Aircraft Engineering and Aerospace TechnologyFast image matching via multi-scale Gaussian mutation pigeon-inspired optimization for low cost quadrotorShanjun Chen, Haibin Duan,

Article information:To cite this document:Shanjun Chen, Haibin Duan, (2017) "Fast image matching via multi-scale Gaussian mutation pigeon-inspired optimization forlow cost quadrotor", Aircraft Engineering and Aerospace Technology, Vol. 89 Issue: 6, pp.777-790, https://doi.org/10.1108/AEAT-01-2015-0020Permanent link to this document:https://doi.org/10.1108/AEAT-01-2015-0020

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Fast image matching via multi-scaleGaussian mutation pigeon-inspired

optimization for low cost quadrotorShanjun Chen and Haibin Duan

Science and Technology on Aircraft Control Laboratory, Beijing University of Aeronautics and Astronautics, Beijing, China

AbstractPurpose – The purpose of this paper is to propose an improved optimization method for image matching problem, which is based on multi-scaleGaussian mutation pigeon-inspired optimization (MGMPIO) algorithm, with the objective of accomplishing the complicated image matching quickly.Design/methodology/approach – The hybrid model of multi-scale Gaussian mutation (MGM) mechanism and pigeon-inspired optimization (PIO)algorithm is established for image matching problem. The MGM mechanism is a nonlinear model, which can adjust the position of pigeons bymutation operation. In addition, the variable parameter (VP) mechanism is exploited to adjust the map and compass factor of the original PIO.Low-cost quadrotor, a type of electric multiple rotorcraft, is used as a carrier of binocular camera to obtain the images.Findings – This work improved the PIO algorithm by modifying the search strategy and adding some limits, so that it can have better performancewhen applied to the image matching problem. Experimental results show that the proposed method demonstrates satisfying performance inconvergence speed, robustness and stability.Practical implications – The proposed MGMPIO algorithm can be easily applied to solve practical problems and accelerate convergence speed ofthe original PIO, and thus enhancing the speed of matching process, which will considerably increase the effectiveness of algorithm.Originality/value – A hybrid model of the MGM mechanism and PIO algorithm is proposed for image matching problem. The VP mechanism andlow-cost quadrotor is also utilized in image matching problem.

Keywords Quadrotor, Pigeon-inspired optimization (PIO), Image matching, Multi-scale Gaussian mutation (MGM),Unmanned aerial vehicles (UAVs), Variable parameter (VP)

Paper type Research paper

IntroductionUnmanned aerial vehicles (UAVs) are currently becomingincreasingly popular in civilian and military fields, which havearoused great interests for its application. UAV is a type ofvery complex system which integrates different hardware andsoftware components. The hardware components includeglobal positioning system (GPS), camera, controller, inertialmanagement unit (IMU), and the software componentsinclude image processing, path planning and inner loopcontrol. UAVs with the ability to perform difficult tasks inhazardous environments have been used in various places.However, there are some defects for traditional UAVs such ashigh cost, low flexibility and large volume. Compared withtraditional UAVs, the miniature UAVs like quadrotor has itsown advantages in the field of computer vision, and it has beenused widely. For example, quadrotor has been used in theChina’s variety show to shoot many times. Quadrotor wasexploited to test six degrees of freedom flight (Yu and Ding,2012). Low-cost quadrotor was used for autonomous visualtracking and landing (Bi and Duan, 2013). Based on

considerations of cost and performance, we use the low-costquadrotor assembled by ourselves as a carrier to carrybinocular camera to obtain these images for image matching.

The development of image technology plays a veryimportant role in the field of vision navigation, imageprocessing and computer vision. For example, a binocularvision-based UAVs autonomous aerial refueling platform wasestablished (Duan et al., 2016). A new image processingmethod for discriminating internal layers was proposed (Langet al., 2014). The collapsed buildings were detected with theaerial images captured from UAV (Hua et al., 2016), andvision navigation for aircrafts based on 3D reconstruction wasutilized (Zhu et al., 2015). While, image matching has alwaysbeen a highlighted research topic in image processing, as it isa fundamental task for many applications of computer visionsuch as image registration and image fusion (Koutaki et al.,2013). Image matching has also been widely applied in thefields of pattern recognition, three-dimensional reconstructionand motion analysis (Brown, 1992; Candocia and Adjouadi,1997). As the importance of the image matching, manyevolutionary algorithms (EAs) and improved methods,

The current issue and full text archive of this journal is available onEmerald Insight at: www.emeraldinsight.com/1748-8842.htm

Aircraft Engineering and Aerospace Technology: An International Journal89/6 (2017) 777–790© Emerald Publishing Limited [ISSN 1748-8842][DOI 10.1108/AEAT-01-2015-0020]

This work was partially supported by National Natural ScienceFoundation of China (NSFC) under grant #61425008, #61333004, and#61273054, and Aeronautical Foundation of China under grant#20135851042.

