision Graphics and Image Processingvol 29 no 3 pp 273ndash285 1985

[12] N Otsu ldquoA threshold selection method from gray-level his-togramsrdquo Automatica vol 11 no 285ndash296 pp 23ndash27 1975

[13] X Li Z Zhao and H D Cheng ldquoFuzzy entropy thresholdapproach to breast cancer detectionrdquo Information Sciences -Applications vol 4 no 1 pp 49ndash56 1995

[14] J Kittler and J Illingworth ldquoMinimum error thresholdingrdquoPattern Recognition vol 19 no 1 pp 41ndash47 1986

[15] Y Xue S Zhong T Ma and J Cao ldquoA hybrid evolution-ary algorithm for numerical optimization problemrdquo IntelligentAutomation amp Soft Computing vol 21 no 4 pp 473ndash490 2015

[16] P-Y Yin ldquoA fast scheme for optimal thresholding using geneticalgorithmsrdquo Signal Processing vol 72 no 2 pp 85ndash95 1999

[17] W Fujun L Junlan L Shiwei Z Xingyu Z Dawei and TYanling ldquoAn improved adaptive genetic algorithm for imagesegmentation and vision alignment used in microelectronicbondingrdquo IEEEASMETransactions onMechatronics vol 19 no3 pp 916ndash923 2014

[18] S Banerjee and N D Jana ldquoBi level kapurs entropy basedimage segmentation using particle swarm optimizationrdquo inProceedings of the 3rd International Conference on ComputerCommunication Control and InformationTechnology (C3IT rsquo15)pp 1ndash4 Hooghly India February 2015

[19] M-H Horng ldquoMultilevel thresholding selection based on theartificial bee colony algorithm for image segmentationrdquo ExpertSystems with Applications vol 38 no 11 pp 13785ndash13791 2011

[20] D Oliva E Cuevas G Pajares D Zaldivar and V OsunaldquoA multilevel thresholding algorithm using electromagnetismoptimizationrdquo Neurocomputing vol 139 pp 357ndash381 2014

[21] S Sarkar G R Patra and S Das ldquoA differential evolutionbased approach for multilevel image segmentation using mini-mum cross entropy thresholdingrdquo in Swarm Evolutionary andMemetic Computing pp 51ndash58 Springer Berlin Germany 2011

[22] Y Xue Y Zhuang T Ni S Ni and X Wen ldquoSelf-adaptivelearning based discrete differential evolution algorithm forsolving CJWTA problemrdquo Journal of Systems Engineering andElectronics vol 25 no 1 pp 59ndash68 2014

[23] S Agrawal R Panda S Bhuyan and B K Panigrahi ldquoTsallisentropy based optimal multilevel thresholding using cuckoosearch algorithmrdquo Swarm and Evolutionary Computation vol11 pp 16ndash30 2013

[24] PD Sathya andRKayalvizhi ldquoOptimalmultilevel thresholdingusing bacterial foraging algorithmrdquo Expert Systems with Appli-cations vol 38 no 12 pp 15549ndash15564 2011

[25] S Ayas H Dogan E Gedikli and M Ekinci ldquoMicroscopicimage segmentation based on firefly algorithm for detectionof tuberculosis bacteriardquo in Proceedings of the 23rd SignalProcessing and Communications Applications Conference (SIUrsquo15) pp 851ndash854 Malatya Turkey May 2015

[26] S Mirjalili S M Mirjalili and A Lewis ldquoGrey wolf optimizerrdquoAdvances in Engineering Software vol 69 pp 46ndash61 2014

[27] B Akay ldquoA study on particle swarm optimization and artificialbee colony algorithms for multilevel thresholdingrdquo Applied SoftComputing vol 13 no 6 pp 3066ndash3091 2013

[28] A K Bhandari A Kumar and G K Singh ldquoModified artificialbee colony based computationally efficient multilevel thresh-olding for satellite image segmentation using Kapurrsquos Otsu andTsallis functionsrdquo Expert Systems with Applications vol 42 no3 pp 1573ndash1601 2015

[29] P Ghamisi M S Couceiro J A Benediktsson and N M FFerreira ldquoAn efficientmethod for segmentation of images basedon fractional calculus and natural selectionrdquo Expert Systemswith Applications vol 39 no 16 pp 12407ndash12417 2012

[30] L Li L Sun W Kang J Guo C Han and S Li ldquoFuzzymultilevel image thresholding based on modified discrete greywolf optimizer and local information aggregationrdquo IEEE Accessvol 4 pp 6438ndash6450 2016

[31] H-S Wu F-M Zhang and L-S Wu ldquoNew swarm intelligencealgorithm-wolf pack algorithmrdquo Xi Tong Gong Cheng Yu DianZi Ji ShuSystems Engineering and Electronics vol 35 no 11 pp2430ndash2438 2013

[32] H Wu and F Zhang ldquoA uncultivated wolf pack algorithm forhigh-dimensional functions and its application in parametersoptimization of PID controllerrdquo in Proceedings of the IEEECongress on Evolutionary Computation (CEC rsquo14) pp 1477ndash1482Beijing China July 2014

[33] H-S Wu and F-M Zhang ldquoWolf pack algorithm for uncon-strained global optimizationrdquo Mathematical Problems in Engi-neering vol 2014 Article ID 465082 17 pages 2014

[34] Q Zhou and Y Zhou ldquoWolf colony search algorithm based onleader strategyrdquo Application Research of Computers vol 9 pp2629ndash2632 2013

[35] G M Komaki and V Kayvanfar ldquoGrey Wolf Optimizer algo-rithm for the two-stage assembly flow shop scheduling problemwith release timerdquo Journal of Computational Science vol 8 pp109ndash120 2015

16 Computational Intelligence and Neuroscience

[36] L I Wong M H Sulaiman M R Mohamed and M SHong ldquoGrey Wolf Optimizer for solving economic dispatchproblemsrdquo in Proceedings of the IEEE International Conferenceon Power and Energy (PECon rsquo14) pp 150ndash154 KuchingMalaysia December 2014

[37] A Chaman-Motlagh ldquoSuperdefect photonic crystal filter opti-mization using Grey Wolf Optimizerrdquo IEEE Photonics Technol-ogy Letters vol 27 no 22 pp 2355ndash2358 2015

[38] P Q Dzung N T Tien N Dinh Tuyen and H Lee ldquoSelectiveharmonic elimination for cascaded multilevel inverters usinggrey wolf optimizer algorithmrdquo in Proceedings of the 9thInternational Conference on Power Electronics and ECCE Asia(ICPE rsquo15-ECCE Asia) June 2015

[39] N Muangkote K Sunat and S Chiewchanwattana ldquoAnimproved grey wolf optimizer for training q-Gaussian RadialBasis Functional-link netsrdquo in Proceedings of the InternationalComputer Science and Engineering Conference (ICSEC rsquo14) pp209ndash214 Khon Kaen Thailand August 2014

[40] A Zhu C Xu Z Li J Wu and Z Liu ldquoHybridizing grey Wolfoptimization with differential evolution for global optimizationand test scheduling for 3D stacked SoCrdquo Journal of SystemsEngineering and Electronics vol 26 no 2 pp 317ndash328 2015

[41] P ArbelaezMMaire C Fowlkes and JMalik ldquoContour detec-tion and hierarchical image segmentationrdquo IEEE Transactionson Pattern Analysis and Machine Intelligence vol 33 no 5 pp898ndash916 2011

Submit your manuscripts athttpswwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience 11

Table 3 The comparison of MDGWOrsquos efficiency between Otsu and Kapur

Image 119896 Otsu thresholds PSNR Kapur thresholds PSNR

Cameraman

2 70 144 119475 44 106 1446293 58 119 156 129933 44 98 148 1993374 40 93 139 170 160180 39 83 119 156 2116845 35 81 121 149 174 163710 23 58 94 125 159 231191

Lena

2 92 151 131029 93 163 1471643 80 126 171 157626 70 121 172 1751444 75 114 145 180 164291 43 81 127 171 2017295 73 109 136 161 189 167206 41 73 103 141 178 218208

Baboon

2 97 149 124396 78 141 1603023 83 123 160 137731 46 103 151 1863404 70 105 136 167 149493 34 75 117 159 2051985 66 98 125 150 175 160012 29 64 100 134 170 220929

Butterfly

2 100 152 124400 87 150 1493253 81 118 159 142563 62 104 152 1855394 73 101 129 164 146987 49 88 128 168 2107115 69 95 121 149 177 164688 48 80 113 145 180 224539

Maize

2 92 168 136677 84 165 1404073 76 128 187 152676 59 113 171 1658534 65 104 150 200 167309 45 80 125 187 1898185 56 86 123 164 208 185649 39 74 108 147 198 208792

Sea Star

2 85 157 148445 81 160 1485953 69 120 178 176040 60 111 172 1745834 59 99 137 187 194039 46 89 131 184 1944875 51 85 117 150 193 214000 47 83 118 150 196 209681

Smiling Girl

2 60 123 131358 88 145 1800333 47 100 131 128470 44 91 145 1911484 28 74 111 136 156914 24 67 100 145 2007595 20 63 95 124 158 18 2260 44 83 115 152 203 217937

Surfer

2 92 162 125401 52 141 1643433 71 111 177 160569 52 103 168 1893434 47 81 118 179 208786 49 86 131 185 2072185 46 77 105 143 196 216071 24 53 88 126 183 218961

The average value of Kapur is improved averagely by2224 compared to Otsu by checking against the cor-responding PSNR values which are obtained from theMDGWO The maximum value is increased by 5342 forCameraman Image when 119896 = 3 Therefore the Kapurmethod is significantly better than the Otsu method and wealso mainly analyze the effectiveness of Kapurrsquos method inSection 54

54TheComparison ofQuality Assessment by PSNR STD andMEAN This paper adopts PSNR standard to evaluate thesegmentation quality in comparisonwith otherMTmethodsTables 4ndash6 illustrate the PSNR values under different thresh-olds ofMDGWOGWOEMODEABC and theMEANandSTD of objective functions As shown in Table 4 it can be

seen from the PSNR values that MDGWO gets the highestevaluation in most cases Thus it proves that MDGWO getsbetter results on image segmentation In addition when thenumber of thresholds increases it shows superior PSNRvalue In detail the MDGWO algorithm produces higherPSNR values on all items in Table 4 except for the SmilingGirl Image with 119896 = 5 and Surfer Image with 119896 = 4 on theresult of DE

As shown in Table 4 the average value of MDGWO isimproved averagely by 1316 compared toGWOby checkingagainst the corresponding PSNR valuesThemaximum valueis increased by 4505 for Butterfly Image when 119896 = 5

ComparingwithMTEMO the average value ofMDGWOis improved averagely by 1156 by checking against the cor-responding PSNR valuesThemaximumvalue is increased by3994 for Surfer Image when 119896 = 2

