Research on Fuzzy Clustering Image Segmentation Algorithm based on GA and Gray Histogram Baoyi Wang1, a, Long Kang1, b, Shaomin Zhang1, c

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1 3rd Iteratioal Coferee o Mahiery, Materials ad Iforatio Tehology Appliatios (ICMMITA 05 Researh o Fuzzy Clusterig Iage Segetatio Algorith based o GA ad Gray Histogra Baoyi Wag, a, Log Kag, b, Shaoi Zhag, Shool of Cotrol ad Coputer Egieerig, North Chia Eletri Power Uiversity, Baodig, 07003, Chia a eail: wagbaoyiqj@6.o, beail: @qq.o, eail: zhagshaoi@6.o Keywords: Iage Segetatio; Geeti Algorith; FCM; Gray Histogra Abstrat. Whe the traditioal FCM algorith is applied to iage segetatio, it is sesitive to the seletio of lusterig eter ad a ot autoatially deterie the uber of lusterig eter. Aordig to these probles, this paper proposes a fuzzy lusterig iage segetatio algorith based o geeti algorith ad gray histogra. This algorith uses the global searh haraters of geeti algorith to avoid fallig ito loal optial solutio, ad the objetive futio is optiized ad the uber of the luster eter is deteried by gray histogra. Experietal results show that the proposed ethod has strog robustess ad good segetatio effet. Itrodutio Fuzzy -eas lusterig algorith is widely used i the field of iage segetatio [], but it is sesitive to the iitial lusterig eter [4] ad a ot predit the uber of lusterig. Geeti algorith searhes the optial solutio by siulatig the atural evolutio proess of the populatio, ad a avoid the loal optial solutio. Whe the gray value is used to alulate the objetive futio, the repeated alulatio is large. Statistial harateristis of the gray histogra a be used to iprove the overgee rate, ad beause the lusterig eter usually appears i the axiu value of the histogra, the uber of lusterig eter a be deteried by the uber of axiu values []. I this paper, a fuzzy lusterig iage segetatio algorith based o GA ad gray histogra is proposed. The algorith uses gray histogra to optiize the objetive futio ad deterie the uber of lusterig eter. The global optial approxiate solutio of lusterig eter is obtaied by the geeti algorith [3], ad it is used as the iitial lusterig eter of FCM to get the global optial solutio. Iage Segetatio based o Traditioal FCM The geeral expressio of the objetive futio is: J (U, V u dik ( k i u k ( 0 u (3 U is a fuzzy ebership atrix; V is the lusterig eter atrix, ad eah lusterig eter is the gray value of the iage; is the weighted idex, ad [,+ ; is the uber of luster eters; is the uber of all the pixels; u ik is fuzzy ebership of the i-th saple with respet to the k-th lusterig eter; d ik is the distae betwee the i-th saple ad the k-th luster eter. Whe J (U,V gets the iiu value i{j (U,V}, the algorith gets the best lusterig eter. Lagrage uber ultipliatio is used to solve the proble. 05. The authors - Published by Atlatis Press 550

2 u v ( d ik r ir ( d ( u ( u i i k i x The geeral proess of FCM algorith for iage segetatio: Iitializatio:iitialize the luster uber, the weighted idex, the axiu uber of iteratios ax ad the iteratio threshold ε; iitialize iteratio outer t0; iitialize luster eter V (0 {v,v v } radoly,where i ad v i represets the gray value of the iage; Step : Calulate the fuzzy ebership atrix U (t ; u ( t ( t ( dik ( ( dik t r Step : Calulate luster eter V (t+ ; v ( t+ k i i ( t ( u ( t ( u x i (4 (5 (6 Step 3: Calulate the distae betwee V (t+ ad V (t. If V (t -V (t+ ε, the the iteratio is over ad jup to Step 5; Step 4: tt+,if t<ax the jup to Step ; Step 5: Output the lusterig eter V ad the ebership atrix U. Fuzzy Clusterig Iage Segetatio based o Geeti Algorith ad Gray Histogra Deterie eodig shee of GA Real-oded geeti algorith redues the oplexity of the algorith ad a iprove the effiiey, so it is used i this paper. Eode lusterig eter V{v,v v }, where is the uber of the lusterig eter ad v i (0 v i 55 is the gray value of the iage. Deterie the uber of lusterig eter Gray level histogra of the iage reflets the distributio of gray level, ad there are experiets show that the lusterig eter is usually i the axiu value of the histogra [3]. Therefore, the uber of the axiu of gray histogra is used as the uber of lusters. 3 Deterie the fitess futio of GA ad the objetive futio of FCM Whe the objetive futio of FCM obtais the optial solutio, geeti algorith fitess futio reahes the axiu. So the fitess futio is defied as follows: f (8 J U, V + δ ( I order to avoid the eergee deoiator is zero, a sall ostat δ(0<δ a be added i the deoiator, ad δ a take the values of. Whe usig the lusterig algorith to seget the gray iage, the gray values of the iage are take as saples. Beause the gray value is i the rage of L, the gray histogra a be used to out the uber of pixels of eah gray value, ad whe the statisti value of a gray value is ot zero, it is used a saple. This ethod a redue the aout of oputatio by avoidig the repeated alulatio of the distae betwee gray value ad lusterig eter. Defie the saple set X{l 0,l,l l i l }, ad the statistis value of the saple G{g 0,g,g g i g }, where 0 55 ad l i is gray value, ad g i is the uber of pixels (7 55

