research article color image evaluation for small...

Research ArticleColor Image Evaluation for Small Space Based on FA and GEP

Li Deng12 Sui-Huai Yu1 Wen-Jun Wang1 Jun-Xuan Chen1 and Guo-Chang Liu1

1 Institute of Industrial Design Northwestern Polytechnical University Xirsquoan 710072 China2 School of Mechatronic Engineering Southwest Petroleum University Chengdu 610500 China

Correspondence should be addressed to Li Deng dengliswpueducn

Received 4 November 2013 Revised 11 January 2014 Accepted 12 January 2014 Published 26 February 2014

Academic Editor Wang Xing-Yuan

Copyright copy 2014 Li Deng et al This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Aiming at the problem that color image is difficult to quantify this paper proposes an evaluation method of color image forsmall space based on factor analysis (FA) and gene expression programming (GEP) and constructs a correlation model betweencolor image factors and comprehensive color image The basic color samples of small space and color images are evaluated bysemantic differential method (SDmethod) color image factors are selected via dimension reduction in FA factor score function isestablished and by combining the entropy weight method to determine each factor weights then the comprehensive color imagescore is calculated finallyThe best fitting function between color image factors and comprehensive color image is obtained by GEPalgorithm which can predict the usersrsquo color image values A color image evaluation system for small space is developed based onthismodelThe color evaluation of a control roomonAC frequency conversion rig is taken as an example verifying the effectivenessof the proposed method It also can assist the designers in other color designs and provide a fast evaluation tool for testing usersrsquocolor image

1 Introduction

Rerferring to the topic of color image color image processinghas to be reviewed It has become an important research fieldin computer graphics and image processing For instanceWang et al proposed an effective color image retrievalmethod based on texture [1] and later presented a novelmethod for image retrieval based on structure elementsrsquodescriptor [2] The method of image authentication [3] andrestoration [4] was also been put forward The results areplentiful and of guiding significance However in this papercolor image would be discussed from another perspective ofKansei engineering Known from color ergonomics researchcolor affects peoplersquos emotions feelings thoughts and behav-ior unconsciously either direct visual stimulation or indirectassociation As a kind of important visual language differentcolor produces different stimulus to peoplersquos physical andmental moreover psychological effect of color affects personrsquosmood and behavior [5] In traditional color design usuallyaccording to the designersrsquo subjective experience and a lot oftrials and errors to make a decision now the color designtends to satisfy usersrsquo preferences emphasizing feeling and

experience of users Color image is a kind of color charac-teristics that consider color property and color psychologytogether In color design designers must study the emotionalreactions such as the feeling associated with emotional cog-nitive in usersrsquo heart and find out tacit knowledge of users [6]

As one kind of association produced by usersrsquo sensecolor image relates to factors such as usersrsquo vision experienceof life and cultural background belongs to the categoryof mental activity and can be quantitatively studied Atpresent many methods that such as grey theory fuzzytheory [7] neural network [8] genetic algorithm [9 10] andKansei engineering [11 12] have been applied to productrsquosform and color design They attempted to quantify peoplersquospsychological feelings of color [13] and acquired consumersrsquocolor image finally Hsiao and Tasi [14] used grey theory andback-propagation nerve network for children walkerrsquos colorquantitative evaluation research Hsiao et al [15] put forwarda kind of computer aided color selection system based on thecolor harmony fuzzy set theory and so on which could assistconsumer to choose the suitable clothing color matchingaccording to skin color and image preferences Tsai et al [16]proposed a kind of fast concept design method to predict

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014 Article ID 863150 11 pageshttpdxdoiorg1011552014863150

2 Mathematical Problems in Engineering

Usersrsquo tacitknowledge

Subimages

Image 1 Factor 1

Factor 2Image 2

FactorsOverallfactors

Color 2

Color p

Color 1

ExtractDimensionreduction

Image nm lt n

Usersrsquo perceptual image space

Factor m

F1

F2

FP

Map

Color space

R1 R2 Rn

G1 G2 Gn

B1 B2 Bn

Figure 1 The mapping of usersrsquo perceptual cognitive

image evaluation based on fuzzy neural network and greytheory and applied it in electronic lock design Tsai and Chou[17] applied grey theory and genetic algorithm to constructan automatic design support system which could generatecolor matching scheme of two colors according to the imageor evaluate color scheme automatically and it was used toevaluate the color image of kettle Ma et al [18] constructeda design decision-making support model for custom colorcombinations which would be applied to the sofa colordesign

The above research provides an efficient image evaluationcriterion and auxiliary support for product color designHowever these studies mainly focus on product color designalthough there are a few studies about color image andpreferences of interior space [19] that hardly consider colorimage problem of small space Color image is a compre-hensive psychological reaction for color that is producedby a variety of sensory organs The color of small space isdifferent from general product appearance Suppose a personis surrounded by environmental color the color of smallspace will have strong influence on peoplersquos perception Howto validate the fact that the color image designed by designersmatched with usersrsquo expectations Users have numerouscolor images and the image is fuzzy and uncertain howto quickly and accurately reflect the nonlinear relationshipbetween images How to change the perceptual color designto rational calculation and then return to the understandingof perceptual once again after design However very fewstudies have discussed these issues

Therefore the study aims to quantitatively study thepsychological attribute and emotional characteristics of colorand solve the problem that usersrsquo color image perceptionis fuzzy From the perspective of cognitive psychology [20]the methods such as Kansei engineering are used to makethe usersrsquo implicit color preference image externalizationAiming at the complicated nonlinear relation between thecomprehensive color image and color factors meanwhileand considering their intrinsic relevance excellent GEPalgorithm [21] was applied to construct the relationshipmodel between color image and color scheme and a coloroptimization designmethod for small space was built Finallycolor image evaluation system for small space was developedbased on the model and assisted designers to conduct colorevaluation and optimization by usersrsquo preference

2 Problem Description and Outlineof the Method

21 Problem Description Working space [22] refers to theneeded activity space when people are operating machineplus the total space which is occupied by machinery equip-ment appliances tools processing objects and so forthCombining with the definition of working space the conceptof small space is defined It is a closed or semiclosed spacethe range of activity for person is narrow and easily leads tooppression and other uncomfortable feelings Such as aircraftcockpit manned submersibles engineering machinery cabnuclear power plant control room oil rig driller control roomand family car cab in which the persons operate in sitting orstanding posture The space is restricted by various factorsbesides the space of machinery and equipment layout theactivity space for person is very limited The appropriatecolor design for small space will be able to adjust the spaceenvironmentrsquos atmosphere color temperature space size andso on Under the background of customization designersneed to conduct special custom to satisfy the demands ofusers

Color is a sense of perception formed by the brainrsquos visualcortex transmitted from nerve impulse generated by lightstimulate eye The formation of usersrsquo perceptual image is aprocess from the divergent thinking to convergent thinking[23] Color information seen directly and color aestheticpsychology are comprehensively processed by users themostsimilar images close to the space color are searched in thememory and users will combine several subimages to forman overall image On the contrary the deconstruction of theusersrsquo perceptual image is the inverse process In order to getthe usersrsquo overall image we need to decompose and knowits subimages Because of the usersrsquo different life backgroundexperience culture preferences age gender and so on per-ceptual images produced by different users will form a largenumber of subimage sets And the formation of perceptionsoften accompanied by complicated mental process leads tothe fact that the subjective information of images is fuzzyand uncertain So in order to build the mapping relationshipbetween the perceptual information and the color designof small space according to the usersrsquo perceptual cognitivestructure of thinking (shown in Figure 1) via FA to reducedimensionality and form the usersrsquo perceptual image spacethis paper extracted usersrsquo implicit knowledge explored the

Mathematical Problems in Engineering 3

Generation +1

Basic color samples Open-ended questionnaire

Small space samples

Representative colorsamples of small space

The collection of color images

Qualitative analysisand selecting images

Quantitative analysis

The evaluation of SD method

Factor sets of color images

Entropy weight method todetermine the objective weights

Factor score of basic color sample of small spaceand score of comprehensive perceptual image

The prediction model ofcolor image based on GEP

Start End

Coding

Create chromossomesof initial population

Evaluate fitness

Iterate or terminate

Iterate

Terminate

Keep the best individual

Selection

Replication

Mutation

ISRISgene transposition

1-point2-pointgene recombination

New population

Evaluation system

Designers Input color variablesInput image factor score

Color image prediction interface

Step 1

Step 2

Step 3

Step 4

FA

Prediction result of color image

Figure 2 The color image evaluation method for small space

relationship between the color factors and the overall imageand thus mastered usersrsquo color psychology

22 Outline of the Method As shown in Figure 2 the imple-mentation procedures of evaluationmethodmainly comprisethe following steps

Step 1 (choose the basic color samples of small space and colorimages) The test color samples were created by regularlyadjusting the RGB parameters with constant units within therange of 0ndash255 Human material and financial resourceswere comprehensively considered finally the simulationexperiment method of drawing space in plane was adoptedThe extensive color images were acquired by open-endedquestionnaire

Step 2 (analyze the color images qualitatively and quanti-tatively) The color images were qualitatively analyzed bydesigners and the representative adjectives were selectedThen the perceptual image evaluation experiment was car-ried on by SDmethod [24]Through FA to reduce dimension-ality of subimage sets factor score function was establishedand the weight of each factor was determined by the entropyweight method finally the comprehensive perceptual imagescore was calculated

Step 3 (establish the prediction model of color image basedon GEP) By GEP algorithmrsquos strong ability of functionfinding the best fitting function between the color factors andcomprehensive perceptual image was obtained The functioncould predict the usersrsquo color image value and grasp the usersrsquopsychology


Step 4 (construct the color image evaluation system for smallspace) Based on above-mentioned model the color imageevaluation system for small space was developed assisteddesigners to design the color and provided effective tools totest usersrsquo color image