Received 24 January 2015Revised 17 May 2016Accepted 26 May 2016

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including artificial bee colony (ABC) (Karaboga and Basturk,2007), genetic algorithm (GA) (Im et al., 2002), particleswarm optimization (PSO) (Riccardo et al., 2007) and antcolony optimization (ACO) (Duan, 2005), are proposed toachieve a better matching effect. Cauchy biogeography-basedoptimization based on lateral inhibition was used to solve theimage matching problem (Wang and Duan, 2013). Duan andYu utilized predator-prey PSO to achieve parameteridentification of UCAV flight control system (Duan et al.,2013). In general, almost all kinds of image matchingalgorithms which have been proposed (Duan, 2005; Karabogaand Basturk, 2007; Riccardo et al., 2007; Zhang and Chen,2008; Elboher and Werman, 2013; Duan et al., 2013; Koutakiet al., 2013; Wang and Duan, 2013) can be divided into thealgorithm based on image statistics and the algorithm basedon image characteristics (Ma et al., 2009). The algorithmbased on image statistics analyzes the attributes of an image tomeasure the similar degree between the template image andthe reference image under test which is also called the originalimage. Its measurement methods mainly include theminimum distance measurement, correlation function andprobability measure. One of the most commonly usedmethods is the minimum distance measurement, includingsquare difference, mean square difference, absolute differenceand absolute difference. The algorithm-based imagecharacteristics make use of some image features such as spatiallocation, point features, image edge ,texture ,energy, shapeand entropy to evaluate the similar degree of the two images.Because the performance of the algorithm based on imagecharacteristics is associated with the choice of image features,it varies when choosing different image features, which leadsto this type of algorithm with a weak robustness. Thealgorithm based on image statistics is independent from theextensive characteristics extractions. Therefore, it is widelyused and shows a better performance.

Image matching is a process of searching the templateimage in the reference image under test by using a specificalgorithm. In general, the image under test is larger than thetemplate image. As the different of perspectives and filmingequipment, the same object is different in different time ofimaging. In addition, the difference between the templateimage and the image under test is expanded as the influenceof noise, rotating, interference and image pre-processing,which increases the difficulty to matching. At present,during the process of image matching, the matchingprecision, matching speed, versatility and robustness arethe main evaluation standards. To improve these standards,many algorithms have been exploited. Although theapplication of these algorithms has been made greatdevelopment in many ways, there are still many aspectssuch as computing time, stability, and robustness havingroom for improvement. In this paper, multi-scale Gaussianmutation pigeon-inspired optimization (MGMPIO) isutilized for image matching problem, which combines theadvantages of a nonlinear model.

The original pigeon-inspired optimization (PIO) algorithmis a new swarm intelligence optimization algorithm, which wasfirstly proposed by Duan and Qiao (2014), and inspired by thefeatures of the homing pigeons. Here, we are ready to utilizethe PIO algorithm to solve the problem of image matching. In

this type of algorithm, two kinds of operators, including themap and compass operator model based on magnetic field andsun and the landmark operator based on landmarks, are usedto search the optimal solution. In early iterations, the speed ofthe pigeon mainly depends on its previous speed inertiaaccording to the map and compass operator. Thus, the globalsearch ability of PIO is strong because the speed of the pigeonsis randomly given. This operator contributes to the diversity ofpopulation and enables the algorithm to have better stability.While in late iterations, every pigeon is flying straight towardthe center of all pigeons according to the landmark operator.This operator contributes to the convergence rate of thealgorithm. The PIO algorithm has been proven to convergemore quickly and more stable comparing with the standardDE algorithm, and with the increasing of pigeon number, theconvergence performance is much better (Duan and Qiao,2014). However, the basic PIO algorithm falls into localoptimum easily while keeping a higher convergence speed. Toimprove the performance of the basic PIO algorithm,improved mechanism has been investigated such as Li andDuan (2014) used the improved PIO algorithm to accomplishthe target detection task for UAVs. In our work, someimproved mechanism is also exploited in the basic PIOalgorithm.

A nonlinear model can make the system become moreflexible by setting the appropriate parameter. In addition, itcan determine its own value according to the actual situation.The nonlinear model has been applied widely in recent years.For example, Huang and Ma investigated the nonlinearattitude-orbit coupling dynamics and control for thereconfiguration of a two-satellite coulomb tether formationnear earth-moon libration points (Huang et al., 2014). Jeonand Eun, (2014) exploited nonlinear multiple models to studydistributed estimation fusion problem. In this work, thenonlinear models, including the multi-scale Gaussianmutation (MGM) mechanism (Morgan and Druckmüller,2014) and variable parameter (VP) mechanism (Chatterjeeand Siarry, 2004), are proposed to improve the performanceof the basic PIO algorithm for image matching problem andthe improved PIO algorithm is called MGMPIO. Throughadjusting the change of the previous speed inertia part, the VPmechanism makes the PIO algorithm has stronger globalsearching ability at early iterations and stronger local searchingability at later iterations (Riccardo et al., 2007). In that case,the precision and convergence rate of the original PIOalgorithm can be improved. The introduction of MGMmechanism makes some pigeons get rid of the restriction ofthe basic PIO algorithm’s update rule (Tao and Xun, 2009),which can improve the ability to get rid of local optimumeasily.