12 Computational Intelligence and Neuroscience

Table 4 PSNR metrics of MTEMO DE ABC GWO and MDGWO

Image 119896 MTEMO DE ABC GWO MDGWO

Cameraman

2 13626 12584 13920 14279 144633 18803 17584 14462 19696 199344 20586 20111 2081 20809 211685 20661 21282 2240 22404 23119

Lena

2 14672 8823 14590 14680 147163 17247 14386 17197 17416 175144 18251 16151 18559 19762 201735 20019 16720 20321 21299 21820

Baboon

2 16016 8103 16007 16024 160353 16016 12596 18592 18632 186344 18485 13178 18417 20480 205195 20507 13135 20224 22060 22092

Butterfly

2 11065 8702 14402 14762 149323 14176 13028 14504 17873 185534 16725 13028 16189 21021 210715 19026 14786 19286 21485 22453

Maize

2 13633 10549 13590 13950 140403 15229 13022 15295 16201 165854 16280 14270 16346 18713 189815 17211 15079 17046 20410 20879

Sea Star

2 14398 8610 14395 14809 148853 16987 14078 16981 17431 174584 18304 16191 18427 19421 194485 20165 16474 20330 20887 20968

Smiling Girl

2 13420 14986 13514 17989 180033 18254 11243 18069 18742 191144 18860 14556 18826 19823 200755 19840 22980 19769 21214 21793

Surfer

2 11744 9737 11878 16154 164343 18584 11638 18762 18895 189344 19478 21866 19647 20234 207215 20468 19576 20479 21699 21896

By comparing with DE the average value of MDGWO isimproved averagely by 3814 by checking against the cor-responding PSNR values The maximum value is increasedby 9789 for Baboon Image when 119896 = 2 The PSNR of theSmiling Girl with 119896 = 5 and Surfer Image with 119896 = 4 areslightly lower but the gap is not significant

Comparing between ABC and MDGWO the averagevalue of MDGWO is improved averagely by 1055 by check-ing against the corresponding PSNR values The maximumvalue is increased by 3836 for Surfer Image when 119896 = 2

From the perspective of STDwhich is shown in Table 5 itcan be observed that MDGWO shows obviously advantagesover MTEMO DE ABC and GWOThe smaller the STD isthe smaller the change of fitness functions over the course ofiterations will be that is the better stability of segmentation

Therefore the results show that MDGWO obtains excitingeffect in stability So MDGWOrsquos stability is better

Compared with GWO the average value of MDGWO isimproved averagely by 7352 compared to GWO by check-ing against the corresponding STD values The maximumvalue is increased by 9644 for Baboon Image when 119896 = 3and the minimum value is increased by 2492 for BaboonImage when 119896 = 3

By comparing with MTEMO the average value ofMDGWO is improved averagely by 4788 The maximumvalue is increased by 87 for Lena Image when 119896 = 2 and theminimum value is increased by 06 for Surfer Image when119896 = 3

Comparing between DE andMDGWO the average valueofMDGWO is improved averagely by 9560Themaximum

Computational Intelligence and Neuroscience 13

Table 5 STD metrics of MTEMO DE ABC GWO and MDGWO

Image 119896 MTEMO DE ABC GWO MDGWO

Camerman

2 01849 12592 01235 01697 004623 01649 17601 02122 02287 007584 02943 21995 03003 03627 006595 02999 26579 02784 04278 01964

Lena

2 00969 12902 00349 01536 001263 01665 17822 01300 03570 002644 02800 22104 01872 05965 009395 02515 25992 01827 05946 01570

Baboon

2 00108 12862 00358 02171 001023 00393 17678 00202 04376 001564 01727 22126 01610 02986 011845 02868 26239 02660 05377 02316

Butterfly

2 00903 12708 00750 02179 004653 02207 17429 02952 02712 020364 02482 22368 03906 04808 024155 02900 26571 04818 05096 02684

Maize

2 00356 13501 00218 03571 001883 01222 18612 00901 02225 002704 02305 23230 02605 03903 009275 02502 27461 03834 04584 01677

Sea Star

2 01073 13547 01088 01728 002903 01497 18741 01752 02028 003744 01596 23307 01817 05032 011195 02639 27550 02180 04550 01437

Smiling Girl

2 00377 12516 00318 01834 001113 00955 17311 00577 01712 002424 01966 21878 01094 02508 007815 01550 25989 02768 05273 01302

Surfer

2 00579 13213 00303 02681 002453 01002 18337 01646 03014 009964 03382 23317 01686 03162 014245 03690 27846 02580 03815 01706

value is increased by 9921 for Baboon Image when 119896 =2 The minimum value is increased by 8832 for ButterflyImage when 119896 = 3

Comparing with ABC the average value of MDGWOis improved averagely by 4590 The maximum value isincreased by 7970 for Lena Image when 119896 = 3 and theminimum value is increased by 1293 for Baboon Imagewhen 119896 = 5

As far as MEAN is concerned this parameter presentsthe average value of fitness function over the course ofiterations in Table 6 which reflects the algorithm stability tosome extent But its accuracy of evaluation is relatively lowwhich can only reflect the fuzzy stability of the algorithmThe experiment data is offered here just in response to theparameter provided in literature [20] In comparison withGWO MTEWO DE and ABC in Table 6 it can be safely

assumed that inmost casesMDGWOobtains higherMEANof fitness function Moreover the difference is extremelysmall when MDGWOrsquos MEAN is lower

From the analyses of Tables 3ndash6 together with the visualeffects of Figures 2 3 and 4 it can be observed thatMDGWO method obtains better segmentation effect andhas advantage in optimal process accuracy stability androbustnessThereforeMDGWO is aMT algorithmwith highaccuracy and high segmentation quality

6 Conclusion

This paper proposes a modified discrete grey wolf optimizerwhich is used to optimize the image histograms and realizethe multilevel image segmentation Based on the high effi-ciency of GWO in the course of optimization and stability

14 Computational Intelligence and Neuroscience

Table 6 MEANmetrics of MTEMO DE ABC GWO and MDGWO

Image 119896 MTEMO DE ABC GWO MDGWO

Camerman

2 17584 124212 177638 14634 174713 21976 173764 223059 21107 219194 26586 217520 268409 24927 274805 30506 262505 308328 30436 30548

Lena

2 17831 127730 178139 17809 183963 22120 176428 220832 22074 228564 25999 218784 260615 25318 264475 29787 257311 299664 29252 30381

Baboon

2 17625 127333 176760 17679 186193 22269 175005 221276 22129 229494 26688 219010 263912 26194 269005 30800 259681 303464 30067 30076

Butterfly

2 16681 125796 174205 17425 177233 21242 172545 222209 21585 224984 25179 220176 263794 25267 261905 28611 261795 306533 29492 29899

Maize

2 18631 133566 186316 18604 195423 23565 184245 232496 22941 239394 27529 229813 273931 26936 278425 31535 271709 312127 31023 30694

Sea Star

2 18754 134104 187295 18321 195873 23323 185516 232738 23245 239014 27582 230719 275057 27136 282105 31562 272551 314919 31167 31958

Smiling Girl

2 17334 123892 173129 17136 180353 21904 171339 218601 21253 219804 26040 216541 259904 25050 265975 30089 257130 300225 29870 30574

Surfer

2 18339 130786 183393 18283 188693 23231 181492 232889 23243 241354 27863 230548 278017 27275 274475 31823 274979 317335 31384 31325

this paper successfully applies the MDGWO to the field ofMT by improving the location selection mechanism of 120572 120573and 120575 during the hunting and using weight to optimize thefinal position of prey (best threshold)TheMDGWOmethodnot only obtains better segmentation quality but also showsobvious superiority over GWO MTEMO DE and ABC instability accuracy and multilevel thresholding

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work was supported in part by the National NaturalScience Foundation of China (no 61300239 no 71301081and no 61572261) the Postdoctoral Science Foundation (no

2014M551635 and no 1302085B) the Innovation Project ofGraduate Students Foundation of Jiangsu Province (KYLX150841) the Higher Education Revitalization Plan Foundationof Anhui Province (no 2013SQRL102ZD no 2015xdjy196no 2015jyxm728 no 2016jyxm0774 and no 2016jyxm0777)and Natural Science Fund for Colleges and Universities inJiangsu Province (no16KJB520034) A Project Funded by thePriority Academic Program Development of Jiangsu HigherEducation Institutions (PAPD) and Jiangsu CollaborativeInnovation Center on Atmospheric Environment and Equip-ment Technology (CICAEET)

References

[1] M Sonka V Hlavac and R Boyle Image Processing Analysisand Machine Vision Cengage Learning 2014

[2] S Masood M Sharif A Masood M Yasmin and M RazaldquoA survey on medical image segmentationrdquo Current MedicalImaging Reviews vol 11 no 1 pp 3ndash14 2015

Computational Intelligence and Neuroscience 15

[3] PGhamisiM S Couceiro FM LMartins and J A Benedikts-son ldquoMultilevel image segmentation based on fractional-orderdarwinian particle swarm optimizationrdquo IEEE Transactions onGeoscience and Remote Sensing vol 52 no 5 pp 2382ndash23942014

[4] M Waseem Khan ldquoA survey image segmentation techniquesrdquoInternational Journal of Future Computer and Communicationvol 3 no 2 pp 89ndash93 2014

[5] J Li X Li B Yang and X Sun ldquoSegmentation-based imagecopy-move forgery detection schemerdquo IEEE Transactions onInformation Forensics and Security vol 10 no 3 pp 507ndash5182015

[6] Z Pan J Lei Y Zhang X Sun and S Kwong ldquoFast motionestimation based on content property for low-complexityH265HEVC encoderrdquo IEEE Transactions on Broadcasting vol62 no 3 pp 675ndash684 2016

[7] X Chen S Feng and D Pan ldquoAn improved approach oflung image segmentation based on watershed algorithmrdquo inProceedings of the the 7th International Conference on InternetMultimedia Computing and Service pp 1ndash5 Zhangjiajie ChinaAugust 2015

[8] Y Zheng B Jeon D Xu Q M J Wu and H Zhang ldquoImagesegmentation by generalized hierarchical fuzzy C-means algo-rithmrdquo Journal of Intelligent and Fuzzy Systems vol 28 no 2pp 961ndash973 2015

[9] V Osuna-Enciso E Cuevas and H Sossa ldquoA comparison ofnature inspired algorithms for multi-threshold image segmen-tationrdquo Expert Systems with Applications vol 40 no 4 pp 1213ndash1219 2013

[10] T Kurban P Civicioglu R Kurban and E Besdok ldquoCompari-son of evolutionary and swarmbased computational techniquesfor multilevel color image thresholdingrdquo Applied Soft Comput-ing Journal vol 23 pp 128ndash143 2014