3 Prediction Model of Color Image for SmallSpace Based on FA and GEP

31 Theoretical Background

311 FA FA [25] is a method of multivariate statistical anal-ysis which studies how to make numerous original variablescondense into a few factors with the least amount of infor-mation loss and how to make the factors have certain namedexplanatory Suppose that there are 119899 original variables1199091 1199092 1199093 119909

119899 after standardized treatment variables are

expressed by 119898 factors (119898 lt 119899) by means of linearcombination of 119891

1 1198912 1198913 119891

119898

1199091= 11988611

1198911+ 11988612

1198912+ sdot sdot sdot + 119886

1119898119891119898

+ 1205761

1199092= 11988621

1198911+ 11988622

1198912+ sdot sdot sdot + 119886

2119898119891119898

+ 1205762

119909119899

= 1198861198991

1198911+ 1198861198992

1198912+ sdot sdot sdot + 119886

119899119898119891119898

+ 120576119899

(1)

where 119886119894119895

(119894 = 1 2 119899 119895 = 1 2 119898) represents factorloading and 120576

119894(119894 = 1 2 119899) represents special factor

The factor loading is deduced with the method of princi-pal component analysis (PCA) Bymeans of coordinate trans-formation after standardization the original relevant vari-ables 119909

1 1199092 1199093 119909

119899were linearly combined converted

into another set of uncorrelated variables 119910119894

1199101= 12058311

1199091+ 12058312

1199092+ sdot sdot sdot + 120583

1119899119909119899

1199102= 12058321

1199091+ 12058322

1199092+ sdot sdot sdot + 120583

2119899119909119899

119910119899

= 1205831198991

1199091+ 1205831198992

1199092+ sdot sdot sdot + 120583

119899119899119909119899

(2)

where 1199101 1199102 119910

119899 respectively represent the first sec-

ond 119899th principal component of the original variables1199101has the largest proportion in total variance so it has

the strongest ability to synthesize the information of orig-inal variables The rest of principal componentsrsquo ability tosynthesize information declines in turn FA can reduce thevariable dimension and eliminate the correlation betweenthe variables so as to reduce the input of GEP independentvariable in the late

312 Entropy Weight Method German physicist R Clausiusput forward entropy and applied it in thermodynamics C EShannon introduced the concept of entropy in informationtheory later as a measurement of uncertainty or informationof random events [26] In information theory entropy is used

tomeasure the disorder degree of systemWhen the system ismore orderly the information entropy is smaller oppositelythe information entropy is larger The system has a variety ofdifferent state and the probability of each state to appear withthe 119875119894(119894 = 1 2 119898) and then the entropy of the system is

defined as

119890 = minus

119898

sum

119894=1

119875119894sdot ln119875119894 (3)

When 119875119894

= 1119898 (119894 = 1 2 119898) that is to saythe presence of the probability to each state is equal themaximum entropy is 119890max = ln119898

This paper introduced the information entropy to deter-mine the weights in the color image evaluation for smallspace If there are 119898 color samples of small space and 119899 colorfactors the data matrix of original evaluation 119877 = (119903

119894119895)119898times119899

isas follows

119877 =

[

[

[

[

11990311

11990312

sdot sdot sdot 1199031119899

11990321

11990322


sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot

1199031198981

1199031198982


]

]

]

]119898times119899

(4)

A color factor 119903119895has information entropy 119890

119895= minussum

119898

119894=1119875119894119895

sdot

ln119875119894119895and 119875

119894119895= 119903119894119895sum119898

119894=1119903119894119895

(119894 = 1 2 119898 119895 = 1 2 119899)Calculation steps of entropy weights are as follows

Step 1 Calculate the 119895th color factor of the 119894th color sampleof small spacersquos index weight 119875

119894119895 119875119894119895

= 119903119894119895sum119898

119894=1119903119894119895

Step 2 Calculate the entropy of the 119895th color factor 119890119895 119890119895=

minus119896sum119898

119894=1119875119894119895

sdot ln119875119894119895 and 119896 = 1 ln119898

Step 3 Calculate the deviation degree of the 119895th color factor(difference coefficient) 119892

119895 119892119895= 1 minus 119890

119895

Step 4 Calculate the entropy of 119895th factor 119908119895

119908119895

= 119892119895

sum119899

119895=1119892119895

313 GEP Algorithm GEP is a new random search and opti-mization algorithm invented and put forward by the Por-tuguese scientist Ferreira [27] GEP combines the advantagesof genetic algorithm and genetic programming algorithm Itis a new kind of efficient and ideal data mining techniquetaking the biotic genetic gene expression patterns as refer-ence Using adaptive random search method and withoutrelying on any prior knowledge GEP can discover formulawhich can describe data inherent law from the data andshows strong universality and accuracy In GEP a computerprogram is coded into fixed length of linear symbol strings(chromosome) while in the individual fitness calculation itwill be expressed to different shapes and sizes of expressiontrees so as to solve the problem As shown in Figure 2 themain steps of using GEP for function mining are as follows[28]

Step 1 Code the individual and create the initial populationPopulation contains a number of individuals (chromosomes)


Chromosome is comprised of more than one gene andthe genes are connected through linking function Gene iscomprised of head and tail Head consists of function set orterminal set and end consists of terminal set

Step 2 Calculate the fitness The fitness of each individual iscalculated through fitness function Fitness reflects the extentof excellence of individual to achieve the optimal solutionin the course of evolution If the optimal individual satisfiesend condition it will be transferred to the output If nottransferred to genetic operation steps and then producesoffspring with new characteristics

Step 3 Do a series of genetic operation to produce a newgeneration of population using principle of survival of thefittest to guide the evolution including (1) keep the bestindividual (2) selection (3) replication (4) mutation (5)transposition and (6) recombination

32 PredictionModel of Color Image for Small Space Thecoretechnology of GEP is that the mutation process is completelyseparated from the evaluation process Fixed linear stringis used in mutation process and expression tree is used inevaluation process

First of all determine the symbols representing chro-mosome namely select function set and terminal set whichsuited the solution GEP = (119865 119879) Suppose function set119865 = + minus lowast sin cos and common function includearithmetic operators elementary mathematics functionBoolean operator and relational operators terminal set 119879 =

1199091 1199092 1199093 119909

119899 1199091 1199092 1199093 119909

119899represents color image

factor setSecondly determine the genetic structure and the length

of gene head According to the complexity of the problem todefine the length of gene head ℎ the length of tail 119905 and thelength of head ℎ satisfy the relationship that 119905 = ℎ(119899minus1)+1 Inthe formula 119899 represents the maximum number of operationnumbers in function set namely the number involved inthe operation variable It can guarantee that the genes arelegitimate in this way Suppose that a gene is composed of theelements in + minus lowast sin cos 119909

1 1199092 1199093 1199094 1199095 1199096 so 119899 = 2

If ℎ = 6 then 119905 = 6(2 minus 1) + 1 = 7 Randomly generate alegitimate GEP gene as follows

sinminus1199095

lowastlowast+ 1199094119909111990921199093119909611990931199095 (5)

The italicized part represents the tail The correspondingexpression tree is shown in Figure 3

The length of each gene is fixed in GEP coding Gene ismade up of two parts the front effective K-expression and theback of filler components From top to bottom left to rightsequence the expression trees in Figure 3 are traversed andthe K-expression of expression trees is obtainedThe effectivelength of the gene has 10 characters sinminus119909

5

lowastlowast+1199094119909111990921199093 So

the mathematical expression is as follows

sin (1199095minus 11990941199091(1199092+ 1199093)) (6)

Again determine the number of genes in each chromo-some and the linking function to connect the genes

Sin

X5

X4 X3X1 X2

lowast

lowast

minus

+

Figure 3 Gene expression tree

Fourth select the fitness functionThere are three kinds ofclassical fitness function in GEP algorithm According to thecharacteristics of the problem and reference [29] the fitnessfunction is defined as follows

119891119894=

1000

119864119894+ 1

(7)

In (7) 119864119894

= (1119898)sum119898

119895=1(119862119894119895

minus 119879119895)2 is the mean square

error (MSE) of experimental samples m is the total numberof training set samples 119862

119894119895is the output value of the 119895th

sample of the 119894th individual calculated by the mathematicalexpressions acquired by GEP algorithm modeling 119879

119895is the

target value of the 119895th sampleFinally determine the genetic control parameters before

the algorithm running including the size of the populationevolution generation limit and the probability of each geneticoperators

4 Implementation Procedures

The effectiveness and feasibility of the proposed method aredemonstrated by taking the case of color image evaluation of acontrol room on AC frequency conversion rig for illustrationpurposes The steps involved in implementing the evaluationsystem are described in the following sections

41 Basic Color Samples of Small Space411 Basic Color Samples The amount of basic color samplesshould not only reduce the workload of experiment butalso not affect the measure conditions to express imageAccording to [17] to set color intervals RGB parameterschange with 64 units within the range of 0ndash255 Each primaryaxis gets 5 intervals eventually 5

3= 125 sets of basic color

samples are obtained (shown in Figure 4) defined as 119862 =

1198621 1198622 119862

119899

412 Small Space Samples In order to avoid the mutualinfluence of multivariable this paper only discusses the maincolor of small space and does not consider the impact offactors such as material and form for the moment As shownin Figure 5 the space sample with transparent background


Table 1 Color images obtained from questionnaire

(1) Modern (6) Gorgeous (11) Elegant (16) Quiet (21) Warm (26) Lively(2) Dynamic (7) Noble (12) Graceful (17) Solemn (22) Soft (27) Lightful(3) Simple (8) Male (13) Fresh (18) Classical (23) Joyful (28) Bright(4) Technological (9) Handsome (14) Cool (19) Plain (24) Romantic (29) Roomy(5) Fashionable (10) Female (15) Steady (20) Cozy (25) Popular

