Khoirul Umam 1, Agus Zainal Arifin 2 and Dini Adni Navastara 3

Transcription

1 I J C T A, 9(-A), 016, pp International Science Pre A Novel Strategy of Differential Evolution Algorithm Croover Operator Baed on Graylevel Cluter Similarity for Automatic Multilevel Image Threholding Khoirul Umam 1, Agu Zainal Arifin and Dini Adni Navatara 3 ABSTRACT Automatic multilevel image threholding approach ha wide optimal olution earch pace due to it ability to determine threhold number and poition, imultaneouly Searching it optimal olution uing tandard Differential Evolution (DE) algorithm can decreae it efficiency due to low convergence Therefore, a trategy that can retrict the earch pace i needed in order for optimization being efficient In thi paper we propoe a novel trategy of DE croover operator baed on graylevel cluter imilarity for automatic multilevel image threholding We retrict the earch pace by only recombining graylevel cluter which have mall imilarity Graylevel cluter imilarity i performed by computing the inter-cla and intra-cla variance of adjacent graylevel cluter Experiment on graycale image of Berkeley Segmentation Dataet (BSDS500) how that the propoed croover trategy can generate egmented image with miclaification error of 796% better than thoe of exiting croover trategie which not compute the graylevel cluter imilarity It only require the average of 636 generation to find the optimal olution le than compared croover trategie Keyword: automatic multilevel image threholding, cluter imilarity, croover, Differential Evolution 1 INTRODUCTION Multilevel image threholding i an approach on graylevel threholding technique It can be ued to egment image that ha more than one ditinct object With thi approach, the image hitogram i divided into more than two cluter graylevel by uing a et of threhold [1,, 3, 4] Generally, the number of threhold that ued to egment an image can be determined manually by expert However it can lead the ubjectivity factor in egmentation reult There are alo cae where it difficult to et the threhold number manually [3] Therefore multilevel image threholding evolve into automatic multilevel image threholding On the approach, the number and poition of threhold that are ued to egment an image i determined automatically The number and poition of threhold on multilevel image threholding problem can be found uing optimization method It can be done due to the problem can be conidered a an optimization problem to a certain objective function, generally [5] The method i alo more efficient than the exhautive earch method [3] The algorithm that widely ued to olve optimization problem i metaheuritic algorithm [6] Some tudie have propoed the implementation of metaheuritic algorithm for multilevel image threholding problem Horng and Jiang [7] propoed the implementation of Firefly Algorithm (FA) to locate threhold poition by optimizing maximum entropy function Cueva, et al [] propoed the implementation of 1,,3 Department of Informatic, Faculty of Information Technology, Intitut Teknologi Sepuluh Nopember, Surabaya, Indoneia, 1khoirulumam35@gmailcom, aguza@citacid, 3dini_navatara@ifitacid