[11] J N Kapur P K Sahoo and A K C Wong ldquoA new methodfor gray-level picture thresholding using the entropy of thehistogramrdquo Computer Vision Graphics and Image Processingvol 29 no 3 pp 273ndash285 1985

[12] N Otsu ldquoA threshold selection method from gray-level his-togramsrdquo Automatica vol 11 no 285ndash296 pp 23ndash27 1975

[13] X Li Z Zhao and H D Cheng ldquoFuzzy entropy thresholdapproach to breast cancer detectionrdquo Information Sciences -Applications vol 4 no 1 pp 49ndash56 1995

[14] J Kittler and J Illingworth ldquoMinimum error thresholdingrdquoPattern Recognition vol 19 no 1 pp 41ndash47 1986

[15] Y Xue S Zhong T Ma and J Cao ldquoA hybrid evolution-ary algorithm for numerical optimization problemrdquo IntelligentAutomation amp Soft Computing vol 21 no 4 pp 473ndash490 2015

[16] P-Y Yin ldquoA fast scheme for optimal thresholding using geneticalgorithmsrdquo Signal Processing vol 72 no 2 pp 85ndash95 1999

[17] W Fujun L Junlan L Shiwei Z Xingyu Z Dawei and TYanling ldquoAn improved adaptive genetic algorithm for imagesegmentation and vision alignment used in microelectronicbondingrdquo IEEEASMETransactions onMechatronics vol 19 no3 pp 916ndash923 2014

[18] S Banerjee and N D Jana ldquoBi level kapurs entropy basedimage segmentation using particle swarm optimizationrdquo inProceedings of the 3rd International Conference on ComputerCommunication Control and InformationTechnology (C3IT rsquo15)pp 1ndash4 Hooghly India February 2015

[19] M-H Horng ldquoMultilevel thresholding selection based on theartificial bee colony algorithm for image segmentationrdquo ExpertSystems with Applications vol 38 no 11 pp 13785ndash13791 2011

[20] D Oliva E Cuevas G Pajares D Zaldivar and V OsunaldquoA multilevel thresholding algorithm using electromagnetismoptimizationrdquo Neurocomputing vol 139 pp 357ndash381 2014

[21] S Sarkar G R Patra and S Das ldquoA differential evolutionbased approach for multilevel image segmentation using mini-mum cross entropy thresholdingrdquo in Swarm Evolutionary andMemetic Computing pp 51ndash58 Springer Berlin Germany 2011

[22] Y Xue Y Zhuang T Ni S Ni and X Wen ldquoSelf-adaptivelearning based discrete differential evolution algorithm forsolving CJWTA problemrdquo Journal of Systems Engineering andElectronics vol 25 no 1 pp 59ndash68 2014

[23] S Agrawal R Panda S Bhuyan and B K Panigrahi ldquoTsallisentropy based optimal multilevel thresholding using cuckoosearch algorithmrdquo Swarm and Evolutionary Computation vol11 pp 16ndash30 2013

[24] PD Sathya andRKayalvizhi ldquoOptimalmultilevel thresholdingusing bacterial foraging algorithmrdquo Expert Systems with Appli-cations vol 38 no 12 pp 15549ndash15564 2011

[25] S Ayas H Dogan E Gedikli and M Ekinci ldquoMicroscopicimage segmentation based on firefly algorithm for detectionof tuberculosis bacteriardquo in Proceedings of the 23rd SignalProcessing and Communications Applications Conference (SIUrsquo15) pp 851ndash854 Malatya Turkey May 2015

[26] S Mirjalili S M Mirjalili and A Lewis ldquoGrey wolf optimizerrdquoAdvances in Engineering Software vol 69 pp 46ndash61 2014

[27] B Akay ldquoA study on particle swarm optimization and artificialbee colony algorithms for multilevel thresholdingrdquo Applied SoftComputing vol 13 no 6 pp 3066ndash3091 2013

[28] A K Bhandari A Kumar and G K Singh ldquoModified artificialbee colony based computationally efficient multilevel thresh-olding for satellite image segmentation using Kapurrsquos Otsu andTsallis functionsrdquo Expert Systems with Applications vol 42 no3 pp 1573ndash1601 2015

[29] P Ghamisi M S Couceiro J A Benediktsson and N M FFerreira ldquoAn efficientmethod for segmentation of images basedon fractional calculus and natural selectionrdquo Expert Systemswith Applications vol 39 no 16 pp 12407ndash12417 2012

[30] L Li L Sun W Kang J Guo C Han and S Li ldquoFuzzymultilevel image thresholding based on modified discrete greywolf optimizer and local information aggregationrdquo IEEE Accessvol 4 pp 6438ndash6450 2016

[31] H-S Wu F-M Zhang and L-S Wu ldquoNew swarm intelligencealgorithm-wolf pack algorithmrdquo Xi Tong Gong Cheng Yu DianZi Ji ShuSystems Engineering and Electronics vol 35 no 11 pp2430ndash2438 2013

[32] H Wu and F Zhang ldquoA uncultivated wolf pack algorithm forhigh-dimensional functions and its application in parametersoptimization of PID controllerrdquo in Proceedings of the IEEECongress on Evolutionary Computation (CEC rsquo14) pp 1477ndash1482Beijing China July 2014

[33] H-S Wu and F-M Zhang ldquoWolf pack algorithm for uncon-strained global optimizationrdquo Mathematical Problems in Engi-neering vol 2014 Article ID 465082 17 pages 2014

[34] Q Zhou and Y Zhou ldquoWolf colony search algorithm based onleader strategyrdquo Application Research of Computers vol 9 pp2629ndash2632 2013

[35] G M Komaki and V Kayvanfar ldquoGrey Wolf Optimizer algo-rithm for the two-stage assembly flow shop scheduling problemwith release timerdquo Journal of Computational Science vol 8 pp109ndash120 2015

16 Computational Intelligence and Neuroscience

[36] L I Wong M H Sulaiman M R Mohamed and M SHong ldquoGrey Wolf Optimizer for solving economic dispatchproblemsrdquo in Proceedings of the IEEE International Conferenceon Power and Energy (PECon rsquo14) pp 150ndash154 KuchingMalaysia December 2014

[37] A Chaman-Motlagh ldquoSuperdefect photonic crystal filter opti-mization using Grey Wolf Optimizerrdquo IEEE Photonics Technol-ogy Letters vol 27 no 22 pp 2355ndash2358 2015

[38] P Q Dzung N T Tien N Dinh Tuyen and H Lee ldquoSelectiveharmonic elimination for cascaded multilevel inverters usinggrey wolf optimizer algorithmrdquo in Proceedings of the 9thInternational Conference on Power Electronics and ECCE Asia(ICPE rsquo15-ECCE Asia) June 2015

[39] N Muangkote K Sunat and S Chiewchanwattana ldquoAnimproved grey wolf optimizer for training q-Gaussian RadialBasis Functional-link netsrdquo in Proceedings of the InternationalComputer Science and Engineering Conference (ICSEC rsquo14) pp209ndash214 Khon Kaen Thailand August 2014

[40] A Zhu C Xu Z Li J Wu and Z Liu ldquoHybridizing grey Wolfoptimization with differential evolution for global optimizationand test scheduling for 3D stacked SoCrdquo Journal of SystemsEngineering and Electronics vol 26 no 2 pp 317ndash328 2015

[41] P ArbelaezMMaire C Fowlkes and JMalik ldquoContour detec-tion and hierarchical image segmentationrdquo IEEE Transactionson Pattern Analysis and Machine Intelligence vol 33 no 5 pp898ndash916 2011

Submit your manuscripts athttpswwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

12 Computational Intelligence and Neuroscience

Table 4 PSNR metrics of MTEMO DE ABC GWO and MDGWO

Image 119896 MTEMO DE ABC GWO MDGWO

Cameraman

2 13626 12584 13920 14279 144633 18803 17584 14462 19696 199344 20586 20111 2081 20809 211685 20661 21282 2240 22404 23119

Lena

2 14672 8823 14590 14680 147163 17247 14386 17197 17416 175144 18251 16151 18559 19762 201735 20019 16720 20321 21299 21820

Baboon

2 16016 8103 16007 16024 160353 16016 12596 18592 18632 186344 18485 13178 18417 20480 205195 20507 13135 20224 22060 22092

Butterfly

2 11065 8702 14402 14762 149323 14176 13028 14504 17873 185534 16725 13028 16189 21021 210715 19026 14786 19286 21485 22453

Maize

2 13633 10549 13590 13950 140403 15229 13022 15295 16201 165854 16280 14270 16346 18713 189815 17211 15079 17046 20410 20879

Sea Star

2 14398 8610 14395 14809 148853 16987 14078 16981 17431 174584 18304 16191 18427 19421 194485 20165 16474 20330 20887 20968

Smiling Girl

2 13420 14986 13514 17989 180033 18254 11243 18069 18742 191144 18860 14556 18826 19823 200755 19840 22980 19769 21214 21793

Surfer

2 11744 9737 11878 16154 164343 18584 11638 18762 18895 189344 19478 21866 19647 20234 207215 20468 19576 20479 21699 21896

By comparing with DE the average value of MDGWO isimproved averagely by 3814 by checking against the cor-responding PSNR values The maximum value is increasedby 9789 for Baboon Image when 119896 = 2 The PSNR of theSmiling Girl with 119896 = 5 and Surfer Image with 119896 = 4 areslightly lower but the gap is not significant

Comparing between ABC and MDGWO the averagevalue of MDGWO is improved averagely by 1055 by check-ing against the corresponding PSNR values The maximumvalue is increased by 3836 for Surfer Image when 119896 = 2

From the perspective of STDwhich is shown in Table 5 itcan be observed that MDGWO shows obviously advantagesover MTEMO DE ABC and GWOThe smaller the STD isthe smaller the change of fitness functions over the course ofiterations will be that is the better stability of segmentation

Therefore the results show that MDGWO obtains excitingeffect in stability So MDGWOrsquos stability is better

Compared with GWO the average value of MDGWO isimproved averagely by 7352 compared to GWO by check-ing against the corresponding STD values The maximumvalue is increased by 9644 for Baboon Image when 119896 = 3and the minimum value is increased by 2492 for BaboonImage when 119896 = 3

By comparing with MTEMO the average value ofMDGWO is improved averagely by 4788 The maximumvalue is increased by 87 for Lena Image when 119896 = 2 and theminimum value is increased by 06 for Surfer Image when119896 = 3

Comparing between DE andMDGWO the average valueofMDGWO is improved averagely by 9560Themaximum

Computational Intelligence and Neuroscience 13

Table 5 STD metrics of MTEMO DE ABC GWO and MDGWO

Image 119896 MTEMO DE ABC GWO MDGWO

Camerman

2 01849 12592 01235 01697 004623 01649 17601 02122 02287 007584 02943 21995 03003 03627 006595 02999 26579 02784 04278 01964