The remainder of this paper is organized as follows.Section 2 introduces the low-cost quadrotor. Then, theoriginal PIO algorithm is given in Section3. Section 4describes the MGMPIO algorithm in detail, including theMGM mechanism and VP mechanism. A series ofexperiments are conducted to verify the performance of theMGMPIO algorithm in Section 5. The concluding remarksare contained in the final section.

Fast image matching

Shanjun Chen and Haibin Duan

Aircraft Engineering and Aerospace Technology: An International Journal

Volume 89 · Number 6 · 2017 · 777–790

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Low-cost quadrotorQuadrotor is an electric multiple rotorcraft containing fourrotors, and there are two pairs of counter-rotating, fixed-pitchblades located in the four corners of its body. As early as1920s, the idea of using four rotors is realized as a full-scalehelicopter (http://en.wikipedia.org/wiki/Quadrotor). In recentyears, with the development of computer vision, and newmaterials and new micro-electro mechanical continuallyspring up, quadrotor gets rapid development and wideapplication. There are several advantages in comparison totraditional helicopters, including novel appearance, simplestructure, low cost and excellent performance in a unique wayof flight control (Tian and Xun, 2008). In addition, by usingfour rotors, each individual rotor can have a smaller diameter.In that case, the damage caused by the rotors can be reducedgreatly. Furthermore, quadrotor can finish a variety of flightattitude such as vertical take-off and landing, free hovering. Atthe same time, four rotors can produce greater lift, whichensure that the fuselage can carry a binocular camera. In viewof the above advantages of quadrotor, we utilize a low-costquadrotor with a binocular camera to obtain the imagesneeded by image matching. As a low-cost quadrotor, inaddition to its own advantage of low cost, we assembled thequadrotor by using the selected module where the APM flightcontrol system is used. The APM flight control system is akind of open-source system with the main chip ATMEGAL1280/2560, which supports for three axes, four axes, six axes,fixed wing and helicopter. Meanwhile, this kind of systemexploited two-stage PID control method. The first level isnavigation grade, and the second is to control level. In thisway, the cost will be further compressed. The quadrotor weassembled is shown in Figure 1(a), which is aWi-Fi-controlled quadrotor which is capable of carrying abinocular camera. Height is 300mm and diameter is 650mm.The APM flight control system as a platform offers an open

application programming interface (API) and freelydownloadable software development kit (SDK) for developers(Krajnik et al., 2011). Many useful pieces of developmentinformation can be found on the developers’ websites or theofficial forum. The binocular camera is shown in Figure 1(b),which is a kind of MERCURY series CCD/CMOS industrialcamera.

Pigeon-inspired optimization algorithmAccording to Duan’s theory (Duan and Qiao, 2014) in solvingair robot path planning problem, the PIO algorithm can bedescribed as follows:

Firstly, initialize the parameters. The maximum number ofiterations for the map and compass operator is T1, and T2 is forthe landmark operator. The number of pigeons is set to N.Every pigeon’s position and velocity are randomly initializedwithin the search space. The position and velocity of the ith

pigeon is donated as Xi�t� � �xi1,xi2, . . . . . ., xiD� and Vi ��vi1,vi2, . . . . . ., viD�, where D represents the dimension of thesearch space. Then, choose the best position by calculating thequality of all the pigeons.

In the PIO model, according to the characteristics of thehoming pigeons, two operators, including the map andcompass operator and the landmark operator, are utilized. Atearly iterations, as the scope of optimal position is notconfirmed and pigeons are far away from the destination, themap and compass operator is used, which is based on themagnetic field and sun. In the map and compass operator,the velocity of each pigeon is determined by their own currentvelocity and position, as well as the global optimal positioninformation, which can be depicted by equation (1). Then theposition of each pigeon at next generation is determined byequation (2) (Duan and Qiao, 2014). The pigeons aremanipulated by the following equations (1) and (2):

Figure 1 Quadrotor picture from different views

Fast image matching

Shanjun Chen and Haibin Duan

Aircraft Engineering and Aerospace Technology: An International Journal

Volume 89 · Number 6 · 2017 · 777–790

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Vi(t) � Vi(t � 1) · e�Rt � rand · (Xg � Xi(t � 1)) (1)

Xi(t) � Xi(t � 1) � Vi(t) (2)

where R represents the map and compass factor which cancontrol the changing trend of pigeon’s own speed inertia as theiteration goes. rand is a random number within [0, 1], Xg

represents the current global best position, which can beobtained by comparing all the positions among all the pigeons.