2 764 Khoirul Umam, Agu Zainal Arifin and Dini Adni Navatara Differential Evolution (DE) algorithm to locate threhold poition by optimizing Gauian function parameter Sarkar and Da [8] alo propoed the implementation of DE to locate threhold poition by optimizing maximum Talli entropy function on D hitogram Ali, et al [9] propoed the implementation of Synergetic Differential Evolution (SDE) algorithm, ie a modification of DE to optimize the threhold poition Ayala, et al [10] propoe a Beta Differential Evolution (BDE) algorithm ie alo a modification of DE to optimize threhold poition Djerou, et al [11], Ouadfel and Mehoul [3], Hammouche, et al [1], and Hoeini [6] propoed the implementation of Binary Particle Swarm Optimization (BPSO) algorithm, a hybrid of Particle Swarm Optimization (PSO) with Simulated Annealing (SA) algorithm, Genetic Algorithm (GA), and Intelligent Water Drop (IWD) algorithm for automatic multilevel image threholding problem, repectively Among the optimization algorithm that have been propoed to olve multilevel image threholding problem, DE ha better performance than the other algorithm DE ha ability to maintain convergence to optimal olution better than GA and PSO DE alo can generate better egmentation reult compared with SA, Ant Colony Optimization (ACO), and Tabu Search (TS) [5] Furthermore, DE ha better efficiency level becaue it take le time than PSO and Artificial Bee Colony (ABC) to reach the optimal olution [4] DE ability to reach optimal olution i influenced by the evolution proce of it olution population The proce i performed through erie of operation One of the operation that affect DE evolution proce i croover operation The operation i ued to expand optimal olution earch pace by uing certain trategy In the tandard of DE, the trategy of croover operation involve random value which generated by the ytem and croover rate which determined by expert Comparion of the two value i ued a a benchmark for croover operation [1] DE tandard croover trategy ha proven can be ued to olve the multilevel image threholding problem which only optimizing the combination of threhold poition [, 4, 5,8, 9, 10] But if it i ued in automatic multilevel image threholding problem, then it will affect the change of threhold number and poition combination imultaneouly Thu, the poible combination that will be earched are larger, or in other word the earch pace become wider It can lead to an increae of time or iteration that required for reaching the optimal olution Increaing the population ize in order to cover wider earch pace i alo not an efficient olution becaue it can increae the memory requirement [13] Therefore, a trategy that can retrict the earch pace i needed to find optimal olution more efficient In thi paper we propoe a novel trategy of DE croover operator baed on graylevel cluter imilarity for automatic multilevel image threholding problem The imilarity i calculated baed on the value of adjacent graylevel cluter inter-cla and intra-cla variance [14] which formed in each olution Thu, the earching of optimal olution i only performed on olution that offer combination of threhold number and poition which capable to eparate each graylevel cluter with maximum ditance DIFFERENTIAL EVOLUTION (DE) ALGORITHM DE i an example of evolutionary algorithm that introduced by Storn and Price [1] It earche the optimal olution by applying parallel earching method uing a et of olution in a population Generally, optimization proce uing DE begin by initializing the population The population then evolve through mutation, croover, and election operation The evolutionary proce i repeated until a topping criterion i reached DE population initialization i performed by generating NP olution Each olution i repreented a a vector with D component and called a target vector Each target vector component x,d for = [1,, NP] and d = [1,, D] i randomly initialized by a real-value between pecified lower-bound x min and upperbound x max a formulated in (1):

3 A Novel Strategy of Differential Evolution Algorithm Croover Operator Baed 765 x,d (0) = x min + (x max x min ) rand,d, (1) where rand,d denote a uniform random value between 0 and 1 which generated for dth component of target vector [1, 15] After the initialization phae, the optimization uing DE proceed to mutation On each generation g, the operation will generate NP donor vector V (g)[15] In DE mutation tandard cheme that known a DE/rand/1, the mutation conducted by adding the weight of a target vector 1 (g) with the weighted difference between two other target vector ( (g) and 3 (g)) The weighted difference i caled by a mutation factor F [1] a hown in equation (): V (g) = 1 (g) + F ( (g) 3 (g)) () Target vector 1 (g), (g), and 3 (g) are three different vector that randomly choen and not equal to the target vector (g) Mutation may caue the value of donor vector component v,d (g) violate the pecified boundarie (ie x min and x max ) In order to normalize the component value, a rule that formulated in equation (3) can be ued [16]: v, d g d x v g, v g x x v g, v g x min, d, min max, d, d max Every pair of target vector (g) and donor vector V (g) then recombined into a trial vector U (g) through croover operation Target vector component x,d (g) and donor vector component v,d (g) are mixed to produce trial vector component u,d (g) uing certain trategy The example of croover trategy that can be ued are binomial croover [1], exponential croover [15], and elf-adaptive croover [16] The trategie ue a random generated value and croover rate (CR) to decide the recombination proce of a vector olution component The lat operation on each DE generation i election operation It elect the olution vector that will be maintained on the next generation The election conducted by comparing a target vector fitne value f( (g)) with a trial vector fitne value f(u (g)) Solution vector with the bet fitne value i choen a target vector on the next generation ( (g + 1)) [15] Selection formulation i hown in equation (4): 3 GRAYLEVEL CLUSTERS SIMILARITY,, U g f U g f g g 1 g f U g f g The imilarity of adjacent graylevel cluter can be known by meauring their ditance The farther ditance between two adjacent graylevel cluter indicate maller imilarity between both of graylevel cluter, and vice vera Let n l denote the occurrence frequency of pixel with graylevel l, N denote the total number of pixel in the image, p l denote the probability of pixel occurrence with graylevel l a formulated in (5): (3) (4) nl pl, (5) N C k denote the kth graylevel cluter, t k denote the kth threhold, along with k and k denote the occurrence probability of pixel belonging to C k and the mean of C k, repectively, a formulated in equation (6) and equation (7):