Lena

2 00969 12902 00349 01536 001263 01665 17822 01300 03570 002644 02800 22104 01872 05965 009395 02515 25992 01827 05946 01570

Baboon

2 00108 12862 00358 02171 001023 00393 17678 00202 04376 001564 01727 22126 01610 02986 011845 02868 26239 02660 05377 02316

Butterfly

2 00903 12708 00750 02179 004653 02207 17429 02952 02712 020364 02482 22368 03906 04808 024155 02900 26571 04818 05096 02684

Maize

2 00356 13501 00218 03571 001883 01222 18612 00901 02225 002704 02305 23230 02605 03903 009275 02502 27461 03834 04584 01677

Sea Star

2 01073 13547 01088 01728 002903 01497 18741 01752 02028 003744 01596 23307 01817 05032 011195 02639 27550 02180 04550 01437

Smiling Girl

2 00377 12516 00318 01834 001113 00955 17311 00577 01712 002424 01966 21878 01094 02508 007815 01550 25989 02768 05273 01302

Surfer

2 00579 13213 00303 02681 002453 01002 18337 01646 03014 009964 03382 23317 01686 03162 014245 03690 27846 02580 03815 01706

value is increased by 9921 for Baboon Image when 119896 =2 The minimum value is increased by 8832 for ButterflyImage when 119896 = 3

Comparing with ABC the average value of MDGWOis improved averagely by 4590 The maximum value isincreased by 7970 for Lena Image when 119896 = 3 and theminimum value is increased by 1293 for Baboon Imagewhen 119896 = 5

As far as MEAN is concerned this parameter presentsthe average value of fitness function over the course ofiterations in Table 6 which reflects the algorithm stability tosome extent But its accuracy of evaluation is relatively lowwhich can only reflect the fuzzy stability of the algorithmThe experiment data is offered here just in response to theparameter provided in literature [20] In comparison withGWO MTEWO DE and ABC in Table 6 it can be safely

assumed that inmost casesMDGWOobtains higherMEANof fitness function Moreover the difference is extremelysmall when MDGWOrsquos MEAN is lower

From the analyses of Tables 3ndash6 together with the visualeffects of Figures 2 3 and 4 it can be observed thatMDGWO method obtains better segmentation effect andhas advantage in optimal process accuracy stability androbustnessThereforeMDGWO is aMT algorithmwith highaccuracy and high segmentation quality

6 Conclusion

This paper proposes a modified discrete grey wolf optimizerwhich is used to optimize the image histograms and realizethe multilevel image segmentation Based on the high effi-ciency of GWO in the course of optimization and stability

14 Computational Intelligence and Neuroscience

Table 6 MEANmetrics of MTEMO DE ABC GWO and MDGWO

Image 119896 MTEMO DE ABC GWO MDGWO

Camerman

2 17584 124212 177638 14634 174713 21976 173764 223059 21107 219194 26586 217520 268409 24927 274805 30506 262505 308328 30436 30548

Lena

2 17831 127730 178139 17809 183963 22120 176428 220832 22074 228564 25999 218784 260615 25318 264475 29787 257311 299664 29252 30381

Baboon

2 17625 127333 176760 17679 186193 22269 175005 221276 22129 229494 26688 219010 263912 26194 269005 30800 259681 303464 30067 30076

Butterfly

2 16681 125796 174205 17425 177233 21242 172545 222209 21585 224984 25179 220176 263794 25267 261905 28611 261795 306533 29492 29899

Maize

2 18631 133566 186316 18604 195423 23565 184245 232496 22941 239394 27529 229813 273931 26936 278425 31535 271709 312127 31023 30694

Sea Star

2 18754 134104 187295 18321 195873 23323 185516 232738 23245 239014 27582 230719 275057 27136 282105 31562 272551 314919 31167 31958

Smiling Girl

2 17334 123892 173129 17136 180353 21904 171339 218601 21253 219804 26040 216541 259904 25050 265975 30089 257130 300225 29870 30574

Surfer

2 18339 130786 183393 18283 188693 23231 181492 232889 23243 241354 27863 230548 278017 27275 274475 31823 274979 317335 31384 31325

this paper successfully applies the MDGWO to the field ofMT by improving the location selection mechanism of 120572 120573and 120575 during the hunting and using weight to optimize thefinal position of prey (best threshold)TheMDGWOmethodnot only obtains better segmentation quality but also showsobvious superiority over GWO MTEMO DE and ABC instability accuracy and multilevel thresholding

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work was supported in part by the National NaturalScience Foundation of China (no 61300239 no 71301081and no 61572261) the Postdoctoral Science Foundation (no

2014M551635 and no 1302085B) the Innovation Project ofGraduate Students Foundation of Jiangsu Province (KYLX150841) the Higher Education Revitalization Plan Foundationof Anhui Province (no 2013SQRL102ZD no 2015xdjy196no 2015jyxm728 no 2016jyxm0774 and no 2016jyxm0777)and Natural Science Fund for Colleges and Universities inJiangsu Province (no16KJB520034) A Project Funded by thePriority Academic Program Development of Jiangsu HigherEducation Institutions (PAPD) and Jiangsu CollaborativeInnovation Center on Atmospheric Environment and Equip-ment Technology (CICAEET)

References

[1] M Sonka V Hlavac and R Boyle Image Processing Analysisand Machine Vision Cengage Learning 2014

[2] S Masood M Sharif A Masood M Yasmin and M RazaldquoA survey on medical image segmentationrdquo Current MedicalImaging Reviews vol 11 no 1 pp 3ndash14 2015

Computational Intelligence and Neuroscience 15

[3] PGhamisiM S Couceiro FM LMartins and J A Benedikts-son ldquoMultilevel image segmentation based on fractional-orderdarwinian particle swarm optimizationrdquo IEEE Transactions onGeoscience and Remote Sensing vol 52 no 5 pp 2382ndash23942014

[4] M Waseem Khan ldquoA survey image segmentation techniquesrdquoInternational Journal of Future Computer and Communicationvol 3 no 2 pp 89ndash93 2014

[5] J Li X Li B Yang and X Sun ldquoSegmentation-based imagecopy-move forgery detection schemerdquo IEEE Transactions onInformation Forensics and Security vol 10 no 3 pp 507ndash5182015

[6] Z Pan J Lei Y Zhang X Sun and S Kwong ldquoFast motionestimation based on content property for low-complexityH265HEVC encoderrdquo IEEE Transactions on Broadcasting vol62 no 3 pp 675ndash684 2016

[7] X Chen S Feng and D Pan ldquoAn improved approach oflung image segmentation based on watershed algorithmrdquo inProceedings of the the 7th International Conference on InternetMultimedia Computing and Service pp 1ndash5 Zhangjiajie ChinaAugust 2015

[8] Y Zheng B Jeon D Xu Q M J Wu and H Zhang ldquoImagesegmentation by generalized hierarchical fuzzy C-means algo-rithmrdquo Journal of Intelligent and Fuzzy Systems vol 28 no 2pp 961ndash973 2015

[9] V Osuna-Enciso E Cuevas and H Sossa ldquoA comparison ofnature inspired algorithms for multi-threshold image segmen-tationrdquo Expert Systems with Applications vol 40 no 4 pp 1213ndash1219 2013

[10] T Kurban P Civicioglu R Kurban and E Besdok ldquoCompari-son of evolutionary and swarmbased computational techniquesfor multilevel color image thresholdingrdquo Applied Soft Comput-ing Journal vol 23 pp 128ndash143 2014

[11] J N Kapur P K Sahoo and A K C Wong ldquoA new methodfor gray-level picture thresholding using the entropy of thehistogramrdquo Computer Vision Graphics and Image Processingvol 29 no 3 pp 273ndash285 1985

[12] N Otsu ldquoA threshold selection method from gray-level his-togramsrdquo Automatica vol 11 no 285ndash296 pp 23ndash27 1975

[13] X Li Z Zhao and H D Cheng ldquoFuzzy entropy thresholdapproach to breast cancer detectionrdquo Information Sciences -Applications vol 4 no 1 pp 49ndash56 1995

[14] J Kittler and J Illingworth ldquoMinimum error thresholdingrdquoPattern Recognition vol 19 no 1 pp 41ndash47 1986

[15] Y Xue S Zhong T Ma and J Cao ldquoA hybrid evolution-ary algorithm for numerical optimization problemrdquo IntelligentAutomation amp Soft Computing vol 21 no 4 pp 473ndash490 2015

[16] P-Y Yin ldquoA fast scheme for optimal thresholding using geneticalgorithmsrdquo Signal Processing vol 72 no 2 pp 85ndash95 1999

[17] W Fujun L Junlan L Shiwei Z Xingyu Z Dawei and TYanling ldquoAn improved adaptive genetic algorithm for imagesegmentation and vision alignment used in microelectronicbondingrdquo IEEEASMETransactions onMechatronics vol 19 no3 pp 916ndash923 2014

[18] S Banerjee and N D Jana ldquoBi level kapurs entropy basedimage segmentation using particle swarm optimizationrdquo inProceedings of the 3rd International Conference on ComputerCommunication Control and InformationTechnology (C3IT rsquo15)pp 1ndash4 Hooghly India February 2015

[19] M-H Horng ldquoMultilevel thresholding selection based on theartificial bee colony algorithm for image segmentationrdquo ExpertSystems with Applications vol 38 no 11 pp 13785ndash13791 2011

[20] D Oliva E Cuevas G Pajares D Zaldivar and V OsunaldquoA multilevel thresholding algorithm using electromagnetismoptimizationrdquo Neurocomputing vol 139 pp 357ndash381 2014

[21] S Sarkar G R Patra and S Das ldquoA differential evolutionbased approach for multilevel image segmentation using mini-mum cross entropy thresholdingrdquo in Swarm Evolutionary andMemetic Computing pp 51ndash58 Springer Berlin Germany 2011

[22] Y Xue Y Zhuang T Ni S Ni and X Wen ldquoSelf-adaptivelearning based discrete differential evolution algorithm forsolving CJWTA problemrdquo Journal of Systems Engineering andElectronics vol 25 no 1 pp 59ndash68 2014

[23] S Agrawal R Panda S Bhuyan and B K Panigrahi ldquoTsallisentropy based optimal multilevel thresholding using cuckoosearch algorithmrdquo Swarm and Evolutionary Computation vol11 pp 16ndash30 2013

[24] PD Sathya andRKayalvizhi ldquoOptimalmultilevel thresholdingusing bacterial foraging algorithmrdquo Expert Systems with Appli-cations vol 38 no 12 pp 15549ndash15564 2011

[25] S Ayas H Dogan E Gedikli and M Ekinci ldquoMicroscopicimage segmentation based on firefly algorithm for detectionof tuberculosis bacteriardquo in Proceedings of the 23rd SignalProcessing and Communications Applications Conference (SIUrsquo15) pp 851ndash854 Malatya Turkey May 2015