000

6400

12800

19200

25500

0640

64640

128640

192640

255640

01280

641280

1281280

1921280

2551280

01920

641920

1281920

1921920

2551920

02550

642550

1282550

1922550

2552550

0064

64064

128064

1920

64255064

00128

640128

1280128

1920128

2550128

00192

640192

1280192

1920192

2550192

00255

640255

1280255

1920255

2550255

06464

646464

1286464

1926464

2556464

064128

6464128

12864128

19264128

25564128

064192

6464192

12864192

19264192

25564192

064255

6464255

12864255

19264255

25564255

012864

6412864

12812864

19212864

25512864

0128128

64128128

128128128

192128128

255128128

0128192

64128192

128128192

192128192

255128192

0128255

64128255

128128255

192128255

255128255

019264

6419264

12819264

19219264

25519264

0192128

64192128

128192128

192192128

255192128

0192192

64192192

128192192

192192192

255192192

0192255

64192255

128192255

192192255

255192255

025564

6425564

12825564

19225564

25525564

0255128

64255128

128255128

192255128

255255128

0255192

64255192

128255192

192255192

255255192

0255255

64255255

128255255

192255255

255255255

Figure 4 RGB values of 125 basic color samples

Figure 5 Master page of the space sample

is made as a master page In test process the randomsuperposition of the 125 color samples which can formthe color samples of small space to meet the experimentaldemand is shown in Figure 6

42 Qualitative and Quantitative Analysis of Color Image

421 Qualitative Analysis Through open-ended question-naire [30] to acquire extensive color images they were qual-itatively analyzed by designers according to their practicalwork experience The repeated meaning words were deletedand the similar meaning words were merged Ultimatelythe selected representative adjectives covered color semanticcognitive space as much as possible 29 color images arepreliminary selected (shown in Table 1)

422 Quantitative Analysis 40 subjects (half male and halffemale) are invited to take part in the experiment All of them

are students aged between 20 and 28 years old and both eye-sight and color vision are normal As shown in Figures 7 and 5points psychology scale is used to represent the differentdimensions of psychological variation The evaluation valueof color image for small space is set between 0 and 1 the largervalue represents the more close to the feeling of color image

The color samples of small space randomly are displayedon the computer screen and the subjects evaluate themaccording to the 29 color images respectively The experi-mental results are analyzed with SPSS Statistics190 softwarefor FA First by calculating the correlation coefficient matrixanti-image correlationmatrix Bartlettrsquos test of sphericity andKaiser-Meyer-Olkin (KMO) test the relationship betweenvariables is tested The statistics observed value is 5456468in Bartlettrsquos test of sphericity since the corresponding prob-ability of 119875 value is close to 0 less than the significancelevel of 120572 (120572 equal to 005) it can be regarded as that thereis significant difference between the correlation coefficientmatrix and unitmatrixThe value of KMO is 0886 accordingto the KMOmetrics provided by Kaiser the original variablesare suitable to conduct FA

According to the principle [25] that ldquousually select thenumber of eigenvalues as factor number when cumulativevariance contribution rate is greater than 085rdquo the factorsare extracted by the method of PCA Six factors of colorimage are extracted the corresponding cumulative variancecontribution rate reaches 87289 (shown in Table 2) andmeets the above principle

In Table 3 the data shown in bold in each columnrepresent the color images as having high loading on the6 factors respectively For example the fifth factor mainlyexplains four color images the lightful bright lively androomy Therefore we can summarize some conclusions thatthe first factor mainly explains the feeling of being modernand fashionable the second factormainly explains the feelingof being relaxed and calm the third factormainly explains thefeeling of being sweet and elegant the fourth factor mainly


Table 2 Total variance explained

Component Initial eigenvalues Extraction sums of squared loadings Rotation sums of Squared loadingsTotal of variance Cumulative Total of variance Cumulative Total of variance Cumulative

1 13085 45119 45119 13085 45119 45119 5757 19851 198512 4529 15618 60737 4529 15618 60737 5129 17687 375383 3611 12450 73187 3611 12450 73187 4404 15185 527234 2196 7573 80761 2196 7573 80761 3643 12562 652855 1036 3574 84335 1036 3574 84335 3347 11541 768266 0857 2954 87289 0857 2954 87289 3034 10463 872897 0650 2242 895318 0565 1949 91480

28 0018 0062 9995929 0012 0041 100000

Figure 6 An example of the color sample of small space

No Somewhat Neutral Very Extremely

0 025 05 075 1

Figure 7 The image scale of color evaluation words

explains the feeling of personality and being solemn thefifth factor main explains the feeling of being bright androomy and the sixth factor main explains the feeling of beinggorgeous and noble In this way the dimension of 29 variablesis reduced to 6 factors and can reflect most of the informationof the original variables

Regression method is used to estimate the factor scorecoefficient Component sore coefficient matrix is calculatedand the function of factor score is expressed as follows

1198651198941

= 0327 lowast image 1 + 0104 lowast image 2

+ sdot sdot sdot minus 0028 lowast image 28 + 0037 lowast image 29

1198651198942

= minus 0147 lowast image 1 minus 0017 lowast image 2

+ sdot sdot sdot + 0008 lowast image 28 + 0008 lowast image 29

1198651198943

= 0019 lowast image 1 minus 0208 lowast image 2


1198651198944



1198651198945

= minus 0080 lowast image 1 + 0162 lowast image 2


1198651198946


+ sdot sdot sdot + 0030 lowast image 28 minus 0006 lowast image 29

(8)

The factor score of each color sample of small space can becalculated by (8) then the method of calculating total scoreby factor weight is adopted and the overall image is assessedcomprehensively Determining the weight of the factors isthe key Based on the principle of information entropy andthe original evaluation data information this paper used thedifferences between the values which reflected ldquoinformation


Table 3 Rotated component matrix

Component1 2 3 4 5 6

Image 1 0902 0180 minus0120 0210 minus0023 0034Image 5 0856 0141 minus0201 0267 0106 0141Image 3 0814 0332 minus0209 0191 0177 minus0103Image 25 0793 0410 0017 0117 0111 minus0249Image 4 0720 0435 minus0293 0349 0068 minus0051Image 18 0480 0348 minus0049 0439 minus0368 0416Image 19 0458 0174 0054 0429 minus0361 0420Image 13 0311 0908 0045 0051 0132 minus0119Image 14 0337 0864 minus0086 0166 0168 minus0207Image 16 0307 0790 minus0209 0406 0063 minus0148Image 15 0400 0650 minus0191 0540 minus0099 minus0037Image 23 0613 0637 0130 0114 0179 minus0275Image 20 0020 minus0027 0912 minus0115 0027 0150Image 24 minus0115 0085 0835 minus0066 minus0030 0023Image 22 minus0117 minus0218 0803 minus0253 0116 0048Image 11 minus0188 minus0035 0679 minus0060 minus0177 0575Image 21 minus0208 minus0541 0598 minus0358 0073 0208Image 9 0356 0137 minus0328 0821 0041 minus0093Image 8 0440 0329 minus0351 0703 0047 minus0142Image 10 minus0315 minus0181 0546 minus0642 minus0075 0167Image 17 0416 0561 minus0191 0609 minus0146 0031Image 27 0233 0231 0017 0092 0871 minus0165Image 28 0239 0236 minus0001 0033 0853 minus0234Image 26 minus0265 minus0167 0003 minus0166 0777 0006Image 29 0472 0403 0011 0187 0603 minus0220Image 2 0047 minus0397 minus0330 minus0457 0524 0255Image 6 minus0043 minus0231 0120 minus0171 minus0001 0864Image 7 minus0002 minus0315 0227 0005 minus0221 0798Image 12 minus0111 0007 0611 minus0070 minus0265 0631

Table 4 The weight of factors

Weight Factor 1 Factor 2 Factor 3 Factor 4 Factor 5 Factor 6119908s119894 0199 0177 0152 0126 0115 0105119908o119894 0105 0154 0135 0378 0089 0138119908119894

0148 0193 0146 0338 0073 0103

valuerdquo of factor to determine theweight SDmethod is used toquantify the color image of subjectsrsquo preferences evaluationdata is sorted and described as follows

[

[

[

[

[

[

[

119909119896

11119909119896

12119909119896

13sdot sdot sdot 119909

119896

1119899

119909119896

21119909119896

22119909119896


119896

2119899

sdot sdot sdot sdot sdot sdot sdot sdot sdot 119909119896

119894119895sdot sdot sdot

119909119896

1198981119909119896

1198982119909119896

1198983sdot sdot sdot 119909119896

119898119899

]

]

]

]

]

]

]

(9)

where 119898 represents the number of color samples of smallspace 119899 represents the number of factors 119909119896

119894119895represents the

119896th subjectrsquos preference to the 119895th factor of the 119894th colorsample of small space

According to the above-mentioned calculation steps ofentropy weights the objective weight of each factor can becalculated denoted as 119908

119900119894= (119908

1199001 1199081199002

119908119900119899

) Entropyweight method is a kind of objective method In order toretain experts and policymakersrsquo subjective opinions namelybalance subjective and objective aspect the entropy weight

method is combined with each factor variance contributionrate in the above-mentioned FA Suppose the variance con-tribution rate calculated in FA is subjective weight 119908

119904119894and

entropy 119908119900119894is the objective weight the combination weight

119908119894of the 119894th factor can be calculated as follows

119908119894=

119908119904119894119908119900119894

sum119899

119894=1119908119904119894119908119900119894

(10)

Table 4 shows the calculation results of weights Thecomprehensive color image evaluation of small space is asfollows

119865119894= 11990811198651198941

+ 11990821198651198942

+ 11990831198651198943

+ 11990841198651198944

+ 11990851198651198945

+ 11990861198651198946 (11)