4 766 Khoirul Umam, Agu Zainal Arifin and Dini Adni Navatara u (6) tk k lt 1 1 p, k l 1 lp (7) tk k ltk1 1 l k The ditance of two adjacent graylevel cluter C k and C 1 k (Dit C k, C 1 k can be calculated uing inter-cla and intra-cla variance of the adjacent graylevel cluter a formulated in equation (8): Inter-cla variance of Ck and 1 k k k I k k A k k Dit C, C C C C C (8) C I Ck Ck 1 i defined a um of the quare ditance between the mean of the two graylevel cluter and the total mean of both cluter While intra-cla variance of C k 1 and k C A Ck Ck 1 i defined a variance of all pixel graylevel value in the merged cluter [14] Formulation for both of value are hown in equation (9) and equation (10), repectively: where M Ck Ck 1 I Ck C 1 k k 1 k k 1 k k k 1 tk 1 A Ck C 1 k l t l M C k k C k p l k 1 k 1 (10) denote the global mean of Ck and C 1 k which formulated in equation (11): 1): (9) k1 k1 k k k Ck M C 1 k1 k (11) 4 METHOD In thi ection we decribe our propoed croover trategy and DE cheme that implement the trategy Figure 1: Flowchart of propoed croover

5 A Novel Strategy of Differential Evolution Algorithm Croover Operator Baed Propoed Croover Strategy A mentioned before, in thi paper we propoe a novel trategy of DE croover operator baed on graylevel cluter imilarity that formed at threholding olution The threholding olution are repreented by target vector and donor vector For the convenience, we denote our propoed croover trategy a Graylevel Cluter Similarity (GCS) trategy Recombination procedure on GCS i conducted by comparing the adjacent graylevel cluter imilarity which repreented by target vector component with the adjacent graylevel cluter imilarity which repreented by donor vector component Solution vector component which repreent graylevel cluter with lower imilarity (ie farther ditance) are choen to recombine into trial vector component The procedure i repeated until all component have been recombined into trial vector a illutrated in Figure 1 Thu, the formed trial vector i expected can repreent a threholding olution that ha low graylevel cluter imilarity Therefore, the earching of optimal threholding olution can be retricted only on threholding olution which able to minimize the graylevel cluter imilarity Aume that K graylevel cluter and K V graylevel cluter are formed at threholding olution which repreented by target vector (g) and donor vector V (g), repectively It indicate that there are K 1 threhold in the threhold et T of threholding olution which repreented by (g) T t1,, t K 1 It alo indicate that there are K v 1 threhold in the threhold et TV of threholding olution which V V repreented by V (g) TV t1,, t K 1 V If the larget graylevel intenity that appear on the image L max i conidered a Kth threhold (ie t k = L max ), then T t1,, tk, L V V 1 max and TV t1,, tk, L 1 max V Let L min denote the mallet graylevel intenity that appear on the image, c denote the cluter firt graylevel, V C m denote graylevel cluter which repreented by (g), C n denote nth graylevel cluter which repreented by V (g), along with D and DV denote the ditance of two adjacent graylevel cluter at (g) and V (g), repectively The algorithm of (g) and V (g) recombination proce to produce trial vector U (g) in GCS i decribed in Algorithm 1 Algorithm 1 Propoed Croover Strategy Algorithm 1 Initialize c c = L min V Chooe threhold in T t m and nth threhold in n TV t where cloet to c and have greater graylevel intenity value than c repectively t m a well a t V n are located 3 Form two adjacent graylevel cluter on threholding olution which repreented by (g) and V (g) repectively: C C,, t and C t 1,, t a m m m1 m m1 C c,, t and C t 1,, t V V V V V b n n n1 n n1 4 Meaure the adjacent graylevel cluter imilarity or ditance uing equation (8): a D Dit Cm Cm 1, V V b DV Dit Cn Cn 1,