[26] S Mirjalili S M Mirjalili and A Lewis ldquoGrey wolf optimizerrdquoAdvances in Engineering Software vol 69 pp 46ndash61 2014

[27] B Akay ldquoA study on particle swarm optimization and artificialbee colony algorithms for multilevel thresholdingrdquo Applied SoftComputing vol 13 no 6 pp 3066ndash3091 2013

[28] A K Bhandari A Kumar and G K Singh ldquoModified artificialbee colony based computationally efficient multilevel thresh-olding for satellite image segmentation using Kapurrsquos Otsu andTsallis functionsrdquo Expert Systems with Applications vol 42 no3 pp 1573ndash1601 2015

[29] P Ghamisi M S Couceiro J A Benediktsson and N M FFerreira ldquoAn efficientmethod for segmentation of images basedon fractional calculus and natural selectionrdquo Expert Systemswith Applications vol 39 no 16 pp 12407ndash12417 2012

[30] L Li L Sun W Kang J Guo C Han and S Li ldquoFuzzymultilevel image thresholding based on modified discrete greywolf optimizer and local information aggregationrdquo IEEE Accessvol 4 pp 6438ndash6450 2016

[31] H-S Wu F-M Zhang and L-S Wu ldquoNew swarm intelligencealgorithm-wolf pack algorithmrdquo Xi Tong Gong Cheng Yu DianZi Ji ShuSystems Engineering and Electronics vol 35 no 11 pp2430ndash2438 2013

[32] H Wu and F Zhang ldquoA uncultivated wolf pack algorithm forhigh-dimensional functions and its application in parametersoptimization of PID controllerrdquo in Proceedings of the IEEECongress on Evolutionary Computation (CEC rsquo14) pp 1477ndash1482Beijing China July 2014

[33] H-S Wu and F-M Zhang ldquoWolf pack algorithm for uncon-strained global optimizationrdquo Mathematical Problems in Engi-neering vol 2014 Article ID 465082 17 pages 2014

[34] Q Zhou and Y Zhou ldquoWolf colony search algorithm based onleader strategyrdquo Application Research of Computers vol 9 pp2629ndash2632 2013

[35] G M Komaki and V Kayvanfar ldquoGrey Wolf Optimizer algo-rithm for the two-stage assembly flow shop scheduling problemwith release timerdquo Journal of Computational Science vol 8 pp109ndash120 2015

16 Computational Intelligence and Neuroscience

[36] L I Wong M H Sulaiman M R Mohamed and M SHong ldquoGrey Wolf Optimizer for solving economic dispatchproblemsrdquo in Proceedings of the IEEE International Conferenceon Power and Energy (PECon rsquo14) pp 150ndash154 KuchingMalaysia December 2014

[37] A Chaman-Motlagh ldquoSuperdefect photonic crystal filter opti-mization using Grey Wolf Optimizerrdquo IEEE Photonics Technol-ogy Letters vol 27 no 22 pp 2355ndash2358 2015

[38] P Q Dzung N T Tien N Dinh Tuyen and H Lee ldquoSelectiveharmonic elimination for cascaded multilevel inverters usinggrey wolf optimizer algorithmrdquo in Proceedings of the 9thInternational Conference on Power Electronics and ECCE Asia(ICPE rsquo15-ECCE Asia) June 2015

[39] N Muangkote K Sunat and S Chiewchanwattana ldquoAnimproved grey wolf optimizer for training q-Gaussian RadialBasis Functional-link netsrdquo in Proceedings of the InternationalComputer Science and Engineering Conference (ICSEC rsquo14) pp209ndash214 Khon Kaen Thailand August 2014

[40] A Zhu C Xu Z Li J Wu and Z Liu ldquoHybridizing grey Wolfoptimization with differential evolution for global optimizationand test scheduling for 3D stacked SoCrdquo Journal of SystemsEngineering and Electronics vol 26 no 2 pp 317ndash328 2015

[41] P ArbelaezMMaire C Fowlkes and JMalik ldquoContour detec-tion and hierarchical image segmentationrdquo IEEE Transactionson Pattern Analysis and Machine Intelligence vol 33 no 5 pp898ndash916 2011

Submit your manuscripts athttpswwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience 13

Table 5 STD metrics of MTEMO DE ABC GWO and MDGWO

Image 119896 MTEMO DE ABC GWO MDGWO

Camerman

2 01849 12592 01235 01697 004623 01649 17601 02122 02287 007584 02943 21995 03003 03627 006595 02999 26579 02784 04278 01964

Lena

2 00969 12902 00349 01536 001263 01665 17822 01300 03570 002644 02800 22104 01872 05965 009395 02515 25992 01827 05946 01570

Baboon

2 00108 12862 00358 02171 001023 00393 17678 00202 04376 001564 01727 22126 01610 02986 011845 02868 26239 02660 05377 02316

Butterfly

2 00903 12708 00750 02179 004653 02207 17429 02952 02712 020364 02482 22368 03906 04808 024155 02900 26571 04818 05096 02684

Maize

2 00356 13501 00218 03571 001883 01222 18612 00901 02225 002704 02305 23230 02605 03903 009275 02502 27461 03834 04584 01677

Sea Star

2 01073 13547 01088 01728 002903 01497 18741 01752 02028 003744 01596 23307 01817 05032 011195 02639 27550 02180 04550 01437

Smiling Girl

2 00377 12516 00318 01834 001113 00955 17311 00577 01712 002424 01966 21878 01094 02508 007815 01550 25989 02768 05273 01302

Surfer

2 00579 13213 00303 02681 002453 01002 18337 01646 03014 009964 03382 23317 01686 03162 014245 03690 27846 02580 03815 01706

value is increased by 9921 for Baboon Image when 119896 =2 The minimum value is increased by 8832 for ButterflyImage when 119896 = 3

Comparing with ABC the average value of MDGWOis improved averagely by 4590 The maximum value isincreased by 7970 for Lena Image when 119896 = 3 and theminimum value is increased by 1293 for Baboon Imagewhen 119896 = 5

As far as MEAN is concerned this parameter presentsthe average value of fitness function over the course ofiterations in Table 6 which reflects the algorithm stability tosome extent But its accuracy of evaluation is relatively lowwhich can only reflect the fuzzy stability of the algorithmThe experiment data is offered here just in response to theparameter provided in literature [20] In comparison withGWO MTEWO DE and ABC in Table 6 it can be safely

assumed that inmost casesMDGWOobtains higherMEANof fitness function Moreover the difference is extremelysmall when MDGWOrsquos MEAN is lower

From the analyses of Tables 3ndash6 together with the visualeffects of Figures 2 3 and 4 it can be observed thatMDGWO method obtains better segmentation effect andhas advantage in optimal process accuracy stability androbustnessThereforeMDGWO is aMT algorithmwith highaccuracy and high segmentation quality

6 Conclusion

This paper proposes a modified discrete grey wolf optimizerwhich is used to optimize the image histograms and realizethe multilevel image segmentation Based on the high effi-ciency of GWO in the course of optimization and stability

14 Computational Intelligence and Neuroscience

Table 6 MEANmetrics of MTEMO DE ABC GWO and MDGWO

Image 119896 MTEMO DE ABC GWO MDGWO

Camerman

2 17584 124212 177638 14634 174713 21976 173764 223059 21107 219194 26586 217520 268409 24927 274805 30506 262505 308328 30436 30548

Lena

2 17831 127730 178139 17809 183963 22120 176428 220832 22074 228564 25999 218784 260615 25318 264475 29787 257311 299664 29252 30381

Baboon

2 17625 127333 176760 17679 186193 22269 175005 221276 22129 229494 26688 219010 263912 26194 269005 30800 259681 303464 30067 30076

Butterfly

2 16681 125796 174205 17425 177233 21242 172545 222209 21585 224984 25179 220176 263794 25267 261905 28611 261795 306533 29492 29899

Maize

2 18631 133566 186316 18604 195423 23565 184245 232496 22941 239394 27529 229813 273931 26936 278425 31535 271709 312127 31023 30694

Sea Star

2 18754 134104 187295 18321 195873 23323 185516 232738 23245 239014 27582 230719 275057 27136 282105 31562 272551 314919 31167 31958

Smiling Girl

2 17334 123892 173129 17136 180353 21904 171339 218601 21253 219804 26040 216541 259904 25050 265975 30089 257130 300225 29870 30574

Surfer

2 18339 130786 183393 18283 188693 23231 181492 232889 23243 241354 27863 230548 278017 27275 274475 31823 274979 317335 31384 31325

this paper successfully applies the MDGWO to the field ofMT by improving the location selection mechanism of 120572 120573and 120575 during the hunting and using weight to optimize thefinal position of prey (best threshold)TheMDGWOmethodnot only obtains better segmentation quality but also showsobvious superiority over GWO MTEMO DE and ABC instability accuracy and multilevel thresholding

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work was supported in part by the National NaturalScience Foundation of China (no 61300239 no 71301081and no 61572261) the Postdoctoral Science Foundation (no

2014M551635 and no 1302085B) the Innovation Project ofGraduate Students Foundation of Jiangsu Province (KYLX150841) the Higher Education Revitalization Plan Foundationof Anhui Province (no 2013SQRL102ZD no 2015xdjy196no 2015jyxm728 no 2016jyxm0774 and no 2016jyxm0777)and Natural Science Fund for Colleges and Universities inJiangsu Province (no16KJB520034) A Project Funded by thePriority Academic Program Development of Jiangsu HigherEducation Institutions (PAPD) and Jiangsu CollaborativeInnovation Center on Atmospheric Environment and Equip-ment Technology (CICAEET)

References

[1] M Sonka V Hlavac and R Boyle Image Processing Analysisand Machine Vision Cengage Learning 2014

[2] S Masood M Sharif A Masood M Yasmin and M RazaldquoA survey on medical image segmentationrdquo Current MedicalImaging Reviews vol 11 no 1 pp 3ndash14 2015

Computational Intelligence and Neuroscience 15

[3] PGhamisiM S Couceiro FM LMartins and J A Benedikts-son ldquoMultilevel image segmentation based on fractional-orderdarwinian particle swarm optimizationrdquo IEEE Transactions onGeoscience and Remote Sensing vol 52 no 5 pp 2382ndash23942014

[4] M Waseem Khan ldquoA survey image segmentation techniquesrdquoInternational Journal of Future Computer and Communicationvol 3 no 2 pp 89ndash93 2014

[5] J Li X Li B Yang and X Sun ldquoSegmentation-based imagecopy-move forgery detection schemerdquo IEEE Transactions onInformation Forensics and Security vol 10 no 3 pp 507ndash5182015

[6] Z Pan J Lei Y Zhang X Sun and S Kwong ldquoFast motionestimation based on content property for low-complexityH265HEVC encoderrdquo IEEE Transactions on Broadcasting vol62 no 3 pp 675ndash684 2016