43 Color Image Prediction Based on GEP 84 groups of datawere randomly selected from 125 groups of experimentaldata as the training set and the rest as a validation setTable 5 shows the main operation parameters in GEP modelIn function set Sqrt represents square root 1198832 repre-sents square Avg 2 represents the mean of two variables


minusminus

x1 x5

x5

x4 x4

x2

x3 x6

x1

x6

x6

x5

x2

x2

x4

Sub-ET 1 Sub-ET 2 Sub-ET 3

lowast

lowast

lowast

lowast

+

c2

c4

c5

c9

Avg 2 Avg 2

Avg 2

Avg 2 Avg 2

Avg 2

Figure 8 The sub-ET of optimal individual

Table 5 GEP parameter set

Parameter names Parameter valuesFunction set 119865 = + minus lowast Sqrt 1198832Avg2Neg InvTerminal set 119879 = 119909

1 1199092 1199093 1199094 1199095 1199096

Generation 1000Number of chromosomes 30Number of genes 3Linking function +Head size 8Mutation rate 0002One-pointTwo-pointgenerecombination rate

0003

ISRISgenetransposition rate 0005

Numerical constant (minus10 10)

Neg represents negative Inv represents inverse In terminalset 1199091 1199092 1199093 1199094 1199095 1199096 respectively represent the 6 factors

obtained from FA The visual basic programming is used toexpress the GEP algorithm and the program runs multipletimes to get the best individual The best individualrsquos expres-sion tree is shown in Figure 8 Each expression tree representsa gene and genes are connected by linking function ldquo+rdquoto form a chromosome The best individual translated intomathematical expression is as follows

119865 (119909) =

1

2

(

1199091+ 1199095

2

+

1199094+ 1199094

2

)

+

1

2

(

1199092minus 1199095+ 1199093

2

sdot

1199095+ 1199096

2

+ (037141199096)2

)

+

minus49771 minus 277111199091

(minus51091 minus 1199096)2

sdot 1199094

(12)

Figure 9 shows the curve fitting of GEP algorithm inthe training set MSE and 119877-square are used to verify thevalidity of the algorithm and the ability of the predictionTheformulas are as follows

MSE =

1

119899

119899

sum

119894=1

(1199101015840

119894minus 119910119894)

2

119877-square = 1 minus

sum119899

119894=1(1199101015840

119894minus 119910119894)

2

sum119899

119894=1(119910119894minus 119910avg)

2

(13)

0010203040506

0

Com

preh

ensiv

e col

or

Training set

TargetModel

5 10 20 30 40 5015 25 35 45 6055 7065 80 8575

imag

e val

ue

Figure 9 The fitting curve of training set

0015

02025

03035

04045

05055

06

Validation set

Com

preh

ensiv

e col

or

TargetModel

imag

e val

ue

3 6 9 12 15 18 21 24 27 30 33 36 39 42

Figure 10 The fitting curve of validation set

In (13) 1199101015840

119894 119910119894 and 119910avg represent the predicted value

the actual value and the actual average value respectivelyThe range of 119877-square is [0 1] the closer to 1 showing thatthe equationrsquos 6 variables have stronger ability to explainthe comprehensive color image 119865(119909) The calculation resultshows that the MSE and 119877-square of training set are 00006and 09614 respectively In order to verify the validity of theGEP model 41 sets of data are taken into the model and thecurve fitting of validation set is shown in Figure 10 The MSEand 119877-square are 00007 and 09453 respectively achievingthe ideal effect

44 Evaluation System According to the above-mentionedmethod VB is used to develop a color image evaluationsystem for small space The system can assist designers incolor design In the system designers input color value andusersrsquo factor score of color scheme According to the function


Table 6 The comparison of evaluation results

Color scheme Color value (R G and B) The value of questionnaire The value of this method Deviation1 (112 171 244) 07 06824 001762 (229 178 232) 055 05073 004273 (250 10 72) 02 01941 000594 (32 32 242) 055 05447 000535 (123 131 130) 045 04635 001356 (159 248 164) 055 05641 001417 (240 249 88) 025 02703 002038 (112 171 244) 03 02978 000229 (235 235 235) 075 07022 0047810 (209 226 246) 075 07705 00205

Figure 11 The evaluation interface of color image for small space

constructed by GEP algorithm the system automaticallypredicts and outputs comprehensive color image value Asshown in Figure 11 the designer selects color value in thewindow (112 171 and 244) inputs the user rating of the 6factors 088 095 041 058 090 and 042 and then clickon ldquoevaluationrdquo button the comprehensive color image valueof this small space can be calculated that is 06824

In order to verify the color image evaluation methodsof small space 10 unspecified color schemes of small spaceevaluated by system were evaluated by questionnaire again50 subjects (half male and half female) are invited to ratethe color scheme scoring criteria is 0 to 1 The questionnaireresults and the evaluation results using the method proposedin this paper are compared Table 6 shows that the deviationbetween the value of questionnaire and above-mentionedmethod is among 00022sim00478 and the average deviationof 10 color schemes is 0019 Therefore the color imageevaluation method for small space put forward in this papercan accurately predict the usersrsquo image

5 Conclusion

Image perception is fuzzy so the color image of small space isuncertain for usersThe relationship between all color factorsis undefined and there is complex nonlinear relationshipbetween the comprehensive color image value and colorimage factors For the first time this paper is proposed toapply GEP algorithm to the color design of small spaceBased on the research method and framework proposed inthis paper FA was used to preprocess the experimental dataon the premise of reserving the main information data thecorrelation of data was removed and the data dimension wasreduced effectively The training samples were not reducedmoreover the correlation of the GEPrsquos input variable waseliminated Combining the entropy weight method to obtainthe objective weights of color factors 125 groups of evaluationdata were the data base of prediction model The colorimage prediction model for small space realized automaticmodeling of complex function based on GEP algorithm


The calculation and analysis results of application exampleshowed that the prediction result was close to the targetand it had high prediction accuracy The example of colorimage evaluation of driller control roomproved that GEP hadstrongnonlinear and global search ability to find function andprovided a solution way for rapid evaluation of color imageIn the next step of research work different algorithms will beused to compare the results and analysis At the same timethe color collocation and the coupling relationship betweencolor and shape will be the research content in next step

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research was supported by the National Natural ScienceFund Project of China no 51105310 and partly supported bythe 111 Project Grant no B13044

References

[1] X-Y Wang Z-F Chen and J-J Yun ldquoAn effective method forcolor image retrieval based on texturerdquo Computer Standards ampInterfaces vol 34 no 1 pp 31ndash35 2012

[2] X Y Wang and Z Y Wang ldquoA novel method for imageretrieval based on structure elementsrsquo descriptorrdquo Journal ofVisual Communication and Image Representation vol 24 no 1pp 63ndash74 2013

[3] X Y Wang D D Zhang and X Guo ldquoAuthentication andrecovery of images using standard deviationrdquo Journal of Elec-tronic Imaging vol 22 no 3 Article ID 033012 2013

[4] X Y Wang D D Zhang and X Guo ldquoA novel image recoverymethod based on discrete cosine transform and matchedblocksrdquoNonlinear Dynamics vol 73 no 3 pp 1945ndash1954 2013

[5] S E Palmer and K B Schloss ldquoAn ecological valence theory ofhuman color preferencerdquo Proceedings of the National Academyof Sciences of the United States of America vol 107 no 19 pp8877ndash8882 2010

[6] S-J Luo S-S Zhu F-T Ying and J-S Zhang ldquoStatues andprogress of research on usersrsquo tacit knowledge in productdesignrdquoComputer IntegratedManufacturing Systems vol 16 no4 pp 673ndash688 2010

[7] S-W Hsiao ldquoFuzzy set theory on car-color designrdquo ColorResearch amp Application vol 19 no 3 pp 202ndash213 1994

[8] S J Cai A Study on Building the Color Combination SystemUsing Neural Network and Genetic Algorithm National ChengKung University Taiwan China 2003

[9] S-WHsiao C-FHsu andK-WTang ldquoA consultation and sim-ulation system for product color planning based on interactivegenetic algorithmsrdquoColor Research amp Application vol 38 no 5pp 375ndash390 2013

[10] Y Sun W-L Wang Y-W Zhao and X-J Liu ldquoUser image ori-ented interactive genetic algorithm evaluationmode in productdevelopmentrdquoComputer IntegratedManufacturing Systems vol18 no 2 pp 276ndash281 2012

[11] M Nagamachi ldquoKansei engineering as a powerful consumer-oriented technology for product developmentrdquo Applied Ergo-nomics vol 33 no 3 pp 289ndash294 2002

[12] M Nagamachi ldquoKansei engineering a new ergonomic con-sumer-oriented technology for product developmentrdquo Interna-tional Journal of Industrial Ergonomics vol 15 no 1 pp 3ndash111995

[13] S-W Hsiao F-Y Chiu and C S Chen ldquoApplying aestheticsmeasurement to product designrdquo International Journal of Indus-trial Ergonomics vol 38 no 11-12 pp 910ndash920 2008

[14] S-W Hsiao and H-C Tsai ldquoUse of gray system theory in prod-uct-color planningrdquo Color Research amp Application vol 29 no3 pp 222ndash231 2004

[15] S-W Hsiao F-Y Chiu and H-Y Hsu ldquoA computer-assistedcolour selection system based on aesthetic measure for colourharmony and fuzzy logic theoryrdquo Color Research amp Applicationvol 33 no 5 pp 411ndash423 2008

[16] H-C Tsai S-W Hsiao and F-K Hung ldquoAn image evaluationapproach for parameter-based product form and color designrdquoComputer-Aided Design vol 38 no 2 pp 157ndash171 2006

[17] H-C Tsai and J-R Chou ldquoAutomatic design support and imageevaluation of two-coloured products using colour associationand colour harmony scales and genetic algorithmrdquo Computer-Aided Design vol 39 no 9 pp 818ndash828 2007

[18] M-YMa C-Y Chen and F-GWu ldquoA design decision-makingsupport model for customized product color combinationrdquoComputers in Industry vol 58 no 6 pp 504ndash518 2007

[19] J Y Lin A Study of Spatial Color Image for Living Space AnInvestigation of Living Space for Demostic Units in Taipei MingChuan University Taiwan China 2005