6 768 Khoirul Umam, Agu Zainal Arifin and Dini Adni Navatara 5 Compare D with DV and do one of following condition: a If D > DV, then: i u,d (g) = x,d (g), for d = [(c L min + 1),, ( t L + 1)] m min ii Update c c tm 1 1 b If D DV, then: i u,d (g) = v,d (g), for d = [(c L min + 1),, ( t V n L min + 1)] V ii Update c c tn Repeat tep -5 until c > L max On the lat iteration of each recombination proce uing GCS there i poibility that the lat graylevel cluter C K of (g) or V (g) threholding olution are remain and not recombined yet into U (g) In order for the calculation and comparion of graylevel cluter imilarity can till be made on C K, we aume that there i a dummy cluter C K+1 It act a neighbor of C K on each threholding olution a illutrated on Figure It i aumed ha threhold t K+1 = L max + 1 and probability K+1 = 0 In order for two adjacent graylevel cluter imilarity or ditance value till ha meaning even though one of graylevel cluter ha 0 probability value, the inter-cla variance formulation in equation (9) i modified into equation (1): C C 1 k 1 k k k I k1 k k1 k 1 (1) 4 Optimization Scheme In thi paper, the optimization cheme uing DE to olve the automatic multilevel image threholding problem i illutrated by flowchart on Figure 3 For the convenience, we denote the cheme which implement GCS trategy uing DE cheme naming rule decribed in [1,15] a DE/rand/1/-GCS The optimization ue DE o that DE general phae (ie initialization, mutation, croover, and election) are ued Moreover, we alo add three tage of binarization phae and an evaluation phae Figure : Illutration of dummy cluter poition

7 A Novel Strategy of Differential Evolution Algorithm Croover Operator Baed 769 where fitne value of each founded threholding olution i computed The brief decription for each phae i decribed in next ubection 41 Initialization In thi phae, target vector (g) are generated, where each (g) i conit of D component Each component x,d (g) i initialized uing equation (1) The value of NP, x min, and x max are manually defined, the value of rand,d i automatically and randomly generated by ytem, wherea the value of D i depending on image L min and L max value a formulated in equation (13): 4 Binarization D = L max L min (13) Binarization i a phae to encode real-value of each olution vector component (ie target vector, donor vector, or trial vector) into binary-value The binary-value are ued to indicate the poition and number of threhold which offered by threholding olution that repreented by the olution vector If the binarization reult of dth component in vector olution x g i aumed a kth threhold (t k ) But if x g, 1, then the graylevel l which aociated to the component d, d 0, then l i not aumed a t k The connectivity between indice of olution vector component d with l i formulated in equation (14): l = L min + d 1 (14) An example of threhold poition that indicated by binary form of a vector olution on Figure 4 Figure 4 illutrate that there are K 1 component of g g i illutrated which have code 1, ie component with index 3, 6, and D Therefore, on the threholding olution that repreented by g, d there are K 1 threhold too, where t 1 = L min +, t = L min + 5,, and t K 1 = L max 3 It will alo lead to the formation of K graylevel cluter ([C 1,, C K ]) In thi paper, L max ha no connectivity with vector olution component and alway conidered to be elected a Kth threhold (t K ) The rule to encode real form of x,d (g) into it binary form x g x, d g Figure 3: Optimization cheme, d 0 rand, d igm x, d g or pl 0 1, rand, d igm x, d g and pl 0 i formulated in equation (15): (15)

8 770 Khoirul Umam, Agu Zainal Arifin and Dini Adni Navatara where igm(y) denote the igmoid value of Y a formulated in equation (16): igm Y 1 Y (16) 1 e The binarization rule in equation (15) lead to graylevel that can be elected a threhold are only graylevel that occur in input image (ie graylevel with probability value p l > 0) Thu, there i no poibility that graylevel cluter C k which ha probability k = 0 i formed in the range of graylevel L min to L max 43 Evaluation In thi phae, the computation of fitne value for each (g) i performed The objective function that ued to compute (g) fitne value i Automatic Threholding Criterion (ATC) function from [17] It conider the number of formed graylevel cluter (K) and the graylevel cluter diimilarity which denoted by it within-cla variance K Figure 4: Example of threhold encoding poition and graylevel cluter forming on image hitogram baed on binarization reult of vector olution component W It i formulated in equation (17): W 1/ ATC K K log K, (17) where i a poitive weighting contant which manually defined The value of K by integrating the total-cla variance T [18] The formulation of each variance are hown in equation (18) (0): can be computed and between-cla variance of K formed graylevel cluter K B K K, (18) W T B l L1 T l0 pl, (19) K K (0) B k 1 k k, W