[7] X Chen S Feng and D Pan ldquoAn improved approach oflung image segmentation based on watershed algorithmrdquo inProceedings of the the 7th International Conference on InternetMultimedia Computing and Service pp 1ndash5 Zhangjiajie ChinaAugust 2015

[8] Y Zheng B Jeon D Xu Q M J Wu and H Zhang ldquoImagesegmentation by generalized hierarchical fuzzy C-means algo-rithmrdquo Journal of Intelligent and Fuzzy Systems vol 28 no 2pp 961ndash973 2015

[9] V Osuna-Enciso E Cuevas and H Sossa ldquoA comparison ofnature inspired algorithms for multi-threshold image segmen-tationrdquo Expert Systems with Applications vol 40 no 4 pp 1213ndash1219 2013

[10] T Kurban P Civicioglu R Kurban and E Besdok ldquoCompari-son of evolutionary and swarmbased computational techniquesfor multilevel color image thresholdingrdquo Applied Soft Comput-ing Journal vol 23 pp 128ndash143 2014

[11] J N Kapur P K Sahoo and A K C Wong ldquoA new methodfor gray-level picture thresholding using the entropy of thehistogramrdquo Computer Vision Graphics and Image Processingvol 29 no 3 pp 273ndash285 1985

[12] N Otsu ldquoA threshold selection method from gray-level his-togramsrdquo Automatica vol 11 no 285ndash296 pp 23ndash27 1975

[13] X Li Z Zhao and H D Cheng ldquoFuzzy entropy thresholdapproach to breast cancer detectionrdquo Information Sciences -Applications vol 4 no 1 pp 49ndash56 1995

[14] J Kittler and J Illingworth ldquoMinimum error thresholdingrdquoPattern Recognition vol 19 no 1 pp 41ndash47 1986

[15] Y Xue S Zhong T Ma and J Cao ldquoA hybrid evolution-ary algorithm for numerical optimization problemrdquo IntelligentAutomation amp Soft Computing vol 21 no 4 pp 473ndash490 2015

[16] P-Y Yin ldquoA fast scheme for optimal thresholding using geneticalgorithmsrdquo Signal Processing vol 72 no 2 pp 85ndash95 1999

[17] W Fujun L Junlan L Shiwei Z Xingyu Z Dawei and TYanling ldquoAn improved adaptive genetic algorithm for imagesegmentation and vision alignment used in microelectronicbondingrdquo IEEEASMETransactions onMechatronics vol 19 no3 pp 916ndash923 2014

[18] S Banerjee and N D Jana ldquoBi level kapurs entropy basedimage segmentation using particle swarm optimizationrdquo inProceedings of the 3rd International Conference on ComputerCommunication Control and InformationTechnology (C3IT rsquo15)pp 1ndash4 Hooghly India February 2015

[19] M-H Horng ldquoMultilevel thresholding selection based on theartificial bee colony algorithm for image segmentationrdquo ExpertSystems with Applications vol 38 no 11 pp 13785ndash13791 2011

[20] D Oliva E Cuevas G Pajares D Zaldivar and V OsunaldquoA multilevel thresholding algorithm using electromagnetismoptimizationrdquo Neurocomputing vol 139 pp 357ndash381 2014

[21] S Sarkar G R Patra and S Das ldquoA differential evolutionbased approach for multilevel image segmentation using mini-mum cross entropy thresholdingrdquo in Swarm Evolutionary andMemetic Computing pp 51ndash58 Springer Berlin Germany 2011

[22] Y Xue Y Zhuang T Ni S Ni and X Wen ldquoSelf-adaptivelearning based discrete differential evolution algorithm forsolving CJWTA problemrdquo Journal of Systems Engineering andElectronics vol 25 no 1 pp 59ndash68 2014

[23] S Agrawal R Panda S Bhuyan and B K Panigrahi ldquoTsallisentropy based optimal multilevel thresholding using cuckoosearch algorithmrdquo Swarm and Evolutionary Computation vol11 pp 16ndash30 2013

[24] PD Sathya andRKayalvizhi ldquoOptimalmultilevel thresholdingusing bacterial foraging algorithmrdquo Expert Systems with Appli-cations vol 38 no 12 pp 15549ndash15564 2011

[25] S Ayas H Dogan E Gedikli and M Ekinci ldquoMicroscopicimage segmentation based on firefly algorithm for detectionof tuberculosis bacteriardquo in Proceedings of the 23rd SignalProcessing and Communications Applications Conference (SIUrsquo15) pp 851ndash854 Malatya Turkey May 2015

[26] S Mirjalili S M Mirjalili and A Lewis ldquoGrey wolf optimizerrdquoAdvances in Engineering Software vol 69 pp 46ndash61 2014

[27] B Akay ldquoA study on particle swarm optimization and artificialbee colony algorithms for multilevel thresholdingrdquo Applied SoftComputing vol 13 no 6 pp 3066ndash3091 2013

[28] A K Bhandari A Kumar and G K Singh ldquoModified artificialbee colony based computationally efficient multilevel thresh-olding for satellite image segmentation using Kapurrsquos Otsu andTsallis functionsrdquo Expert Systems with Applications vol 42 no3 pp 1573ndash1601 2015

[29] P Ghamisi M S Couceiro J A Benediktsson and N M FFerreira ldquoAn efficientmethod for segmentation of images basedon fractional calculus and natural selectionrdquo Expert Systemswith Applications vol 39 no 16 pp 12407ndash12417 2012

[30] L Li L Sun W Kang J Guo C Han and S Li ldquoFuzzymultilevel image thresholding based on modified discrete greywolf optimizer and local information aggregationrdquo IEEE Accessvol 4 pp 6438ndash6450 2016

[31] H-S Wu F-M Zhang and L-S Wu ldquoNew swarm intelligencealgorithm-wolf pack algorithmrdquo Xi Tong Gong Cheng Yu DianZi Ji ShuSystems Engineering and Electronics vol 35 no 11 pp2430ndash2438 2013

[32] H Wu and F Zhang ldquoA uncultivated wolf pack algorithm forhigh-dimensional functions and its application in parametersoptimization of PID controllerrdquo in Proceedings of the IEEECongress on Evolutionary Computation (CEC rsquo14) pp 1477ndash1482Beijing China July 2014

[33] H-S Wu and F-M Zhang ldquoWolf pack algorithm for uncon-strained global optimizationrdquo Mathematical Problems in Engi-neering vol 2014 Article ID 465082 17 pages 2014

[34] Q Zhou and Y Zhou ldquoWolf colony search algorithm based onleader strategyrdquo Application Research of Computers vol 9 pp2629ndash2632 2013

[35] G M Komaki and V Kayvanfar ldquoGrey Wolf Optimizer algo-rithm for the two-stage assembly flow shop scheduling problemwith release timerdquo Journal of Computational Science vol 8 pp109ndash120 2015

16 Computational Intelligence and Neuroscience

[36] L I Wong M H Sulaiman M R Mohamed and M SHong ldquoGrey Wolf Optimizer for solving economic dispatchproblemsrdquo in Proceedings of the IEEE International Conferenceon Power and Energy (PECon rsquo14) pp 150ndash154 KuchingMalaysia December 2014

[37] A Chaman-Motlagh ldquoSuperdefect photonic crystal filter opti-mization using Grey Wolf Optimizerrdquo IEEE Photonics Technol-ogy Letters vol 27 no 22 pp 2355ndash2358 2015

[38] P Q Dzung N T Tien N Dinh Tuyen and H Lee ldquoSelectiveharmonic elimination for cascaded multilevel inverters usinggrey wolf optimizer algorithmrdquo in Proceedings of the 9thInternational Conference on Power Electronics and ECCE Asia(ICPE rsquo15-ECCE Asia) June 2015

[39] N Muangkote K Sunat and S Chiewchanwattana ldquoAnimproved grey wolf optimizer for training q-Gaussian RadialBasis Functional-link netsrdquo in Proceedings of the InternationalComputer Science and Engineering Conference (ICSEC rsquo14) pp209ndash214 Khon Kaen Thailand August 2014

[40] A Zhu C Xu Z Li J Wu and Z Liu ldquoHybridizing grey Wolfoptimization with differential evolution for global optimizationand test scheduling for 3D stacked SoCrdquo Journal of SystemsEngineering and Electronics vol 26 no 2 pp 317ndash328 2015

[41] P ArbelaezMMaire C Fowlkes and JMalik ldquoContour detec-tion and hierarchical image segmentationrdquo IEEE Transactionson Pattern Analysis and Machine Intelligence vol 33 no 5 pp898ndash916 2011

Submit your manuscripts athttpswwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

14 Computational Intelligence and Neuroscience

Table 6 MEANmetrics of MTEMO DE ABC GWO and MDGWO

Image 119896 MTEMO DE ABC GWO MDGWO

Camerman

2 17584 124212 177638 14634 174713 21976 173764 223059 21107 219194 26586 217520 268409 24927 274805 30506 262505 308328 30436 30548

Lena

2 17831 127730 178139 17809 183963 22120 176428 220832 22074 228564 25999 218784 260615 25318 264475 29787 257311 299664 29252 30381

Baboon

2 17625 127333 176760 17679 186193 22269 175005 221276 22129 229494 26688 219010 263912 26194 269005 30800 259681 303464 30067 30076

Butterfly

2 16681 125796 174205 17425 177233 21242 172545 222209 21585 224984 25179 220176 263794 25267 261905 28611 261795 306533 29492 29899

Maize

2 18631 133566 186316 18604 195423 23565 184245 232496 22941 239394 27529 229813 273931 26936 278425 31535 271709 312127 31023 30694

Sea Star

2 18754 134104 187295 18321 195873 23323 185516 232738 23245 239014 27582 230719 275057 27136 282105 31562 272551 314919 31167 31958

Smiling Girl

2 17334 123892 173129 17136 180353 21904 171339 218601 21253 219804 26040 216541 259904 25050 265975 30089 257130 300225 29870 30574

Surfer

2 18339 130786 183393 18283 188693 23231 181492 232889 23243 241354 27863 230548 278017 27275 274475 31823 274979 317335 31384 31325

this paper successfully applies the MDGWO to the field ofMT by improving the location selection mechanism of 120572 120573and 120575 during the hunting and using weight to optimize thefinal position of prey (best threshold)TheMDGWOmethodnot only obtains better segmentation quality but also showsobvious superiority over GWO MTEMO DE and ABC instability accuracy and multilevel thresholding

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work was supported in part by the National NaturalScience Foundation of China (no 61300239 no 71301081and no 61572261) the Postdoctoral Science Foundation (no