3 orrespodig to gray value l i. The, J ( U,V udik gi k i ( d ik u ( d r ir i i k v i (9 ( i ( u g u g x i Fially, the fitess futio is haged to f J UV, + δ ( 4 Iitialize populatio i GA Radoly geerated idividuals as the iitial populatio, ad eah idividual is represeted as {v,v v }. Ad the gray value orrespodig to the axiu values of the gray histogra opose a idividual whih replae a idividual radoly i populatio. 5 Deterie the probability of rossover ad utatio This paper uses the adaptive algorith proposed by Re Ziwu [6] et al to solve the pheoeo of rado roaig. The rossover probability ad utatio probability are deteried as follow: ( P P ( f favg P f f avg P fax favg (3 P f < favg ( P P ( f favg P f f avg P fax favg (4 P f < favg f ax is the axiu fitess; f avg is the average fitess ; f is the fitess of the idividuals i the utatio or the large value i the fitess of the two idividuals i the rossover. 6 Deterie the geeti operator Roulette wheel seletio [7] is used as seletio operator. Sigle rossover is used as rossover operator. Ad the rado utatio operator is used to arry o the utatio operatio. 7 Elite reservatio strategy To esure the best idividual of eah geeratio is ot destroyed, the elite reservatio strategy is used i this paper. Through the elite reservatio strategy, it a prevet the loss of the best idividual of urret populatio [5]. The Algorithi proess Step : Iitialize saples. The ifrared iage is proessed by gray sale, ad the Gauss oise of the iage is eliiated by usig the eighborhood averagig ethod with 3 3 widow. Fially, the saple set X{l 0,l,l l i l }, ad the statistial value set G{g 0,g,g g i g } are extrated as the iput of the algorith fro the gray histogra of the iage, ad 55; Step : Iitialize paraeters. Iitialize rossover ad utatio probability P, P, P, P ; Iitialize geeratio gap g, populatio size, weighted idex, ad the uber of lusters ; set the uber of iteratios t0 ad Iitialize the axiu uber of iteratios ax; Step 3: Iitialize populatio P{V,V V i V }, ad V i {v i,v i v 3 i}; Step 4: Calulate the fitess of populatio aordig to forula (; Step 5: Do the seletio operatio based o Roulette wheel ad the geeratio gap is g; Step 6: Do the sigle rossover operatio, ad ross probability is P ; Step 7: Do the rado utatio operatio, ad utatio probability is P ; 55 (0 ( (