After a certain number of iterations, the pigeons fly close totheir destination and will rely on landmarks neighboring them.The landmark operator instead of the map and compass operatoris exploited to search the best position. In the landmark operator,every pigeon can fly straight to the destination which is the centerof all pigeons, and the number of pigeons decreases to half of thelast generation. Half of all the pigeons that are far fromthe destination and unfamiliar to the landmarks will follow thepigeons who are familiar to the landmarks. In that case, it ispossible for two pigeons at the same position, and the destinationwill be found by the pigeons that are close to their destinationquickly. In Duan’s model (Duan and Qiao, 2014), the center ofall pigeons is their destination in the tth iteration, which can bewritten as:

Xc ��Xi(t) · fitness(Xi(t))

Np ·� fitnesss(Xi(t))(3)

where fitness�� is the function to evaluate the quality of thepigeon individually, Np represents the number of pigeons inthe tth iteration, which is the half of last iteration amount. Theposition of each pigeon is updated by the following equation:

Xi(t) � Xi(t � 1) � rand · (Xc(t) � Xi(t � 1)) (4)

The PIO algorithm has been proven to be effective andfeasible when it is exploited to solve air robot path planningproblem. But it is easy to get into the local optimumsometimes; thus, it is essential improve the robustness andstability of the basic PIO algorithm.

Model development

Variable parameter mechanismIn the basic PIO algorithm, according to equation (2), we cansee that the next iteration position of pigeon decided jointly bythe current speed and position of pigeon’s own, and the speeddirection and size of current pigeon determine the change ofpigeon’s direction and size of next generation. We can alsoknow that the current speed relies on previous speed inertiaand global optimal position Xg by equation (1). We hope thatthe PIO algorithm has larger global search ability at earlyiterations, so that we can quickly narrow the range of thesearching space for the optimal value to improve theconvergence speed of algorithm, and in later iterations withstronger local development ability (Tian and Xun, 2008). Inthe original PIO, there is a formula e�Rt in the previous speedinertia part which represents Vi�t � 1� · e�Rt. The value of theformula e�Rt decreases gradually with the increase of thenumber of iterations, so that at early iterations, the previousspeed inertia part takes a heavy weight in determining the

current velocity, and the effect of the global optimal positionXg part, which represents rand · �Xg � Xi�t � 1��, is relativelylight. Therefore, the current speed of pigeons mainly dependson the previous speed inertia part (Chatterjee and Siarry,2004). Because the previous speed inertia part represents thepigeons’ own information, different pigeon has differentinformation, which has strong subjectivity and uncertainty. Inthat case, at early iterations, pigeons can locate any location ofsearch space, and the PIO algorithm shows great globalsearching ability. On the contrary, in the late of iterations, theprevious speed inertia part has become small. The currentspeed of pigeons mainly depends on the global optimalposition Xg part (Duan and Qiao, 2014). As the global optimalposition Xg part represents the global shared information, ithas the characteristics of prompting aggregation andconvergence. In that case, it can accelerate the convergencespeed of the original PIO algorithm. However, throughanalysis, we find that once R is established, the value offormula e�Rt has normally a fast reduced trend as the increaseof the number of iterations. There is a high chance that thevalue of formula e�Rt has become very small in the case ofhaving not found the range of the global optimal position forthe original PIO algorithm, which leads to the loss of strongglobal search ability. Therefore, it will be easy for the originalPIO algorithm trapped in local optimal position and cannotfind the global optimal position finally.

Based on the above shortcomings, here imitating thethought of inertia weight (Shi and Eberhart, 1998), we adjustR by utilizing the VP mechanism to control the change of theprevious speed inertia part on the basis of the PIO algorithm.This new algorithm is called R-adjustable PIO (RPIO)algorithm. The improved previous speed inertia part has aslow attenuation trend at early iterations, so that it has astronger global search ability to enhance the probability offinding the range of global optimal position accurately. In thelater of iterations, the improved previous speed inertia part hasa rapid attenuation trend, so that it can find the global optimalposition quickly on the basis of finding the range of the globaloptimal position, speeding up the convergence speed of thebasic PIO algorithm. The specific improvement is as follows:

The VP mechanism is designed as (5). The speed of eachpigeon is updated by equation (6), where t represents thecurrent generation, T1 represents the largest number ofiterations for the map and compass operator and n representsa parameter, which can set freely by us (Chatterjee and Siarry,2004).

R � Rmin � (Rmax � Rmin ) · � tT1�n

(5)

Vi(t) � Vi(t � 1) · e(�R) � rand · (Xg � Xi(t � 1)) (6)

Here, a series of comparative experiments are conducted whenn � 1, n � 2, n � 3, n � 6 and the original version that has notbeen improved for the previous speed inertia part to test effect.The comparative results for the speed of the previous inertialpart are presented in Figure 2, where the X-axis denotes thenumber of iterations and has no units, and the Y-axisrepresents the previous speed inertia (Vi�t � 1� · e�Rt) inequation (1) and its unit is m/s.

Fast image matching

Shanjun Chen and Haibin Duan

Aircraft Engineering and Aerospace Technology: An International Journal

Volume 89 · Number 6 · 2017 · 777–790

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In Figure 2 represents the changing trend curves of noprocessing previous speed inertia part. The parameters are setas: Vi�t � 1� � 100, Rmax � 11, Rmin � 1, T1 � 50, and theno processing parameter R is set to 1.1. From Figure 2, we cansee that the changing trend of the previous speed inertial parthas a distinct improvement. At early iterations, the declinecurves show that the previous speed inertia part that not beimproved has a fast reducing trend, and rapidly decay trendsto 0. But the improved previous speed inertia part has a slowattenuation trend. Especially when n � 6, it almost did notreduce in early iterations. At the same time, in the late ofiterations, the improved previous speed inertia part reducedquickly. In that case, The RPIO algorithm not only can ensurelarger global search ability, but also has stronger local searchability.