9 A Novel Strategy of Differential Evolution Algorithm Croover Operator Baed 771 where denote the total mean of all image pixel If there are L graylevel in the image, then of image can be computed uing equation (1): (1) L1 l0 lpl The ATC value of a threholding olution can indicate the olution quality The maller ATC value of the olution indicate that the olution ha better quality, and vice vera Therefore, the fitne value of threholding olution that repreented by (g) (f( (g))) i inverely proportional with the olution ATC value a formulated in equation (): f g 1 ATC g () 44 Mutation In thi phae, (g) i mutated uing mutation cheme DE/rand/1 which formulated in equation () until V (g) i produced for = [1,, NP] The value of F which ued on the cheme i manually defined The contraint handling rule for v,d (g) which formulated in equation (3) i alo ued in thi phae 45 Croover In thi phae, NP pair of (g) and V (g) are recombined uing GCS trategy that decribed on Subection 41 Thi phae will produce NP trial vector U (g) 46 Selection In thi phae, the election of olution vector that will be maintained on the next generation i performed Selection rule in thi paper i following the general DE election rule which formulated in equation (4) 47 Segmentation After the iteration or generation of optimal olution earching reache the maximum generation, the earching i topped and the optimal olution i obtained The optimal olution i a threholding olution that repreented by binary form of global bet vector gbet (g) on g max ( gbet (g max )) gbet (g) i defined a a olution vector that ha the bet fitne value compared with the other vector from the firt generation until the lat generation [16] Threholding olution that repreented by gbet (g max ) i ued for egmenting input image into egmented image Segmentation are conducted by changing the graylevel intenity l on each image pixel (pix(l)) into the rounding reult of k*th graylevel cluter mean k * where l i located The formulation of egmentation i hown in equation (3): pix(l) = round( k *) (3) for l C k *, l = [L min,, L max ], and k* = [1,, K*], where K* denote the number of graylevel cluter repreented by optimal olution 5 EPERIMENTS AND RESULTS In thi paper we ue image from Berkeley Segmentation Dataet (BSDS500) 1 a teting image The dataet provide real-cene color image along with it human egmentation a the ground truth We chooe 150 image randomly for teting But before we ue it in teting, we convert each image into graycale image uing rgbgray function on Matlab Figure 5 how the ample image from BSDS500

10 77 Khoirul Umam, Agu Zainal Arifin and Dini Adni Navatara Figure 5: Sample image from BSDS500 (a)-(d) Image 1 Image 4 (e)-(h) Ground truth which have been converted into graycale image that ued in teting along with it ground truth The ground truth are colored uing labelrgb function in Matlab with jet color map in order to point out different threhold level in a better way Teting i performed uing Matlab R013a oftware It run on M Window 7 operating ytem in computer that ue Intel i3 4 GHz proceor and 3 GB of RAM DE algorithm that implement GCS trategy (DE/rand/1/GCS cheme) ue pecified DE parameter ie NP, g max, F, x min, and x max to find the optimal threholding olution (number and poition of threhold) for each teting image Thee parameter value are et to 50, 500, 05, -5, and 5, repectively While parameter that ued on ATC function i et to 04 Thee value are the optimal value for each parameter that obtained from erie of teting A the compared trategie, we alo implement the exiting croover trategy ie binomial, exponential, and elf-adaptive croover trategie which decribed in [1,15,16] into croover phae in optimization cheme (Figure 3) We called the compared cheme a DE/rand/1/bin, DE/rand/1/exp, and DE/rand/1/ elf-adaptive cheme, repectively Each cheme then ued to find the optimal threholding olution for each teting image uing ame aforementioned parameter etting Specifically for DE/rand/1/bin and DE/rand/1/exp cheme which alo ue CR parameter, thi parameter value i et to 08 a uggeted by [] Figure 6: Segmentation reult uing DE/rand/1/GCS cheme (a)-(d) Segmented image of ample image (e)-(h) Threhold poition for each egmented reult (indicated by red bar)