4 Step 8: Calulate the fitess of the ext geeratio; Step 9: Exeute the elite retetio strategy, ad radoly geerate idividuals to fill sub populatio to esure that the populatio size is ; Step 0: To ake tt+, if t<ax, the jup to Step 4 ad otiue the iteratio; Step : The optial luster eters, whih are obtaied by geeti algorith, is used as the iitial lusterig eter of FCM ad FCM is used to seget the iage. Experiet ad Result Aalysis Aordig to the above odel ad algorith, this paper uses Matlab R05a as the prograig tool, ad selets the sized iage the 0kV trasforer bushig ad the lie joit as the experietal objet. Iitialize the paraeters as P 0.9, P 0.6, P 0., P 0.0,, g0.9, 0. Experiets were oduted usig the proposed algorith, geeti algorith ad rado iitial lusterig eter FCM algorith for ifrared iage segetatio, the the segetatio results of eah algorith are aalyzed. The results are as follows: (athe origial iage (b Geeti algorith ( Proposed algorith (d Rado FCM ( (e Traditioal FCM ( Fig. Segetatio results of differet algoriths (the 0kV trasforer bushig (athe origial iage (b Geeti algorith ( Proposed algorith (d Rado FCM ( (e Traditioal FCM ( Fig. Segetatio results of differet algoriths (the lie joit (a Experiet (b Experiet Fig. 3 Optial solutio urve (the 0kV trasforer bushig 553

5 Experiet Experiet Experiet (a Experiet (b Experiet Fig. 4 Optial solutio urve (the lie joit Table Iteratio ties, tie osuig ad lusterig eters of differet algoriths (The 0kv trasforer bushig ad 5 Geeti algorith The proposed algorith Rado FCM ( iteratio ties tie osuig (s lusterig eters iteratio ties tie osuig (s lusterig eters Geeti algorith The proposed algorith Rado FCM ( Table Iteratio ties, tie osuig ad lusterig eters of differet algoriths (The lie joit ad 3 Geeti algorith The proposed algorith Rado FCM ( iteratio ties tie osuig (s lusterig eters Experiet iteratio ties tie osuig (s Geeti algorith The proposed algorith Rado FCM ( lusterig eters

6 The followig harateristis a be obtaied by aalysis: The segetatio results of figure (a~( ad figure (a~( show that, all of the proposed algorith, geeti algorith ad rado iitial lusterig eter FCM algorith a effetively seget the iage; but as show i figure (d ~ (e ad figure (d ~ (e, as well as table ad table, beause of the sesitivity of the rado iitial lusterig eter FCM algorith to the iitial lusterig eter, the fial lusterig eter of FCM is ustable, whih affets the lusterig results ad the robustess is poor. Aordig to figure 3 ad figure 4, as well as table ad table, whe opared to the geeti algorith, the optial solutio ad lusterig eter of the algorith proposed by this paper have saller volatility ad stroger robustess. Colusio I this paper, a fuzzy lusterig iage segetatio algorith based o GA ad gray histogra is proposed to deal with the proble that the traditioal FCM is easy to fall ito loal optial solutio ad a ot predit the uber of lusterig eter. The uber of luster eters is deteried by the uber of peaks of gray histogra, ad the statistial values of the gray level are used to redue the aout of oputatio i the proess of lusterig. Ad the lusterig eter of the FCM is iitialized by the global optial solutio of geeti algorith. Experiets show that the proposed algorith is ore robust tha the traditioal FCM, ad has a better segetatio effet. Akowledgeet I this paper, the researh was sposored by Sietifi researh projet of Hebei Provie (Projet No. Z0077. Referees [] Li Wei. Researh o iage segetatio algorith based o fuzzy C eas lusterig [D]. Harbi Egieerig Uiversity. 03. [] Zhao Ya. Researh o iage segetatio tehology based o FCM algorith [D]. Harbi Istitute of Tehology. 0. [3] Lou Yixia, Cheg Mig, We Gaoji, et al. Iage fuzzy lusterig aalysis based o FCM ad geeti algorith [J]. Coputer egieerig ad Appliatio, 00 46( , 95. [4] Bai Suqi, Hui Chagku, Wu Xiaoju, Wag Shitog. A fuzzy lusterig algorith based o geeti algorith ad its obiatio with FCM algorith [J]. Joural of East Chia Shipbuildig Istitute (NATURAL SCIENCE EDITION, 00 5( [5] Liu Yu. Researh ad appliatio of fuzzy lusterig based o geeti algorith [D]. Hea Uiversity [6] Re Ziwu, Sa zhi. Researh o the iproveet of adaptive geeti algorith ad its appliatio i syste idetifiatio [J]. Joural of syste siulatio, 006 8( [7] Tia Xiaoei, Gog Jig. A review of real eodig geeti algorith [J]. Joural of Hua Voatioal College of Eviroetal Biology, 005 (