Multi-scale Gaussian mutation mechanismThrough the improvement of the above VP mechanism, theRPIO algorithm has a good performance in comparison withthe original PIO algorithm. By many times test, we find thatthe large R value is conductive to the improvement of theconvergence speed. To ensure a faster convergence speed, wecan increase the value of Rmax and Rmin . But it will speed upthe declining trend of the previous speed inertial part. Fromequation (6), we can see that the closer to the current globalbest position Xg, the velocity is smaller. Therefore, during theprocess of chasing the best position, the PIO algorithm showsa stronger convergence as the iteration goes. Especially in thelate of iterations, it will become particularly evident. If theregion of the best position has not been found at earlyiterations, as the increase of the R value, it will be easier to fallinto local optimal position and eventually cannot find theglobal optimal position. In view of above analysis, if the speedor position of pigeons makes variation (Morgan andDruckmüller, 2014), the pigeons can get rid of the restrictionsof the PIO algorithm’s update rule to achieve the search of theother space, jumping out of the local optimal position andfurther improving the probability to find the global optimalposition. Through systematic analysis and comparison, here

we use the MGM mechanism (Li et al., 2004) to make afurther improvement for the RPIO algorithm. This newimproved algorithm is called MGMPIO. The Gaussiandistribution is also called the normal distribution, which isdecided by the standard deviation � and the mean � of twoparameters. Obey one-dimensional Gaussian distributiondenoted as N��, ��. Its density function f�x� is defined asequation (7):

f(x) �1

�2��· e

(x � �)2

2 · �2 (7)

Gaussian mutation is a process that any dimension of pigeon’sposition makes variation according to a certain probability P(Morgan and Druckmüller, 2014). Formula is as equation (8),where i represents the ith pigeon, j represents the jth

dimension:

Xij � Xij � N(�, �) (8)

According to the Gaussian distribution’s theory, the size of thestandard deviation determines the distance of mutated pigeonaway from the original position. The greater standarddeviation, the probability of the mutated pigeon far away fromthe original position is bigger. The smaller standard deviation,the pigeon will remain in its own original position with a largeprobability. If we determine the size of the standard deviation� according to the size of the position’s fitness of pigeon (Liet al., 2004), the pigeon that has a smaller fitness gets a biggerstandard deviation �, which can make it has a greaterprobability to locate other locations of the search space tosearch, and the pigeon that has a greater fitness gets a smallerstandard deviation �, which can make a further search to allaround the current position. In that case, the MGMPIOalgorithm not only can enhance the probability of jumping outof local optimal position, but also accelerate the convergencespeed of the algorithm. The specific design is as equation (9):

� � L · �1 �fitness(Pnow)fitness(Pfinal)

· (Xij max �Xij min) (9)

where L represents a parameter which depends on the specificsituation, fitness�� represents the objective function whichdescribes the similarity of the image under test and thetemplate, fitness�Pnow� represents the similarity value of thecurrent pigeon position, fitness�Pfinal� represents the similarityvalue of the global optimal expected position and�Xij min, Xij max� represents the search interval of the jdimension.

On the basis of the above improvements, if we also adoptMGM mutation to the current global optimal position Xg aftereach iteration, we can change the update of the pigeonsvelocity at the next iteration by changing the Xg, which canmake pigeons locate other parts of the searching space tosearch, so as to further increase the probability of finding theglobal optimal position. But the MGM mechanism cannot beadded randomly; it should satisfy some conditions. Here, weintroduce the notion of the degree of pigeon’s focus (Li et al.,2004); its function D�Xi, Xg� is defined as equation (10).

Figure 2 The changing trend of pigeon’s own previous speedinertia for different situations

0 10 20 30 40 500

5

10

15

20

25

30

35

40

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prev

ious

spe

ed in

ertia

(m

/s)

pren = 1n = 2n = 4n = 6

Fast image matching

Shanjun Chen and Haibin Duan

Aircraft Engineering and Aerospace Technology: An International Journal

Volume 89 · Number 6 · 2017 · 777–790

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D(Xi, Xj) � maxi�1,2,. . . . . .,N�

j�1

D

(Xgj � Xij)2 (10)

As the D�Xi, Xg� value will get smaller as the iteration goes, weestablished bounds A (Karaboga and Basturk, 2007). When D�Xi, Xg� is smaller than the value of the A, it indicates that thepigeons gather closely, which will make the algorithm have aweak ability to search in the global search space. In that case, theMGMPIO algorithm will show a strong convergence as theiteration goes and falls into local optimal position easily. Same asabove, here we determine the size of the standard deviation �according to the size of the global optimal position’s fitness of thetth iteration and use the MGM mechanism again. The specificdesign is as equations (11) and (12).

� � L · �1 �fitness(Xg)

fitness(Pfinal) · (Xij max �Xij min) (11)

Xgj � Xgj � N(�, �) (12)

where j represents the j dimension likewise. Through theabove improvements, the MGMPIO algorithm furthercontributes to the jumping out of the local optima.