2014M551635 and no 1302085B) the Innovation Project ofGraduate Students Foundation of Jiangsu Province (KYLX150841) the Higher Education Revitalization Plan Foundationof Anhui Province (no 2013SQRL102ZD no 2015xdjy196no 2015jyxm728 no 2016jyxm0774 and no 2016jyxm0777)and Natural Science Fund for Colleges and Universities inJiangsu Province (no16KJB520034) A Project Funded by thePriority Academic Program Development of Jiangsu HigherEducation Institutions (PAPD) and Jiangsu CollaborativeInnovation Center on Atmospheric Environment and Equip-ment Technology (CICAEET)

References

[1] M Sonka V Hlavac and R Boyle Image Processing Analysisand Machine Vision Cengage Learning 2014

[2] S Masood M Sharif A Masood M Yasmin and M RazaldquoA survey on medical image segmentationrdquo Current MedicalImaging Reviews vol 11 no 1 pp 3ndash14 2015

Computational Intelligence and Neuroscience 15

[3] PGhamisiM S Couceiro FM LMartins and J A Benedikts-son ldquoMultilevel image segmentation based on fractional-orderdarwinian particle swarm optimizationrdquo IEEE Transactions onGeoscience and Remote Sensing vol 52 no 5 pp 2382ndash23942014

[4] M Waseem Khan ldquoA survey image segmentation techniquesrdquoInternational Journal of Future Computer and Communicationvol 3 no 2 pp 89ndash93 2014

[5] J Li X Li B Yang and X Sun ldquoSegmentation-based imagecopy-move forgery detection schemerdquo IEEE Transactions onInformation Forensics and Security vol 10 no 3 pp 507ndash5182015

[6] Z Pan J Lei Y Zhang X Sun and S Kwong ldquoFast motionestimation based on content property for low-complexityH265HEVC encoderrdquo IEEE Transactions on Broadcasting vol62 no 3 pp 675ndash684 2016

[7] X Chen S Feng and D Pan ldquoAn improved approach oflung image segmentation based on watershed algorithmrdquo inProceedings of the the 7th International Conference on InternetMultimedia Computing and Service pp 1ndash5 Zhangjiajie ChinaAugust 2015

[8] Y Zheng B Jeon D Xu Q M J Wu and H Zhang ldquoImagesegmentation by generalized hierarchical fuzzy C-means algo-rithmrdquo Journal of Intelligent and Fuzzy Systems vol 28 no 2pp 961ndash973 2015

[9] V Osuna-Enciso E Cuevas and H Sossa ldquoA comparison ofnature inspired algorithms for multi-threshold image segmen-tationrdquo Expert Systems with Applications vol 40 no 4 pp 1213ndash1219 2013

[10] T Kurban P Civicioglu R Kurban and E Besdok ldquoCompari-son of evolutionary and swarmbased computational techniquesfor multilevel color image thresholdingrdquo Applied Soft Comput-ing Journal vol 23 pp 128ndash143 2014

[11] J N Kapur P K Sahoo and A K C Wong ldquoA new methodfor gray-level picture thresholding using the entropy of thehistogramrdquo Computer Vision Graphics and Image Processingvol 29 no 3 pp 273ndash285 1985

[12] N Otsu ldquoA threshold selection method from gray-level his-togramsrdquo Automatica vol 11 no 285ndash296 pp 23ndash27 1975

[13] X Li Z Zhao and H D Cheng ldquoFuzzy entropy thresholdapproach to breast cancer detectionrdquo Information Sciences -Applications vol 4 no 1 pp 49ndash56 1995

[14] J Kittler and J Illingworth ldquoMinimum error thresholdingrdquoPattern Recognition vol 19 no 1 pp 41ndash47 1986

[15] Y Xue S Zhong T Ma and J Cao ldquoA hybrid evolution-ary algorithm for numerical optimization problemrdquo IntelligentAutomation amp Soft Computing vol 21 no 4 pp 473ndash490 2015

[16] P-Y Yin ldquoA fast scheme for optimal thresholding using geneticalgorithmsrdquo Signal Processing vol 72 no 2 pp 85ndash95 1999

[17] W Fujun L Junlan L Shiwei Z Xingyu Z Dawei and TYanling ldquoAn improved adaptive genetic algorithm for imagesegmentation and vision alignment used in microelectronicbondingrdquo IEEEASMETransactions onMechatronics vol 19 no3 pp 916ndash923 2014

[18] S Banerjee and N D Jana ldquoBi level kapurs entropy basedimage segmentation using particle swarm optimizationrdquo inProceedings of the 3rd International Conference on ComputerCommunication Control and InformationTechnology (C3IT rsquo15)pp 1ndash4 Hooghly India February 2015

[19] M-H Horng ldquoMultilevel thresholding selection based on theartificial bee colony algorithm for image segmentationrdquo ExpertSystems with Applications vol 38 no 11 pp 13785ndash13791 2011

[20] D Oliva E Cuevas G Pajares D Zaldivar and V OsunaldquoA multilevel thresholding algorithm using electromagnetismoptimizationrdquo Neurocomputing vol 139 pp 357ndash381 2014

[21] S Sarkar G R Patra and S Das ldquoA differential evolutionbased approach for multilevel image segmentation using mini-mum cross entropy thresholdingrdquo in Swarm Evolutionary andMemetic Computing pp 51ndash58 Springer Berlin Germany 2011

[22] Y Xue Y Zhuang T Ni S Ni and X Wen ldquoSelf-adaptivelearning based discrete differential evolution algorithm forsolving CJWTA problemrdquo Journal of Systems Engineering andElectronics vol 25 no 1 pp 59ndash68 2014

[23] S Agrawal R Panda S Bhuyan and B K Panigrahi ldquoTsallisentropy based optimal multilevel thresholding using cuckoosearch algorithmrdquo Swarm and Evolutionary Computation vol11 pp 16ndash30 2013

[24] PD Sathya andRKayalvizhi ldquoOptimalmultilevel thresholdingusing bacterial foraging algorithmrdquo Expert Systems with Appli-cations vol 38 no 12 pp 15549ndash15564 2011

[25] S Ayas H Dogan E Gedikli and M Ekinci ldquoMicroscopicimage segmentation based on firefly algorithm for detectionof tuberculosis bacteriardquo in Proceedings of the 23rd SignalProcessing and Communications Applications Conference (SIUrsquo15) pp 851ndash854 Malatya Turkey May 2015

[26] S Mirjalili S M Mirjalili and A Lewis ldquoGrey wolf optimizerrdquoAdvances in Engineering Software vol 69 pp 46ndash61 2014

[27] B Akay ldquoA study on particle swarm optimization and artificialbee colony algorithms for multilevel thresholdingrdquo Applied SoftComputing vol 13 no 6 pp 3066ndash3091 2013

[28] A K Bhandari A Kumar and G K Singh ldquoModified artificialbee colony based computationally efficient multilevel thresh-olding for satellite image segmentation using Kapurrsquos Otsu andTsallis functionsrdquo Expert Systems with Applications vol 42 no3 pp 1573ndash1601 2015

[29] P Ghamisi M S Couceiro J A Benediktsson and N M FFerreira ldquoAn efficientmethod for segmentation of images basedon fractional calculus and natural selectionrdquo Expert Systemswith Applications vol 39 no 16 pp 12407ndash12417 2012

[30] L Li L Sun W Kang J Guo C Han and S Li ldquoFuzzymultilevel image thresholding based on modified discrete greywolf optimizer and local information aggregationrdquo IEEE Accessvol 4 pp 6438ndash6450 2016

[31] H-S Wu F-M Zhang and L-S Wu ldquoNew swarm intelligencealgorithm-wolf pack algorithmrdquo Xi Tong Gong Cheng Yu DianZi Ji ShuSystems Engineering and Electronics vol 35 no 11 pp2430ndash2438 2013

[32] H Wu and F Zhang ldquoA uncultivated wolf pack algorithm forhigh-dimensional functions and its application in parametersoptimization of PID controllerrdquo in Proceedings of the IEEECongress on Evolutionary Computation (CEC rsquo14) pp 1477ndash1482Beijing China July 2014

[33] H-S Wu and F-M Zhang ldquoWolf pack algorithm for uncon-strained global optimizationrdquo Mathematical Problems in Engi-neering vol 2014 Article ID 465082 17 pages 2014

[34] Q Zhou and Y Zhou ldquoWolf colony search algorithm based onleader strategyrdquo Application Research of Computers vol 9 pp2629ndash2632 2013

[35] G M Komaki and V Kayvanfar ldquoGrey Wolf Optimizer algo-rithm for the two-stage assembly flow shop scheduling problemwith release timerdquo Journal of Computational Science vol 8 pp109ndash120 2015

16 Computational Intelligence and Neuroscience

[36] L I Wong M H Sulaiman M R Mohamed and M SHong ldquoGrey Wolf Optimizer for solving economic dispatchproblemsrdquo in Proceedings of the IEEE International Conferenceon Power and Energy (PECon rsquo14) pp 150ndash154 KuchingMalaysia December 2014

[37] A Chaman-Motlagh ldquoSuperdefect photonic crystal filter opti-mization using Grey Wolf Optimizerrdquo IEEE Photonics Technol-ogy Letters vol 27 no 22 pp 2355ndash2358 2015

[38] P Q Dzung N T Tien N Dinh Tuyen and H Lee ldquoSelectiveharmonic elimination for cascaded multilevel inverters usinggrey wolf optimizer algorithmrdquo in Proceedings of the 9thInternational Conference on Power Electronics and ECCE Asia(ICPE rsquo15-ECCE Asia) June 2015

[39] N Muangkote K Sunat and S Chiewchanwattana ldquoAnimproved grey wolf optimizer for training q-Gaussian RadialBasis Functional-link netsrdquo in Proceedings of the InternationalComputer Science and Engineering Conference (ICSEC rsquo14) pp209ndash214 Khon Kaen Thailand August 2014

[40] A Zhu C Xu Z Li J Wu and Z Liu ldquoHybridizing grey Wolfoptimization with differential evolution for global optimizationand test scheduling for 3D stacked SoCrdquo Journal of SystemsEngineering and Electronics vol 26 no 2 pp 317ndash328 2015

[41] P ArbelaezMMaire C Fowlkes and JMalik ldquoContour detec-tion and hierarchical image segmentationrdquo IEEE Transactionson Pattern Analysis and Machine Intelligence vol 33 no 5 pp898ndash916 2011

Submit your manuscripts athttpswwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience 15

[3] PGhamisiM S Couceiro FM LMartins and J A Benedikts-son ldquoMultilevel image segmentation based on fractional-orderdarwinian particle swarm optimizationrdquo IEEE Transactions onGeoscience and Remote Sensing vol 52 no 5 pp 2382ndash23942014

[4] M Waseem Khan ldquoA survey image segmentation techniquesrdquoInternational Journal of Future Computer and Communicationvol 3 no 2 pp 89ndash93 2014