[20] Y L Qin CognItive Psychology and Itrsquos Implications Posts ampTelecom Press Beijing China 2012

[21] C Ferreira ldquoGene expression programming in problem solv-ingrdquo in Soft Computing and Industry pp 635ndash653 SpringerLondon UK 2002

[22] C R LiuTheApplication of Ergonomics Shanghai Peoplersquos FineArts Publishing House Shanghai China 2nd edition 2009

[23] Y Zhang Y Yang S J Luo and Y H Pan ldquoMental constructionof user perception image in product designrdquo Journal of Mechan-ical Engineering vol 46 no 2 pp 178ndash184 2010

[24] C E Osgood The Measurement of Meaning University ofIllinois Press Urbana Ill USA 1957

[25] WXue Statistical Analysis and SPSSApplication ChinaRenminUniversity Press Beijing China 3rd edition 2011

[26] J G Zhang and P S Vijay Information EntropymdashTheory andApplication China WaterPower Press Beijing China 2012

[27] C Ferreira ldquoGene expression programming a new adaptivealgorithm for solving problemsrdquo Complex Systems vol 13 no2 pp 87ndash129 2001

[28] J Zuo Core Technology Research on Gene Expression Program-ming Sichuan University Chengdu China 2004

[29] X Li C Zhou P C Nelson and T M Tirpak ldquoInvestigation ofconstant creation techniques in the context of gene expressionprogrammingrdquo in Proceedings of the Genetic and EvolutionaryComputation Conference Seattle Wash USA June 2004

[30] J N Su and H Q Li ldquoMethod of product form design based onperceptual imagerdquo Chinese Journal of Mechanical Engineeringvol 40 no 4 pp 164ndash167 2004

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


Usersrsquo tacitknowledge

Subimages

Image 1 Factor 1

Factor 2Image 2

FactorsOverallfactors

Color 2

Color p

Color 1

ExtractDimensionreduction

Image nm lt n

Usersrsquo perceptual image space

Factor m

F1

F2

FP

Map

Color space

R1 R2 Rn

G1 G2 Gn

B1 B2 Bn

Figure 1 The mapping of usersrsquo perceptual cognitive

image evaluation based on fuzzy neural network and greytheory and applied it in electronic lock design Tsai and Chou[17] applied grey theory and genetic algorithm to constructan automatic design support system which could generatecolor matching scheme of two colors according to the imageor evaluate color scheme automatically and it was used toevaluate the color image of kettle Ma et al [18] constructeda design decision-making support model for custom colorcombinations which would be applied to the sofa colordesign

The above research provides an efficient image evaluationcriterion and auxiliary support for product color designHowever these studies mainly focus on product color designalthough there are a few studies about color image andpreferences of interior space [19] that hardly consider colorimage problem of small space Color image is a compre-hensive psychological reaction for color that is producedby a variety of sensory organs The color of small space isdifferent from general product appearance Suppose a personis surrounded by environmental color the color of smallspace will have strong influence on peoplersquos perception Howto validate the fact that the color image designed by designersmatched with usersrsquo expectations Users have numerouscolor images and the image is fuzzy and uncertain howto quickly and accurately reflect the nonlinear relationshipbetween images How to change the perceptual color designto rational calculation and then return to the understandingof perceptual once again after design However very fewstudies have discussed these issues

Therefore the study aims to quantitatively study thepsychological attribute and emotional characteristics of colorand solve the problem that usersrsquo color image perceptionis fuzzy From the perspective of cognitive psychology [20]the methods such as Kansei engineering are used to makethe usersrsquo implicit color preference image externalizationAiming at the complicated nonlinear relation between thecomprehensive color image and color factors meanwhileand considering their intrinsic relevance excellent GEPalgorithm [21] was applied to construct the relationshipmodel between color image and color scheme and a coloroptimization designmethod for small space was built Finallycolor image evaluation system for small space was developedbased on the model and assisted designers to conduct colorevaluation and optimization by usersrsquo preference

2 Problem Description and Outlineof the Method

21 Problem Description Working space [22] refers to theneeded activity space when people are operating machineplus the total space which is occupied by machinery equip-ment appliances tools processing objects and so forthCombining with the definition of working space the conceptof small space is defined It is a closed or semiclosed spacethe range of activity for person is narrow and easily leads tooppression and other uncomfortable feelings Such as aircraftcockpit manned submersibles engineering machinery cabnuclear power plant control room oil rig driller control roomand family car cab in which the persons operate in sitting orstanding posture The space is restricted by various factorsbesides the space of machinery and equipment layout theactivity space for person is very limited The appropriatecolor design for small space will be able to adjust the spaceenvironmentrsquos atmosphere color temperature space size andso on Under the background of customization designersneed to conduct special custom to satisfy the demands ofusers

Color is a sense of perception formed by the brainrsquos visualcortex transmitted from nerve impulse generated by lightstimulate eye The formation of usersrsquo perceptual image is aprocess from the divergent thinking to convergent thinking[23] Color information seen directly and color aestheticpsychology are comprehensively processed by users themostsimilar images close to the space color are searched in thememory and users will combine several subimages to forman overall image On the contrary the deconstruction of theusersrsquo perceptual image is the inverse process In order to getthe usersrsquo overall image we need to decompose and knowits subimages Because of the usersrsquo different life backgroundexperience culture preferences age gender and so on per-ceptual images produced by different users will form a largenumber of subimage sets And the formation of perceptionsoften accompanied by complicated mental process leads tothe fact that the subjective information of images is fuzzyand uncertain So in order to build the mapping relationshipbetween the perceptual information and the color designof small space according to the usersrsquo perceptual cognitivestructure of thinking (shown in Figure 1) via FA to reducedimensionality and form the usersrsquo perceptual image spacethis paper extracted usersrsquo implicit knowledge explored the


Generation +1


Small space samples










Start End

Coding


Evaluate fitness


Iterate

Terminate


Selection

Replication

Mutation



New population

Evaluation system



Step 1

Step 2

Step 3

Step 4

FA















1 1198912 1198913 119891

119898

1199091= 11988611

1198911+ 11988612

1198912+ sdot sdot sdot + 119886

1119898119891119898

+ 1205761

1199092= 11988621

1198911+ 11988622

1198912+ sdot sdot sdot + 119886

2119898119891119898

+ 1205762

119909119899

= 1198861198991

1198911+ 1198861198992

1198912+ sdot sdot sdot + 119886

119899119898119891119898

+ 120576119899

(1)

where 119886119894119895




1 1199092 1199093 119909



1199101= 12058311

1199091+ 12058312

1199092+ sdot sdot sdot + 120583

1119899119909119899

1199102= 12058321

1199091+ 12058322

1199092+ sdot sdot sdot + 120583

2119899119909119899

119910119899

= 1205831198991

1199091+ 1205831198992

1199092+ sdot sdot sdot + 120583

119899119899119909119899

(2)

where 1199101 1199102 119910






defined as

119890 = minus

119898

sum

119894=1

119875119894sdot ln119875119894 (3)

When 119875119894



119894119895)119898times119899

isas follows

119877 =

[

[

[

[

11990311

11990312


11990321

11990322



1199031198981

1199031198982


]

]

]

]119898times119899

(4)


119895= minussum

119898

119894=1119875119894119895

sdot

ln119875119894119895and 119875

119894119895= 119903119894119895sum119898

119894=1119903119894119895



119894119895 119875119894119895

= 119903119894119895sum119898

119894=1119903119894119895



119894=1119875119894119895

sdot ln119875119894119895 and 119896 = 1 ln119898


119895 119892119895= 1 minus 119890

119895


119908119895

= 119892119895

sum119899

119895=1119892119895









1199091 1199092 1199093 119909

119899 1199091 1199092 1199093 119909




1 1199092 1199093 1199094 1199095 1199096 so 119899 = 2


sinminus1199095

lowastlowast+ 1199094119909111990921199093119909611990931199095 (5)



5

lowastlowast+1199094119909111990921199093 So


sin (1199095minus 11990941199091(1199092+ 1199093)) (6)


Sin

X5

X4 X3X1 X2

lowast

lowast

minus

+



119891119894=

1000

119864119894+ 1

(7)

In (7) 119864119894

= (1119898)sum119898

119895=1(119862119894119895





119895is the








1198621 1198622 119862

119899





000

6400

12800

19200

25500

0640

64640

128640

192640

255640

01280

641280

1281280

1921280

2551280

01920

641920

1281920

1921920

2551920

02550

642550

1282550

1922550

2552550

0064

64064

128064

1920

64255064

00128

640128

1280128

1920128

2550128

00192

640192

1280192

1920192

2550192

00255

640255

1280255

1920255

2550255

06464

646464

1286464

1926464

2556464

064128

6464128

12864128

19264128

25564128

064192

6464192

12864192

19264192

25564192

064255

6464255

12864255

19264255

25564255

012864

6412864

12812864

19212864

25512864

0128128

64128128

128128128

192128128

255128128

0128192

64128192

128128192

192128192

255128192

0128255

64128255

128128255

192128255

255128255

019264

6419264

12819264

19219264

25519264

0192128

64192128

128192128

192192128

255192128

0192192

64192192

128192192

192192192

255192192

0192255

64192255

128192255

192192255

255192255

025564

6425564

12825564

19225564

25525564

0255128

64255128

128255128

192255128

255255128

0255192

64255192

128255192

192255192

255255192

0255255

64255255

128255255

192255255

255255255














1 13085 45119 45119 13085 45119 45119 5757 19851 198512 4529 15618 60737 4529 15618 60737 5129 17687 375383 3611 12450 73187 3611 12450 73187 4404 15185 527234 2196 7573 80761 2196 7573 80761 3643 12562 652855 1036 3574 84335 1036 3574 84335 3347 11541 768266 0857 2954 87289 0857 2954 87289 3034 10463 872897 0650 2242 895318 0565 1949 91480