Implementation procedureThe implementation procedure of our MGMPIO can bedescribed as follows:● Step 1: Image pre-processing. Obtain the original image

and the template image. Then, convert them intogray-scale format.

● Step 2: Initialize parameters. Initialize the parameters ofthe MGMPIO algorithm such as the number of pigeons N,the value of bounds A, the search space dimension D, thevalue range of the factor for the map and compass operator�Rmin, Rmax � and the maximum number of iteration T1 andT2 for two operators.

● Step 3: Initialize the velocity and position of each pigeonrandomly within the scope of the allowed. Compare eachpigeon and calculate the fitness value, finding out theoptimal pigeon to initialize the global optimal fitness valueand optimal position.

● Step 4: Operate map and compass operator. Utilizeequation (5) to update the factor R firstly.

● Step 5: Update pigeons. Update the velocity and positionof every pigeon by using equations (2) and (6) andcalculate the fitness of the newly generated pigeons.

● Step 6: Add MGM. Compare with the establishedprobability P, if a random value between 0 and 1 is smaller.Then add MGM to the newly generated pigeons’ positionaccording to equations (8) and (9).

● Step 7: Compare the fitness of pigeons before and aftermutation. If the fitness added by the MGM is better,replace the position of pigeons before mutation with thebetter pigeons’ position. Otherwise, remain the same asbefore.

● Step 8: If N newly generated pigeons have been generated,go to Step 9. Otherwise, go to Step 5.

● Step 9: Update the global optimal position Xg and optimal

fitness. Calculate and compare all the newly generatedpigeons’ fitness and find the new best position.

● Step 10: Calculate the degree of pigeon’s focus D�Xi, Xg�according to equation (10).

● Step 11: Add MGM. Compare with the established boundsA, if the value of the formula D�Xi, Xg� is smaller. Then,add MGM to the global optimal position Xg according toequations (11) and (12).

● Step 12: Calculate and compare the fitness of the newlygenerated Xg before and after mutation, if the fitness addedby the MGM is better, then replace the pigeons’ globaloptimal position before mutation with the better globaloptimal position. Otherwise, remain the same as before.

● Step 13: If the number of iterations is more than T1, go toStep 14. Otherwise, go to Step 4.

● Step 14: Operate the landmark operator. Rank all pigeonsaccording their fitness values and update the number ofpigeons where half of the pigeons whose fitness is low willbe discarded.

● Step 15: Calculate the center position of all pigeonsaccording to equation (3). This center position is thedesirable destination, and all pigeons will fly to thedestination by adjusting their flying direction according toequation (4).

● Step 16: Update the global optimal position Xg and optimalfitness.

● Step 17: If the current number of iteration t reaches toT1 � T2, stop the iteration and output the solution.Otherwise, go to Step 14.

The detailed flow chart of the improved MGMPIO approachfor image matching is shown in Figure 3.

Theoretical analysisThe theoretical analysis of evolutionary algorithms is veryimportant. Here, we have concisely analyzed our MGMPIOalgorithm in respect of global convergence property andcomputational complexity. In the original PIO algorithm,through the landmark operator, the algorithm is able to quicklyconverge to the optimum position in later iterations. InMGMPIO, the speed of pigeons adjusted by the VP mechanismcan accelerate the rate of finding the region of the global optimalposition; thus, there is faster convergence rate compared theoriginal PIO. In addition, the MGM mechanism enables thealgorithm to get rid of local optimal position, which is conductiveto global convergence. So, the global convergence performanceof MGMPIO is superior to the original PIO.

We analyzed the time complexity of each operation in theoriginal PIO and that of these added operation in MGMPIO.And, the result is given in the Table I. Therefore, the totalcomplexity of the added operations in MGMPIO in alliterations is ��2NT1�. Although, these added operationsimplement more calculations on the original of PIO. It isworthy for the significant improvement of performance.

Comparative experimental results and analysisTo test the performance of our proposed MGMPIO, we chosethree cases to carry out experiments. For Case 1, the originalimage is shown in Figure 4(a), and the template image isshown in Figure 4(b). The task is to find out two benches in

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the original image. In this paper, the parameters forMGMPIO are shown in Table II. All the pictures used forexperiments originate from our assembled low-cost quadrotorand binocular camera introduced in Section 2, and all thefollowing experiments are implemented on a PC with IntelCore i5, 2.6-GHz CPU, 4-GB memory and 64-bit Windows

7. All algorithms are implemented by MATLAB8.0.0.783(R2012b).

The control parameters in the MGMPIO algorithms arechosen as follows: parameter P denotes the probability forGaussian mutation, and its value depends on the specificsituation. In general, for complex problems, mutation