[5] J Li X Li B Yang and X Sun ldquoSegmentation-based imagecopy-move forgery detection schemerdquo IEEE Transactions onInformation Forensics and Security vol 10 no 3 pp 507ndash5182015

[6] Z Pan J Lei Y Zhang X Sun and S Kwong ldquoFast motionestimation based on content property for low-complexityH265HEVC encoderrdquo IEEE Transactions on Broadcasting vol62 no 3 pp 675ndash684 2016

[7] X Chen S Feng and D Pan ldquoAn improved approach oflung image segmentation based on watershed algorithmrdquo inProceedings of the the 7th International Conference on InternetMultimedia Computing and Service pp 1ndash5 Zhangjiajie ChinaAugust 2015

[8] Y Zheng B Jeon D Xu Q M J Wu and H Zhang ldquoImagesegmentation by generalized hierarchical fuzzy C-means algo-rithmrdquo Journal of Intelligent and Fuzzy Systems vol 28 no 2pp 961ndash973 2015

[9] V Osuna-Enciso E Cuevas and H Sossa ldquoA comparison ofnature inspired algorithms for multi-threshold image segmen-tationrdquo Expert Systems with Applications vol 40 no 4 pp 1213ndash1219 2013

[10] T Kurban P Civicioglu R Kurban and E Besdok ldquoCompari-son of evolutionary and swarmbased computational techniquesfor multilevel color image thresholdingrdquo Applied Soft Comput-ing Journal vol 23 pp 128ndash143 2014

[11] J N Kapur P K Sahoo and A K C Wong ldquoA new methodfor gray-level picture thresholding using the entropy of thehistogramrdquo Computer Vision Graphics and Image Processingvol 29 no 3 pp 273ndash285 1985

[12] N Otsu ldquoA threshold selection method from gray-level his-togramsrdquo Automatica vol 11 no 285ndash296 pp 23ndash27 1975

[13] X Li Z Zhao and H D Cheng ldquoFuzzy entropy thresholdapproach to breast cancer detectionrdquo Information Sciences -Applications vol 4 no 1 pp 49ndash56 1995

[14] J Kittler and J Illingworth ldquoMinimum error thresholdingrdquoPattern Recognition vol 19 no 1 pp 41ndash47 1986

[15] Y Xue S Zhong T Ma and J Cao ldquoA hybrid evolution-ary algorithm for numerical optimization problemrdquo IntelligentAutomation amp Soft Computing vol 21 no 4 pp 473ndash490 2015

[16] P-Y Yin ldquoA fast scheme for optimal thresholding using geneticalgorithmsrdquo Signal Processing vol 72 no 2 pp 85ndash95 1999

[17] W Fujun L Junlan L Shiwei Z Xingyu Z Dawei and TYanling ldquoAn improved adaptive genetic algorithm for imagesegmentation and vision alignment used in microelectronicbondingrdquo IEEEASMETransactions onMechatronics vol 19 no3 pp 916ndash923 2014

[18] S Banerjee and N D Jana ldquoBi level kapurs entropy basedimage segmentation using particle swarm optimizationrdquo inProceedings of the 3rd International Conference on ComputerCommunication Control and InformationTechnology (C3IT rsquo15)pp 1ndash4 Hooghly India February 2015

[19] M-H Horng ldquoMultilevel thresholding selection based on theartificial bee colony algorithm for image segmentationrdquo ExpertSystems with Applications vol 38 no 11 pp 13785ndash13791 2011

[20] D Oliva E Cuevas G Pajares D Zaldivar and V OsunaldquoA multilevel thresholding algorithm using electromagnetismoptimizationrdquo Neurocomputing vol 139 pp 357ndash381 2014

[21] S Sarkar G R Patra and S Das ldquoA differential evolutionbased approach for multilevel image segmentation using mini-mum cross entropy thresholdingrdquo in Swarm Evolutionary andMemetic Computing pp 51ndash58 Springer Berlin Germany 2011

[22] Y Xue Y Zhuang T Ni S Ni and X Wen ldquoSelf-adaptivelearning based discrete differential evolution algorithm forsolving CJWTA problemrdquo Journal of Systems Engineering andElectronics vol 25 no 1 pp 59ndash68 2014

[23] S Agrawal R Panda S Bhuyan and B K Panigrahi ldquoTsallisentropy based optimal multilevel thresholding using cuckoosearch algorithmrdquo Swarm and Evolutionary Computation vol11 pp 16ndash30 2013

[24] PD Sathya andRKayalvizhi ldquoOptimalmultilevel thresholdingusing bacterial foraging algorithmrdquo Expert Systems with Appli-cations vol 38 no 12 pp 15549ndash15564 2011

[25] S Ayas H Dogan E Gedikli and M Ekinci ldquoMicroscopicimage segmentation based on firefly algorithm for detectionof tuberculosis bacteriardquo in Proceedings of the 23rd SignalProcessing and Communications Applications Conference (SIUrsquo15) pp 851ndash854 Malatya Turkey May 2015

[26] S Mirjalili S M Mirjalili and A Lewis ldquoGrey wolf optimizerrdquoAdvances in Engineering Software vol 69 pp 46ndash61 2014

[27] B Akay ldquoA study on particle swarm optimization and artificialbee colony algorithms for multilevel thresholdingrdquo Applied SoftComputing vol 13 no 6 pp 3066ndash3091 2013

[28] A K Bhandari A Kumar and G K Singh ldquoModified artificialbee colony based computationally efficient multilevel thresh-olding for satellite image segmentation using Kapurrsquos Otsu andTsallis functionsrdquo Expert Systems with Applications vol 42 no3 pp 1573ndash1601 2015

[29] P Ghamisi M S Couceiro J A Benediktsson and N M FFerreira ldquoAn efficientmethod for segmentation of images basedon fractional calculus and natural selectionrdquo Expert Systemswith Applications vol 39 no 16 pp 12407ndash12417 2012

[30] L Li L Sun W Kang J Guo C Han and S Li ldquoFuzzymultilevel image thresholding based on modified discrete greywolf optimizer and local information aggregationrdquo IEEE Accessvol 4 pp 6438ndash6450 2016

[31] H-S Wu F-M Zhang and L-S Wu ldquoNew swarm intelligencealgorithm-wolf pack algorithmrdquo Xi Tong Gong Cheng Yu DianZi Ji ShuSystems Engineering and Electronics vol 35 no 11 pp2430ndash2438 2013

[32] H Wu and F Zhang ldquoA uncultivated wolf pack algorithm forhigh-dimensional functions and its application in parametersoptimization of PID controllerrdquo in Proceedings of the IEEECongress on Evolutionary Computation (CEC rsquo14) pp 1477ndash1482Beijing China July 2014

[33] H-S Wu and F-M Zhang ldquoWolf pack algorithm for uncon-strained global optimizationrdquo Mathematical Problems in Engi-neering vol 2014 Article ID 465082 17 pages 2014

[34] Q Zhou and Y Zhou ldquoWolf colony search algorithm based onleader strategyrdquo Application Research of Computers vol 9 pp2629ndash2632 2013

[35] G M Komaki and V Kayvanfar ldquoGrey Wolf Optimizer algo-rithm for the two-stage assembly flow shop scheduling problemwith release timerdquo Journal of Computational Science vol 8 pp109ndash120 2015

16 Computational Intelligence and Neuroscience

[36] L I Wong M H Sulaiman M R Mohamed and M SHong ldquoGrey Wolf Optimizer for solving economic dispatchproblemsrdquo in Proceedings of the IEEE International Conferenceon Power and Energy (PECon rsquo14) pp 150ndash154 KuchingMalaysia December 2014

[37] A Chaman-Motlagh ldquoSuperdefect photonic crystal filter opti-mization using Grey Wolf Optimizerrdquo IEEE Photonics Technol-ogy Letters vol 27 no 22 pp 2355ndash2358 2015

[38] P Q Dzung N T Tien N Dinh Tuyen and H Lee ldquoSelectiveharmonic elimination for cascaded multilevel inverters usinggrey wolf optimizer algorithmrdquo in Proceedings of the 9thInternational Conference on Power Electronics and ECCE Asia(ICPE rsquo15-ECCE Asia) June 2015

[39] N Muangkote K Sunat and S Chiewchanwattana ldquoAnimproved grey wolf optimizer for training q-Gaussian RadialBasis Functional-link netsrdquo in Proceedings of the InternationalComputer Science and Engineering Conference (ICSEC rsquo14) pp209ndash214 Khon Kaen Thailand August 2014

[40] A Zhu C Xu Z Li J Wu and Z Liu ldquoHybridizing grey Wolfoptimization with differential evolution for global optimizationand test scheduling for 3D stacked SoCrdquo Journal of SystemsEngineering and Electronics vol 26 no 2 pp 317ndash328 2015

[41] P ArbelaezMMaire C Fowlkes and JMalik ldquoContour detec-tion and hierarchical image segmentationrdquo IEEE Transactionson Pattern Analysis and Machine Intelligence vol 33 no 5 pp898ndash916 2011

Submit your manuscripts athttpswwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

16 Computational Intelligence and Neuroscience

[36] L I Wong M H Sulaiman M R Mohamed and M SHong ldquoGrey Wolf Optimizer for solving economic dispatchproblemsrdquo in Proceedings of the IEEE International Conferenceon Power and Energy (PECon rsquo14) pp 150ndash154 KuchingMalaysia December 2014

[37] A Chaman-Motlagh ldquoSuperdefect photonic crystal filter opti-mization using Grey Wolf Optimizerrdquo IEEE Photonics Technol-ogy Letters vol 27 no 22 pp 2355ndash2358 2015

[38] P Q Dzung N T Tien N Dinh Tuyen and H Lee ldquoSelectiveharmonic elimination for cascaded multilevel inverters usinggrey wolf optimizer algorithmrdquo in Proceedings of the 9thInternational Conference on Power Electronics and ECCE Asia(ICPE rsquo15-ECCE Asia) June 2015

[39] N Muangkote K Sunat and S Chiewchanwattana ldquoAnimproved grey wolf optimizer for training q-Gaussian RadialBasis Functional-link netsrdquo in Proceedings of the InternationalComputer Science and Engineering Conference (ICSEC rsquo14) pp209ndash214 Khon Kaen Thailand August 2014

[40] A Zhu C Xu Z Li J Wu and Z Liu ldquoHybridizing grey Wolfoptimization with differential evolution for global optimizationand test scheduling for 3D stacked SoCrdquo Journal of SystemsEngineering and Electronics vol 26 no 2 pp 317ndash328 2015

[41] P ArbelaezMMaire C Fowlkes and JMalik ldquoContour detec-tion and hierarchical image segmentationrdquo IEEE Transactionson Pattern Analysis and Machine Intelligence vol 33 no 5 pp898ndash916 2011

Submit your manuscripts athttpswwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Submit your manuscripts athttpswwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014