28 0018 0062 9995929 0012 0041 100000



0 025 05 075 1




1198651198941



1198651198942



1198651198943



1198651198944



1198651198945



1198651198946



(8)








0148 0193 0146 0338 0073 0103


[

[

[

[

[

[

[

119909119896

11119909119896

12119909119896


119896

1119899

119909119896

21119909119896

22119909119896


119896

2119899



119909119896

1198981119909119896

1198982119909119896

1198983sdot sdot sdot 119909119896

119898119899

]

]

]

]

]

]

]

(9)





119900119894= (119908

1199001 1199081199002

119908119900119899



119904119894and



119908119894=

119908119904119894119908119900119894

sum119899

119894=1119908119904119894119908119900119894

(10)


119865119894= 11990811198651198941

+ 11990821198651198942

+ 11990831198651198943

+ 11990841198651198944

+ 11990851198651198945

+ 11990861198651198946 (11)



minusminus

x1 x5

x5

x4 x4

x2

x3 x6

x1

x6

x6

x5

x2

x2

x4


lowast

lowast

lowast

lowast

+

c2

c4

c5

c9

Avg 2 Avg 2

Avg 2

Avg 2 Avg 2

Avg 2




1 1199092 1199093 1199094 1199095 1199096


0003





119865 (119909) =

1

2

(

1199091+ 1199095

2

+

1199094+ 1199094

2

)

+

1

2

(

1199092minus 1199095+ 1199093

2

sdot

1199095+ 1199096

2

+ (037141199096)2

)

+

minus49771 minus 277111199091

(minus51091 minus 1199096)2

sdot 1199094

(12)


MSE =

1

119899

119899

sum

119894=1

(1199101015840

119894minus 119910119894)

2


sum119899

119894=1(1199101015840

119894minus 119910119894)

2

sum119899

119894=1(119910119894minus 119910avg)

2

(13)

0010203040506

0

Com

preh

ensiv

e col

or

Training set

TargetModel

5 10 20 30 40 5015 25 35 45 6055 7065 80 8575

imag

e val

ue


0015

02025

03035

04045

05055

06

Validation set

Com

preh

ensiv

e col

or

TargetModel

imag

e val

ue

3 6 9 12 15 18 21 24 27 30 33 36 39 42


In (13) 1199101015840










5 Conclusion






Acknowledgment


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Generation +1


Small space samples










Start End

Coding


Evaluate fitness


Iterate

Terminate


Selection

Replication

Mutation



New population

Evaluation system



Step 1

Step 2

Step 3

Step 4

FA















1 1198912 1198913 119891

119898

1199091= 11988611

1198911+ 11988612

1198912+ sdot sdot sdot + 119886

1119898119891119898

+ 1205761

1199092= 11988621

1198911+ 11988622

1198912+ sdot sdot sdot + 119886

2119898119891119898

+ 1205762

119909119899

= 1198861198991

1198911+ 1198861198992

1198912+ sdot sdot sdot + 119886

119899119898119891119898

+ 120576119899

(1)

where 119886119894119895




1 1199092 1199093 119909



1199101= 12058311

1199091+ 12058312

1199092+ sdot sdot sdot + 120583

1119899119909119899

1199102= 12058321

1199091+ 12058322

1199092+ sdot sdot sdot + 120583

2119899119909119899

119910119899

= 1205831198991

1199091+ 1205831198992

1199092+ sdot sdot sdot + 120583

119899119899119909119899

(2)

where 1199101 1199102 119910






defined as

119890 = minus

119898

sum

119894=1

119875119894sdot ln119875119894 (3)

When 119875119894



119894119895)119898times119899

isas follows

119877 =

[

[

[

[

11990311

11990312


11990321

11990322



1199031198981

1199031198982


]

]

]

]119898times119899

(4)


119895= minussum

119898

119894=1119875119894119895

sdot

ln119875119894119895and 119875

119894119895= 119903119894119895sum119898

119894=1119903119894119895



119894119895 119875119894119895

= 119903119894119895sum119898

119894=1119903119894119895



119894=1119875119894119895

sdot ln119875119894119895 and 119896 = 1 ln119898


119895 119892119895= 1 minus 119890

119895


119908119895

= 119892119895

sum119899

119895=1119892119895









1199091 1199092 1199093 119909

119899 1199091 1199092 1199093 119909




1 1199092 1199093 1199094 1199095 1199096 so 119899 = 2


sinminus1199095

lowastlowast+ 1199094119909111990921199093119909611990931199095 (5)



5

lowastlowast+1199094119909111990921199093 So


sin (1199095minus 11990941199091(1199092+ 1199093)) (6)


Sin

X5

X4 X3X1 X2

lowast

lowast

minus

+



119891119894=

1000

119864119894+ 1

(7)

In (7) 119864119894

= (1119898)sum119898

119895=1(119862119894119895





119895is the








1198621 1198622 119862

119899





000

6400

12800

19200

25500

0640

64640

128640

192640

255640

01280

641280

1281280

1921280

2551280

01920

641920

1281920

1921920

2551920

02550

642550

1282550

1922550

2552550

0064

64064

128064

1920

64255064

00128

640128

1280128

1920128

2550128

00192

640192

1280192

1920192

2550192

00255

640255

1280255

1920255

2550255

06464

646464

1286464

1926464

2556464

064128

6464128

12864128

19264128

25564128

064192

6464192

12864192

19264192

25564192

064255

6464255

12864255

19264255

25564255

012864

6412864

12812864

19212864

25512864

0128128

64128128

128128128

192128128

255128128

0128192

64128192

128128192

192128192

255128192

0128255

64128255

128128255

192128255

255128255

019264

6419264

12819264

19219264

25519264

0192128

64192128

128192128

192192128

255192128

0192192

64192192

128192192

192192192

255192192

0192255

64192255

128192255

192192255

255192255

025564

6425564

12825564

19225564

25525564

0255128

64255128

128255128

192255128

255255128

0255192

64255192

128255192

192255192

255255192

0255255

64255255

128255255

192255255

255255255














1 13085 45119 45119 13085 45119 45119 5757 19851 198512 4529 15618 60737 4529 15618 60737 5129 17687 375383 3611 12450 73187 3611 12450 73187 4404 15185 527234 2196 7573 80761 2196 7573 80761 3643 12562 652855 1036 3574 84335 1036 3574 84335 3347 11541 768266 0857 2954 87289 0857 2954 87289 3034 10463 872897 0650 2242 895318 0565 1949 91480

28 0018 0062 9995929 0012 0041 100000



0 025 05 075 1




1198651198941



1198651198942



1198651198943



1198651198944



1198651198945



1198651198946



(8)








0148 0193 0146 0338 0073 0103


[

[

[

[

[

[

[

119909119896

11119909119896

12119909119896


119896

1119899

119909119896

21119909119896

22119909119896


119896

2119899



119909119896

1198981119909119896

1198982119909119896

1198983sdot sdot sdot 119909119896

119898119899

]

]

]

]

]

]

]

(9)





119900119894= (119908

1199001 1199081199002

119908119900119899



119904119894and



119908119894=

119908119904119894119908119900119894

sum119899

119894=1119908119904119894119908119900119894

(10)


119865119894= 11990811198651198941

+ 11990821198651198942

+ 11990831198651198943

+ 11990841198651198944

+ 11990851198651198945

+ 11990861198651198946 (11)



minusminus

x1 x5

x5

x4 x4

x2

x3 x6

x1

x6

x6

x5

x2

x2

x4


lowast

lowast

lowast

lowast

+

c2

c4

c5

c9

Avg 2 Avg 2

Avg 2

Avg 2 Avg 2

Avg 2




1 1199092 1199093 1199094 1199095 1199096


0003





119865 (119909) =

1

2

(

1199091+ 1199095

2

+

1199094+ 1199094

2

)

+

1

2

(

1199092minus 1199095+ 1199093

2

sdot

1199095+ 1199096

2

+ (037141199096)2

)

+

minus49771 minus 277111199091

(minus51091 minus 1199096)2

sdot 1199094

(12)


MSE =

1

119899

119899

sum

119894=1

(1199101015840

119894minus 119910119894)

2


sum119899

119894=1(1199101015840

119894minus 119910119894)

2

sum119899

119894=1(119910119894minus 119910avg)

2

(13)

0010203040506

0

Com

preh

ensiv

e col

or

Training set

TargetModel

5 10 20 30 40 5015 25 35 45 6055 7065 80 8575

imag

e val

ue


0015

02025

03035

04045

05055

06

Validation set

Com

preh

ensiv

e col

or

TargetModel

imag

e val

ue

3 6 9 12 15 18 21 24 27 30 33 36 39 42


In (13) 1199101015840










5 Conclusion






Acknowledgment


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















1 1198912 1198913 119891

119898

1199091= 11988611

1198911+ 11988612

1198912+ sdot sdot sdot + 119886

1119898119891119898

+ 1205761

1199092= 11988621

1198911+ 11988622

1198912+ sdot sdot sdot + 119886

2119898119891119898

+ 1205762

119909119899

= 1198861198991

1198911+ 1198861198992

1198912+ sdot sdot sdot + 119886

119899119898119891119898

+ 120576119899

(1)

where 119886119894119895




1 1199092 1199093 119909



1199101= 12058311

1199091+ 12058312

1199092+ sdot sdot sdot + 120583

1119899119909119899

1199102= 12058321

1199091+ 12058322

1199092+ sdot sdot sdot + 120583

2119899119909119899

119910119899

= 1205831198991

1199091+ 1205831198992

1199092+ sdot sdot sdot + 120583

119899119899119909119899

(2)

where 1199101 1199102 119910






defined as

119890 = minus

119898

sum

119894=1

119875119894sdot ln119875119894 (3)

When 119875119894



119894119895)119898times119899

isas follows

119877 =

[

[

[

[

11990311

11990312


11990321

11990322



1199031198981

1199031198982


]

]