Figure 3 Detailed flow chart of the improved MGMPIO

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operation is able to strengthen the ability of the algorithm tofind the optimal solution, and it is essential to appropriatelyincrease the probability of mutation operation. But in somesimple questions, good results can be obtained by the standardalgorithm. In this paper, we choose p � 0.32 is appropriate.Parameter A is as the reference for aggregation degree; itmainly depends on the number of pigeons. Its value can beroughly determined by the formula � · A2 � 15N and theprecise adjustment is then carried out. When the scope ofthe search space is large, a larger A is necessary. In this paper,we choose A � 26 is appropriate. Parameter L in equation (9)controls the range of the standard deviation, usually preferablyfrom one to two times of the search space. In this paper, wechoose L � 2. The large R value is conductive to theimprovement of the convergence speed. To ensure a fasterconvergence speed, we can increase the value of Rmax andRmin . But it will speed up the declining trend of the previousspeed inertial part in equation (1). As the R value increases, itwill be easier to fall into local optimal position and eventuallycannot find the global optimal position. Through furtheranalysis, we find that, in addition to the parameter n, the valueof �Rmax � Rmin � also affects the changing trend of the previousspeed inertial part. Thus, we can set up a large Rmax valuewhile a small Rmin value is determined. Through a series oftests, we find that a good performance can be achieved whenRmax � 10, Rmin � 0.1, n � 12. Other parameters are selectedempirically through trial and error.

The matching result for Case 1 is shown in Figure 4(c).From Figure 4(c), it is obvious that the MGMPIO algorithmcan accurately find the location of the template image in theoriginal image, which indicates that the MGMPIO algorithmis feasible. To test the advantages of the MGMPIO algorithmrelative to the original PIO algorithm, we conducted a set ofcontrast experiments. At the same time, we also choose theother algorithms, including PSO and RPIO, to furthercompare their performance. The result of contrastexperiments is shown in Figure 4(e). It is evident fromFigure 4(e) that the MGMPIO algorithm has the fastestconvergence speed in all of these algorithms, which confirmsthat the MGMPIO algorithm has a better effectiveness. Here,we also show the histogram of image that has been matchedsuccessfully in the Figure 4(d). Its abscissa denotes gray scale,and its ordinate represents the number of pixels. The left of

Figure 4(d) is template image histogram, and the right ofFigure 4(d) is the histogram matched in original image.

Further experiments are given in Figure 5 to test thestability of the improved MGMPIO algorithm. Here, all thealgorithms run for 10 times independently. The experimentalresults for PSO, PIO, RPIO and MGMPIO are shown inFigures 5(a)-(d) separately. Moreover, different algorithmsare applied to the same Case 1, and they have the same fitnessfunction. The number of pigeons and the maximum numberof iterations for different algorithms are set to be same. Fromthe results in Figure 5, it is clear that, compared with theoriginal PIO algorithm, the evolutionary curves of theMGMPIO algorithm are more stable. Compared with othertwo algorithms, the MGMPIO algorithm also shows a betterstability. In the experiment, we decrease the demand for speedto ensure the stability of the original PIO algorithm. If theoriginal PIO algorithm has the same demand for speed as theMGMPIO algorithm, it cannot guarantee to matchsuccessfully in each time. When we just use the VP mechanismto improve the original PIO algorithm, the results inFigure 5(c) indicate that the RPIO algorithm can improve theconvergence speed. But it is easy to fill into local optimalsolution and cannot find the global optimal solution. Afteradding the MGM mechanism, from the results in Figure 5(d),it is obvious that the MGMPIO algorithm not only canimprove convergence speed significantly, but also maintaingood stability.

To further investigate the robustness of the MGMPIOalgorithm, a series of experiments are conducted for the othertwo different cases. Figures 6 and 7 are the results for Case 2and Case 3, respectively. Just like Case 1, Figure 6(a) andFigure 7(a) are original images. Figure 6(b) and Figure 7(b)are template images. Figure 6(d) and Figure 7(d) arehistograms of images that have been matched successfully.Figure 6(e) and Figure 7(e) are the evolutionary curves withPSO, PIO, RPIO and MGMPIO. For Case 2, the task is tofind out the car in the original image. The task for Case 3 is tofind out the aircraft in the original image. Here, theparameters for Case 2 and Case 3 are the same as the Case 1.

From Figure 6(c) and Figure 7(c), it also shows that thelocation of the target template image is found accurately in theoriginal image. The accuracy of our proposed MGMPIO

Table I Parameters for MGMPIO

Operation Time complexity

Operation in original PIO Parameters initialization ��NT1�Update each pigeon’s position during the map and compass operator ��NT1�

Update each pigeon’s velocity during the map and compass operator ��NT1�

Calculate the fitness of each pigeon during the map and compass operator ��NT1�

Arrange all pigeons by ascend during the landmark operator ��2Nlog N�1 � 0.5T2��

Calculate the center coordinates of all individuals ��2N�1 � 0.5T2��

Update each pigeon’s position during the landmark operator ��2N�1 � 0.5T2��

Calculate the fitness of each pigeon during the landmark operator ��2N�1 � 0.5T2��

Added operation in MGMPIO Update the map and compass factor R in each iteration by equation (5) ��T1�

Calculate the standard deviation � by equation (11)Pigeons’ mutation operation by equation (12) ��0.32NT1�

Calculate the degree of pigeon’s focus by equation (10) ��2NT1�

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Figure 4 The experimental results of image matching for Case 1

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shows that it is more reliable than the other three algorithms.Furthermore, it is clear that, compared with other threealgorithms, the MGMPIO algorithm remains its superiority inthe aspects of the effectiveness and the convergence speedfrom Figure 6(e) and Figure 7(e).