11 A Novel Strategy of Differential Evolution Algorithm Croover Operator Baed 773 Figure 7: Segmentation reult uing DE/rand/1/bin cheme (a)-(d) Segmented reult of ample image (e)-(h) Threhold poition for each egmented reult (indicated by red bar) Figure 8: Segmentation reult uing DE/rand/1/exp cheme (a)-(d) Segmented reult of ample image (e)-(h) Threhold poition for each egmented reult (indicated by red bar) Figure 9: Segmentation reult uing DE/rand/1/elf-adaptive cheme (a)-(d) Segmented reult of ample image (e)-(h) Threhold poition for each egmented reult (indicated by red bar)

12 774 Khoirul Umam, Agu Zainal Arifin and Dini Adni Navatara In order to make the combination of random number occurrence i not affecting the optimization reult, the random generator for each data i reet on the beginning of optimization The reetting i performed by uing rng function, ie a built-in function on Matlab R013a Thu the optimization reult and performance are only affected by the croover trategy that implemented on the cheme The egmentation reult of ample image (Image 1 Image 4) that produced by DE/rand/1/-GCS cheme are hown in Figure 6 While the compared egmentation reult of ample image that produced by compared cheme are hown in Figure 7 Figure 9 We coloring the graycale egmented image uing labelrgb function in Matlab with jet color map to point out different threhold level in a better way The performance of each cheme i evaluated by oberving it convergence ability and quality of it generated egmented image The cheme convergence ability can be oberved from it generation number and CPU time that required by the cheme to find the optimal olution The quality of egmentation reult can be oberved uing uniformity meaure and miclaification error (ME) percentage Formulation to meaure the uniformity of a egmented image I T (U) i hown in equation (4): K j1 ic L j i j max min U 1 K 1, N L L where K denote the number of graylevel cluter that formed on I T hitogram, C j denote the jth graylevel cluter on I T, j denote the mean of graylevel intenity on C j, L i denote the graylevel intenity of pixel i on original image, and N denote the total number of I T pixel The value of U i between 0 and 1, where a higher value of U mean that the quality of I T i better [1, 3, 9] While the percentage of I T ME which ha M N dimenion can be calculated baed on the number of I T pixel which have different label of cluter compared with it related pixel on original image a formulated in equation (5) and equation (6): (4) M N m 1 n 1 I0 m, n IT m, n ME M N (5) 0 I m n I m n T 1, I m, n I m, n 0, T, 0, I0 m, n IT m, n where I 0 (m, n) and I T (m, n) denote the label of cluter in ground truth and egmented image, repectively A lower percentage of ME mean the quality of I T i better Equation (5) and equation (6) are a modification of ME formula for bilevel threholding problem which defined in [19] The comparion of each teted cheme ability to reach the optimal olution i depicted by the graph on Figure 10 The graph how the average of the bet fitne value that found on each cheme generation While the comparion of the average of generation number, CPU time that required to find the optimal olution, and CPU time that required to complete the earching proce until the lat generation by each teted cheme i hown in Table 1 along with it average of uniformity value and ME percentage The bet value for each performance are indicated by bolded text 6 DISCUSSION Serie of experiment ha been performed to evaluate the performance of GCS which implemented on DE (DE/rand/1/GCS cheme) to olve the automatic multilevel image threholding problem Exiting DE croover trategie are ued a compared croover trategie Baed on graph in Figure 10, we know that the average of bet fitne value that found on each generation of DE/rand/1/GCS cheme ha the mot (6)