]

]119898times119899

(4)


119895= minussum

119898

119894=1119875119894119895

sdot

ln119875119894119895and 119875

119894119895= 119903119894119895sum119898

119894=1119903119894119895



119894119895 119875119894119895

= 119903119894119895sum119898

119894=1119903119894119895



119894=1119875119894119895

sdot ln119875119894119895 and 119896 = 1 ln119898


119895 119892119895= 1 minus 119890

119895


119908119895

= 119892119895

sum119899

119895=1119892119895









1199091 1199092 1199093 119909

119899 1199091 1199092 1199093 119909




1 1199092 1199093 1199094 1199095 1199096 so 119899 = 2


sinminus1199095

lowastlowast+ 1199094119909111990921199093119909611990931199095 (5)



5

lowastlowast+1199094119909111990921199093 So


sin (1199095minus 11990941199091(1199092+ 1199093)) (6)


Sin

X5

X4 X3X1 X2

lowast

lowast

minus

+



119891119894=

1000

119864119894+ 1

(7)

In (7) 119864119894

= (1119898)sum119898

119895=1(119862119894119895





119895is the








1198621 1198622 119862

119899





000

6400

12800

19200

25500

0640

64640

128640

192640

255640

01280

641280

1281280

1921280

2551280

01920

641920

1281920

1921920

2551920

02550

642550

1282550

1922550

2552550

0064

64064

128064

1920

64255064

00128

640128

1280128

1920128

2550128

00192

640192

1280192

1920192

2550192

00255

640255

1280255

1920255

2550255

06464

646464

1286464

1926464

2556464

064128

6464128

12864128

19264128

25564128

064192

6464192

12864192

19264192

25564192

064255

6464255

12864255

19264255

25564255

012864

6412864

12812864

19212864

25512864

0128128

64128128

128128128

192128128

255128128

0128192

64128192

128128192

192128192

255128192

0128255

64128255

128128255

192128255

255128255

019264

6419264

12819264

19219264

25519264

0192128

64192128

128192128

192192128

255192128

0192192

64192192

128192192

192192192

255192192

0192255

64192255

128192255

192192255

255192255

025564

6425564

12825564

19225564

25525564

0255128

64255128

128255128

192255128

255255128

0255192

64255192

128255192

192255192

255255192

0255255

64255255

128255255

192255255

255255255














1 13085 45119 45119 13085 45119 45119 5757 19851 198512 4529 15618 60737 4529 15618 60737 5129 17687 375383 3611 12450 73187 3611 12450 73187 4404 15185 527234 2196 7573 80761 2196 7573 80761 3643 12562 652855 1036 3574 84335 1036 3574 84335 3347 11541 768266 0857 2954 87289 0857 2954 87289 3034 10463 872897 0650 2242 895318 0565 1949 91480

28 0018 0062 9995929 0012 0041 100000



0 025 05 075 1




1198651198941



1198651198942



1198651198943



1198651198944



1198651198945



1198651198946



(8)








0148 0193 0146 0338 0073 0103


[

[

[

[

[

[

[

119909119896

11119909119896

12119909119896


119896

1119899

119909119896

21119909119896

22119909119896


119896

2119899



119909119896

1198981119909119896

1198982119909119896

1198983sdot sdot sdot 119909119896

119898119899

]

]

]

]

]

]

]

(9)





119900119894= (119908

1199001 1199081199002

119908119900119899



119904119894and



119908119894=

119908119904119894119908119900119894

sum119899

119894=1119908119904119894119908119900119894

(10)


119865119894= 11990811198651198941

+ 11990821198651198942

+ 11990831198651198943

+ 11990841198651198944

+ 11990851198651198945

+ 11990861198651198946 (11)



minusminus

x1 x5

x5

x4 x4

x2

x3 x6

x1

x6

x6

x5

x2

x2

x4


lowast

lowast

lowast

lowast

+

c2

c4

c5

c9

Avg 2 Avg 2

Avg 2

Avg 2 Avg 2

Avg 2




1 1199092 1199093 1199094 1199095 1199096


0003





119865 (119909) =

1

2

(

1199091+ 1199095

2

+

1199094+ 1199094

2

)

+

1

2

(

1199092minus 1199095+ 1199093

2

sdot

1199095+ 1199096

2

+ (037141199096)2

)

+

minus49771 minus 277111199091

(minus51091 minus 1199096)2

sdot 1199094

(12)


MSE =

1

119899

119899

sum

119894=1

(1199101015840

119894minus 119910119894)

2


sum119899

119894=1(1199101015840

119894minus 119910119894)

2

sum119899

119894=1(119910119894minus 119910avg)

2

(13)

0010203040506

0

Com

preh

ensiv

e col

or

Training set

TargetModel

5 10 20 30 40 5015 25 35 45 6055 7065 80 8575

imag

e val

ue


0015

02025

03035

04045

05055

06

Validation set

Com

preh

ensiv

e col

or

TargetModel

imag

e val

ue

3 6 9 12 15 18 21 24 27 30 33 36 39 42


In (13) 1199101015840










5 Conclusion






Acknowledgment


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra















1199091 1199092 1199093 119909

119899 1199091 1199092 1199093 119909




1 1199092 1199093 1199094 1199095 1199096 so 119899 = 2


sinminus1199095

lowastlowast+ 1199094119909111990921199093119909611990931199095 (5)



5

lowastlowast+1199094119909111990921199093 So


sin (1199095minus 11990941199091(1199092+ 1199093)) (6)


Sin

X5

X4 X3X1 X2

lowast

lowast

minus

+



119891119894=

1000

119864119894+ 1

(7)

In (7) 119864119894

= (1119898)sum119898

119895=1(119862119894119895





119895is the








1198621 1198622 119862

119899





000

6400

12800

19200

25500

0640

64640

128640

192640

255640

01280

641280

1281280

1921280

2551280

01920

641920

1281920

1921920

2551920

02550

642550

1282550

1922550

2552550

0064

64064

128064

1920

64255064

00128

640128

1280128

1920128

2550128

00192

640192

1280192

1920192

2550192

00255

640255

1280255

1920255

2550255

06464

646464

1286464

1926464

2556464

064128

6464128

12864128

19264128

25564128

064192

6464192

12864192

19264192

25564192

064255

6464255

12864255

19264255

25564255

012864

6412864

12812864

19212864

25512864

0128128

64128128

128128128

192128128

255128128

0128192

64128192

128128192

192128192

255128192

0128255

64128255

128128255

192128255

255128255

019264

6419264

12819264

19219264

25519264

0192128

64192128

128192128

192192128

255192128

0192192

64192192

128192192

192192192

255192192

0192255

64192255

128192255

192192255

255192255

025564

6425564

12825564

19225564

25525564

0255128

64255128

128255128

192255128

255255128

0255192

64255192

128255192

192255192

255255192

0255255

64255255

128255255

192255255

255255255














1 13085 45119 45119 13085 45119 45119 5757 19851 198512 4529 15618 60737 4529 15618 60737 5129 17687 375383 3611 12450 73187 3611 12450 73187 4404 15185 527234 2196 7573 80761 2196 7573 80761 3643 12562 652855 1036 3574 84335 1036 3574 84335 3347 11541 768266 0857 2954 87289 0857 2954 87289 3034 10463 872897 0650 2242 895318 0565 1949 91480

28 0018 0062 9995929 0012 0041 100000



0 025 05 075 1




1198651198941



1198651198942



1198651198943



1198651198944



1198651198945



1198651198946



(8)








0148 0193 0146 0338 0073 0103


[

[

[

[

[

[

[

119909119896

11119909119896

12119909119896


119896

1119899

119909119896

21119909119896

22119909119896


119896

2119899



119909119896

1198981119909119896

1198982119909119896

1198983sdot sdot sdot 119909119896

119898119899

]

]

]

]

]

]

]

(9)





119900119894= (119908

1199001 1199081199002

119908119900119899



119904119894and



119908119894=

119908119904119894119908119900119894

sum119899

119894=1119908119904119894119908119900119894

(10)


119865119894= 11990811198651198941

+ 11990821198651198942

+ 11990831198651198943

+ 11990841198651198944

+ 11990851198651198945

+ 11990861198651198946 (11)



minusminus

x1 x5

x5

x4 x4

x2

x3 x6

x1

x6

x6

x5

x2

x2

x4


lowast

lowast

lowast

lowast

+

c2

c4

c5

c9

Avg 2 Avg 2

Avg 2

Avg 2 Avg 2

Avg 2




1 1199092 1199093 1199094 1199095 1199096


0003





119865 (119909) =

1

2

(

1199091+ 1199095

2

+

1199094+ 1199094

2

)

+

1

2

(

1199092minus 1199095+ 1199093

2

sdot

1199095+ 1199096

2

+ (037141199096)2

)

+

minus49771 minus 277111199091

(minus51091 minus 1199096)2

sdot 1199094

(12)


MSE =

1

119899

119899

sum

119894=1

(1199101015840

119894minus 119910119894)

2


sum119899

119894=1(1199101015840

119894minus 119910119894)

2

sum119899

119894=1(119910119894minus 119910avg)

2

(13)