During the above three cases, MGMPIO has successfullyfound the global optimum that is the true position of the targetwith higher convergence rate. Although the original PIO hasan acceptable performance compared with PSO, the efficiencyof PIO is low compared with MGMPIO. An intuitive reason isthat the VP mechanism is able to control the change of theprevious speed inertia part in velocity updating formula (1),which can maintain a low-attenuation trend for the improvedprevious speed inertia part at early iterations, so that thealgorithm possesses a stronger global search ability to enhancethe probability of finding the range of global optimal positionaccurately. At the same, at the late of iterations, the rapidattenuation trend for the improved previous speed inertia part

Table II Parameters for MGMPIO

Parameter Description value

N The number of pigeons 150T1 The maximum times of iteration for

the map and compass operator50

T2 The maximum times of iteration forthe landmark operator

50

� The mean of Gaussian distribution 0R Variable parameter [0.1 10]D The dimension of search space 2P The probability for Gaussian mutation 0.32L A set parameter for Gaussian mutation 2A Reference for aggregation degree 26

Figure 5 Results of run 10 times for Case 1

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Figure 6 The experimental results of image matching for Case 2

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Figure 7 The experimental results of image matching for Case 3

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is obtained. Thus, the algorithm can find the global optimalposition quickly on the basis of finding the range of the globaloptimal position, speeding up the convergence speed of thebasic PIO algorithm. In addition, the MGM mechanism isable to make the individual with low fitness value has a greaterprobability to locate other locations of the searching space tosearch and the individual with low fitness value carry furthersearch to all around the current position, which not only canenhance the probability of getting rid of local optimal position,but also accelerate the convergence rate of the algorithm. It isobserved that RPIO has enhanced the robustness of theoriginal PIO, and MGMPIO has further enhanced therobustness of the original RPIO. The fast convergence speedof an algorithm is crucial for image matching, particularly inaerial images with complex backgrounds. Based on an overallconsideration of experiments in the above three groups, theproposed MGMPIO algorithm is superior to threeevolutionary algorithms in solving image matching problem.

ConclusionsIn this paper, the MGMPIO algorithm is proposed toaccomplish the image matching problem, which combines theVP mechanism and the MGM mechanism. The VPmechanism helps to improve convergence speed and enhancethe probability of finding the optimal location. The MGMmechanism contributes to jumping out of the local optimumand preventing from falling into local optimum. Theexperimental results in three test cases show that theMGMPIO algorithm can successfully find the optimalsolution during every run, and it markedly improves theperformance of the original PIO algorithm in terms ofconvergence speed, robustness and stability. Compared withthe RPIO algorithm, MGMPIO also shows a better stabilityby using the MGM mechanism, which provides a more perfectway for the image matching problem. The MGM mechanismused in this paper can enhance the probability of jumping outof local optimal position and accelerate the convergencespeed. But, according to the principle of the MGMmechanism, when there are several objects similar to thetemplate image in original image, it will be not sure to find theoptimal solution accurately. Therefore, further improvementsshould be made in the future work. We will be more focusedon balancing the convergence speed and accuracy of thealgorithm. Moreover, as the uncertainty of the variation, whenthe search space is large enough, the matching difficulty willget larger. We will also focus on the study of better methodsfor strengthening stability and enhancing searching ability. Wewill also apply the proposed approach to solve other real-worldproblems, such as UAV, mobile robots, industry productionline and intelligent transportation.

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Further reading

Duan, H.B. and Li, P. (2014), Bio-Inspired Computation inUnmanned Aerial Vehicles, Springer-Verlag, Berlin,Heidelberg.

About the authors

Shanjun Chen received his BS degree in Automation Scienceand from the University of Science and Technology Beijing,China, in 2015. He is currently a master candidate with theSchool of Automation Science and Electrical Engineering,Beihang University. He is a member of Bio-inspiredAutonomous Flight Systems (BAFS) Research Group ofBUAA. His current research interest includes advanced flightcontrol, computer vision and bio-inspired computation.

Haibin Duan is currently a full professor of School ofAutomation Science and Electrical Engineering, BeihangUniversity (formerly Beijing University of Aeronautics andAstronautics, BUAA), Beijing, China. He is the head ofBio-inspired Autonomous Flight Systems (BAFS) ResearchGroup of BUAA. He received the PhD degree from NanjingUniversity of Aeronautics and Astronautics (NUAA) in 2005.He was an academic visitor of National University ofSingapore (NUS) in 2007, a senior visiting scholar of theUniversity of Suwon (USW) of South Korea in 2011. He iscurrently an IEEE Senior Member. He has published threemonographs and over 70 peer-reviewed papers ininternational journals. His current research interests includebio-inspired computation, advanced flight control andbio-inspired computer vision. Haibin Duan is thecorresponding author and can be contacted at:hbduan@buaa.edu.cn

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Fast image matching

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