13 A Novel Strategy of Differential Evolution Algorithm Croover Operator Baed 775 Figure 10: Comparion of the bet fitne value average that found on each generation for each teted cheme Table 1 Comparion of Each Teted Scheme Performance Average Value Performance Performance Average Value for Each Teted Scheme DE/rand/ DE/rand/ DE/rand/ DE/rand/ 1/GCS 1/bin 1/exp 1/elf adaptive Generation number that required to find the optimal olution Bet fitne value on the lat generation CPU time until optimal olution found (econd) CPU time until the lat generation (econd) Uniformity ME (%) ignificant increment than the average of bet fitne value that found on each generation of compared cheme ince the firt generation It indicate that croover operation baed on graylevel cluter imilarity ha capability to direct the earching proce to olution that able to eparate graylevel cluter with maximum ditance (ie olution with high fitne value) Thu the GCS trategy ha capability to find the optimal olution better than compared croover trategy The number of generation that required by DE/rand/1/GCS cheme to find the optimal olution i alo better than the compared cheme Baed on Table 1, we know that DE/rand/1/GCS cheme require the leat generation number to find the optimal olution It only require average of 636 generation le than compared cheme to find the optimal olution It indicate that croover operation baed on graylevel cluter imilarity able to decreae the generation number that required on finding the optimal olution DE/rand/1/GCS cheme i alo able to reach the average of bet fitne value on the lat generation higher than compared cheme even though it i not ignificant Baed on Table 1 and Figure 10, DE/rand/ 1/GCS cheme only ha ignificant difference of bet fitne value average with DE/rand/-1/elf-adaptive cheme, which i or 1191% higher While compared with DE/rand/1/exp and DE/rand/1/bin cheme, DE/rand/1/GCS cheme only have the average of bet fitne value and (009% and 073%)

14 776 Khoirul Umam, Agu Zainal Arifin and Dini Adni Navatara higher than the cheme, repectively It indicate that GCS trategy ha capability to give threholding olution that have no ignificant difference with binomial and exponential croover trategie, but ignificantly better than elf-adaptive croover trategy The average of uniformity value which obtained by DE/rand/1/GCS cheme i alo indicate that the cheme able to produce the egmentation reult that have le ignificant difference compared with DE/ rand/1/bin and DE/rand/1/exp cheme More ignificant difference of egmentation reult are only hown by DE/rand/1/elf-adaptive cheme Baed on Table 1, DE/rand/1/GCS cheme ha ame average value of uniformity with DE/rand/1/exp cheme and only higher than DE/-rand/1/bin cheme average value of uniformity While comparion with the average value of DE/-rand/1/elf-adaptive cheme uniformity how that the DE/rand/1/GCS cheme ha the average value of uniformity higher than the cheme The average percentage of ME which obtained by DE/rand/1/GCS cheme i alo indicate that the cheme able to produce egmentation reult that have le ignificant difference than DE/rand/1/-bin and DE/rand/1/exp cheme The average percentage of ME which obtained by DE/rand/1/GCS i only 103% higher than the average percentage of ME which obtained by DE/rand/1/exp cheme and only 373% higher than the average percentage of ME which obtained by DE/rand/1/bin cheme Significant difference of ME average percentage i only hown by the comparion with DE/rand/1/elfadaptive cheme DE/ rand/1/gcs cheme ha the average percentage of ME that 1913% better than DE/rand/1/elf-adaptive cheme It mean DE/rand/1/GCS cheme i able to generate egmentation reult with qualitie 796% better than the compared cheme However, when viewed in term of computational time, DE/rand/1/GCS cheme ignificantly require more time than compared cheme Baed on Table 1, we know that DE/rand/1/GCS cheme require the average of CPU time econd (rounded to be econd) or time longer than compared cheme to find the optimal olution While to complete the earching proce until the lat generation, DE/rand/1/GCS require the average of CPU time econd (rounded to be econd) or time longer than compared cheme It indicate that the computation of graylevel cluter imilarity which i the bae of GCS trategy can increae the requirement of computational time Thu, if viewed in term of computational time, then the propoed croover trategy i not more efficient than the exiting DE croover trategie 7 CONCLUSION Thi paper ha propoed and decribed a novel trategy of DE croover operator baed on graylevel cluter imilarity for olving the automatic multilevel image threholding problem The propoed croover trategy trie to retrict the optimal olution earch pace by only recombining vector olution component that repreent combination of graylevel cluter which have maller imilarity Thu, the earching of optimal olution i only performed on olution that offer combination of threhold number and poition which capable to eparate each graylevel cluter with maximum ditance The experimental reult how that the propoed croover trategy i able to provide egmentation reult that have ame quality with egmentation reult that provided by exiting croover trategie, even better In our experiment it egmentation reult qualitie which indicated by it average percentage of ME are 796% better than the compared croover trategie The propoed croover trategy alo require le earching generation than the exiting trategie to provide the egmentation reult It only require 636 generation le than the compared croover trategie NOTES 1

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