0010203040506

0

Com

preh

ensiv

e col

or

Training set

TargetModel

5 10 20 30 40 5015 25 35 45 6055 7065 80 8575

imag

e val

ue


0015

02025

03035

04045

05055

06

Validation set

Com

preh

ensiv

e col

or

TargetModel

imag

e val

ue

3 6 9 12 15 18 21 24 27 30 33 36 39 42


In (13) 1199101015840










5 Conclusion






Acknowledgment


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












000

6400

12800

19200

25500

0640

64640

128640

192640

255640

01280

641280

1281280

1921280

2551280

01920

641920

1281920

1921920

2551920

02550

642550

1282550

1922550

2552550

0064

64064

128064

1920

64255064

00128

640128

1280128

1920128

2550128

00192

640192

1280192

1920192

2550192

00255

640255

1280255

1920255

2550255

06464

646464

1286464

1926464

2556464

064128

6464128

12864128

19264128

25564128

064192

6464192

12864192

19264192

25564192

064255

6464255

12864255

19264255

25564255

012864

6412864

12812864

19212864

25512864

0128128

64128128

128128128

192128128

255128128

0128192

64128192

128128192

192128192

255128192

0128255

64128255

128128255

192128255

255128255

019264

6419264

12819264

19219264

25519264

0192128

64192128

128192128

192192128

255192128

0192192

64192192

128192192

192192192

255192192

0192255

64192255

128192255

192192255

255192255

025564

6425564

12825564

19225564

25525564

0255128

64255128

128255128

192255128

255255128

0255192

64255192

128255192

192255192

255255192

0255255

64255255

128255255

192255255

255255255














1 13085 45119 45119 13085 45119 45119 5757 19851 198512 4529 15618 60737 4529 15618 60737 5129 17687 375383 3611 12450 73187 3611 12450 73187 4404 15185 527234 2196 7573 80761 2196 7573 80761 3643 12562 652855 1036 3574 84335 1036 3574 84335 3347 11541 768266 0857 2954 87289 0857 2954 87289 3034 10463 872897 0650 2242 895318 0565 1949 91480

28 0018 0062 9995929 0012 0041 100000



0 025 05 075 1




1198651198941



1198651198942



1198651198943



1198651198944



1198651198945



1198651198946



(8)








0148 0193 0146 0338 0073 0103


[

[

[

[

[

[

[

119909119896

11119909119896

12119909119896


119896

1119899

119909119896

21119909119896

22119909119896


119896

2119899



119909119896

1198981119909119896

1198982119909119896

1198983sdot sdot sdot 119909119896

119898119899

]

]

]

]

]

]

]

(9)





119900119894= (119908

1199001 1199081199002

119908119900119899



119904119894and



119908119894=

119908119904119894119908119900119894

sum119899

119894=1119908119904119894119908119900119894

(10)


119865119894= 11990811198651198941

+ 11990821198651198942

+ 11990831198651198943

+ 11990841198651198944

+ 11990851198651198945

+ 11990861198651198946 (11)



minusminus

x1 x5

x5

x4 x4

x2

x3 x6

x1

x6

x6

x5

x2

x2

x4


lowast

lowast

lowast

lowast

+

c2

c4

c5

c9

Avg 2 Avg 2

Avg 2

Avg 2 Avg 2

Avg 2




1 1199092 1199093 1199094 1199095 1199096


0003





119865 (119909) =

1

2

(

1199091+ 1199095

2

+

1199094+ 1199094

2

)

+

1

2

(

1199092minus 1199095+ 1199093

2

sdot

1199095+ 1199096

2

+ (037141199096)2

)

+

minus49771 minus 277111199091

(minus51091 minus 1199096)2

sdot 1199094

(12)


MSE =

1

119899

119899

sum

119894=1

(1199101015840

119894minus 119910119894)

2


sum119899

119894=1(1199101015840

119894minus 119910119894)

2

sum119899

119894=1(119910119894minus 119910avg)

2

(13)

0010203040506

0

Com

preh

ensiv

e col

or

Training set

TargetModel

5 10 20 30 40 5015 25 35 45 6055 7065 80 8575

imag

e val

ue


0015

02025

03035

04045

05055

06

Validation set

Com

preh

ensiv

e col

or

TargetModel

imag

e val

ue

3 6 9 12 15 18 21 24 27 30 33 36 39 42


In (13) 1199101015840










5 Conclusion






Acknowledgment


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












1 13085 45119 45119 13085 45119 45119 5757 19851 198512 4529 15618 60737 4529 15618 60737 5129 17687 375383 3611 12450 73187 3611 12450 73187 4404 15185 527234 2196 7573 80761 2196 7573 80761 3643 12562 652855 1036 3574 84335 1036 3574 84335 3347 11541 768266 0857 2954 87289 0857 2954 87289 3034 10463 872897 0650 2242 895318 0565 1949 91480

28 0018 0062 9995929 0012 0041 100000



0 025 05 075 1




1198651198941



1198651198942



1198651198943



1198651198944



1198651198945



1198651198946



(8)








0148 0193 0146 0338 0073 0103


[

[

[

[

[

[

[

119909119896

11119909119896

12119909119896


119896

1119899

119909119896

21119909119896

22119909119896


119896

2119899



119909119896

1198981119909119896

1198982119909119896

1198983sdot sdot sdot 119909119896

119898119899

]

]

]

]

]

]

]

(9)





119900119894= (119908

1199001 1199081199002

119908119900119899



119904119894and



119908119894=

119908119904119894119908119900119894

sum119899

119894=1119908119904119894119908119900119894

(10)


119865119894= 11990811198651198941

+ 11990821198651198942

+ 11990831198651198943

+ 11990841198651198944

+ 11990851198651198945

+ 11990861198651198946 (11)



minusminus

x1 x5

x5

x4 x4

x2

x3 x6

x1

x6

x6

x5

x2

x2

x4


lowast

lowast

lowast

lowast

+

c2

c4

c5

c9

Avg 2 Avg 2

Avg 2

Avg 2 Avg 2

Avg 2




1 1199092 1199093 1199094 1199095 1199096


0003





119865 (119909) =

1

2

(

1199091+ 1199095

2

+

1199094+ 1199094

2

)

+

1

2

(

1199092minus 1199095+ 1199093

2

sdot

1199095+ 1199096

2

+ (037141199096)2

)

+

minus49771 minus 277111199091

(minus51091 minus 1199096)2

sdot 1199094

(12)


MSE =

1

119899

119899

sum

119894=1

(1199101015840

119894minus 119910119894)

2


sum119899

119894=1(1199101015840

119894minus 119910119894)

2

sum119899

119894=1(119910119894minus 119910avg)

2

(13)

0010203040506

0

Com

preh

ensiv

e col

or

Training set

TargetModel

5 10 20 30 40 5015 25 35 45 6055 7065 80 8575

imag

e val

ue


0015

02025

03035

04045

05055

06

Validation set

Com

preh

ensiv

e col

or

TargetModel

imag

e val

ue

3 6 9 12 15 18 21 24 27 30 33 36 39 42


In (13) 1199101015840










5 Conclusion






Acknowledgment


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra















0148 0193 0146 0338 0073 0103


[

[

[

[

[

[

[

119909119896

11119909119896

12119909119896


119896

1119899

119909119896

21119909119896

22119909119896


119896

2119899



119909119896

1198981119909119896

1198982119909119896

1198983sdot sdot sdot 119909119896

119898119899

]

]

]

]

]

]

]

(9)





119900119894= (119908

1199001 1199081199002

119908119900119899



119904119894and



119908119894=

119908119904119894119908119900119894

sum119899

119894=1119908119904119894119908119900119894

(10)


119865119894= 11990811198651198941

+ 11990821198651198942

+ 11990831198651198943

+ 11990841198651198944

+ 11990851198651198945

+ 11990861198651198946 (11)



minusminus

x1 x5

x5

x4 x4

x2

x3 x6

x1

x6

x6

x5

x2

x2

x4


lowast

lowast

lowast

lowast

+

c2

c4

c5

c9

Avg 2 Avg 2

Avg 2

Avg 2 Avg 2

Avg 2




1 1199092 1199093 1199094 1199095 1199096


0003





119865 (119909) =

1

2

(

1199091+ 1199095

2

+

1199094+ 1199094

2

)

+

1

2

(

1199092minus 1199095+ 1199093

2

sdot

1199095+ 1199096

2

+ (037141199096)2

)

+

minus49771 minus 277111199091

(minus51091 minus 1199096)2

sdot 1199094

(12)


MSE =

1

119899

119899

sum

119894=1

(1199101015840

119894minus 119910119894)

2


sum119899

119894=1(1199101015840

119894minus 119910119894)

2

sum119899

119894=1(119910119894minus 119910avg)

2

(13)

0010203040506

0

Com

preh

ensiv

e col

or

Training set

TargetModel

5 10 20 30 40 5015 25 35 45 6055 7065 80 8575

imag

e val

ue


0015

02025

03035

04045

05055

06

Validation set

Com

preh

ensiv

e col

or

TargetModel

imag

e val

ue

3 6 9 12 15 18 21 24 27 30 33 36 39 42


In (13) 1199101015840










5 Conclusion






Acknowledgment


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










minusminus

x1 x5

x5

x4 x4

x2

x3 x6

x1

x6

x6

x5

x2

x2

x4


lowast

lowast

lowast

lowast

+

c2

c4

c5

c9

Avg 2 Avg 2

Avg 2

Avg 2 Avg 2

Avg 2




1 1199092 1199093 1199094 1199095 1199096


0003





119865 (119909) =

1

2

(

1199091+ 1199095

2

+

1199094+ 1199094

2

)

+

1

2

(

1199092minus 1199095+ 1199093

2

sdot

1199095+ 1199096

2

+ (037141199096)2

)

+

minus49771 minus 277111199091

(minus51091 minus 1199096)2

sdot 1199094

(12)


MSE =

1

119899

119899

sum

119894=1

(1199101015840

119894minus 119910119894)

2


sum119899

119894=1(1199101015840

119894minus 119910119894)

2

sum119899

119894=1(119910119894minus 119910avg)

2

(13)

0010203040506

0

Com

preh

ensiv

e col

or

Training set

TargetModel

5 10 20 30 40 5015 25 35 45 6055 7065 80 8575

imag

e val

ue


0015

02025

03035

04045

05055

06

Validation set

Com

preh

ensiv

e col

or

TargetModel

imag

e val

ue

3 6 9 12 15 18 21 24 27 30 33 36 39 42


In (13) 1199101015840










5 Conclusion






Acknowledgment


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra















5 Conclusion






Acknowledgment


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













Acknowledgment


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article color image evaluation for small...

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