Vaseem Durrani Technical Analyst, Aedifico Tech Pvt Ltd., New Delhi, India

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1 Performace Aalysis of Color Image Segmetatio Techiques (K-meas Clusterig ad Probabilistic Fuzzy C-Meas Clusterig ad Desity based Clusterig) Farah Jamal Asari Sectio of Computer Egieerig, Uiversity Polytechic, Faculty of Egieerig ad Techology, Jamia Millia Islamia (A cetral Uiversity) New Delhi-25(Idia) Vaseem Durrai Techical Aalyst, Aedifico Tech Pvt Ltd., New Delhi, Idia Abstract A comparative aalysis of color image segmetatio of three differet techiques is preseted i this paper with differet oise levels. The robustess of each algorithm is checked o the basis of its accuracy of the clusters mapped. We have take K-Meas, FCM ad Desity based image segmetatio approach for the aalysis. I these methods of segmetatio, the objects are distiguished clearly from the backgroud. Basically Image is that type of iformatio which has to be processed effectively ad correctly. Segmetatio of a image requires the separatio or divisio of the image ito regios of similar ad multiple attribute. Image segmetatio assigs a tag to each ad every pixel i a image such that each pixel with the same tag share certai visual characteristic. Basic attribute for segmetatio of a image is its lumiace amplitude for a image ad color compoets for a color image ad its itesity level. Clusterig is oe of the methods which are used for segmetatio. The objective of this paper is to compare the performace of various segmetatio techiques for color images at differet oise levels ad attacks. Keywords: K-Meas clusterig,optimal Fuzzy C-Meas clusterig,segmetatio PSNR ad MSE. I. INTRODUCTION Image segmetatio is the process of dividig a image ito multiple parts ad that parts collectively cover the etire image. Basically, partitios are differet objects i which image have the same texture or color. Because of its complicated backgroud oise, the image segmetatio is the difficult ad very hot research issues o the image processig. This is typically used to idetify objects or other relevat iformatio i digital images. There are may differet ways to perform image segmetatio; oe is Color-based Segmetatio such as K-meas clusterig, ad aother is Optimal Fuzzy C- Meas clusterig. All of the pixels of a image i a regio are similar with respect to some computed property, like color or itesity. Image segmetatio is typically used to locate objects ad boudaries (lies, curves, etc.) i images. Adjacet regios of a image are sigificatly differet with respect to the same characteristics. Some of practical applicatios of image segmetatio are: image processig, computer visio, face recogitio, medical imagig, digital libraries, image ad video retrieval [1]. Image segmetatio methods have five categories: Regio based segmetatio [6], Pixel based segmetatio [7], Edge based segmetatio, ad Clusterig based segmetatio [1], Edge ad regio Hybrid segmetatio. The K-Meas clusterig techique is oe of the most popular method that has bee applied to solve low-level image segmetatio tasks. I k-meas clusterig, it partitios a collectio of data ito a k umber group of data [11, 12]. K-meas algorithm cosists of two separate phases. I the first phase it calculates the k cetroid ad i the secod phase it takes each poit to the cluster which has earest cetroid from the respective data poit. There are differet methods to defie the distace of the earest cetroid ad oe of the most used methods is Euclidea distace [15]. The images are restricted by two mai problems. The first problem is geerated by the fact that o spatial (regioal) cohesio is applied durig the space partitioig process startig coditio (the iitializatio of the iitial cluster ceters), while the secod is geerated by the Fuzzy clusterig techiques have bee effectively used i image processig, patter recogitio ad fuzzy modelig.the OFCM was proposed by Gath ad Geva ad Xuejia Xiog, Kap Luk Cha. A effective method for usupervised optimal fuzzy clusterig based o a geeralized objective fuctio is implemeted i this paper [12]. Volume 4 Issue 4 April ISSN :

2 II. COLOR IMAGE SEGMENTATION USING K- MEANS CLUSTERING The K-Meas clusterig techique is oe of the most popular methods that have bee applied to solve low-level image segmetatio tasks. I k-meas clusterig, it partitios a collectio of data ito a k umber group of data [11, 12]. K-meas algorithm cosists of two separate phases. I the first phase it calculates the k cetroid ad i the secod phase it takes each poit to the cluster which has earest cetroid from the respective data poit [15]. Clusterig algorithm is coverget ad its basic aim is to shape up the partitioig decisios based o a userdefied pre or iitial set of clusters. Applicatios of the clusterig algorithms of segmetatio of image for complex color images are restricted because of two problems. The first problem is with geeratig the cluster ceters ad secod is geeratig by the fact that o regioal cohesio is applied durig the space partitioig process. The k-meas clusterig was proposed by Bo Zhao, Zhogxiag Zhu, Erog Mao ad Zheghe Sog [12]. To produce erroeous decisios the selectio of iitial ceters is very importat because it prevets the algorithms from coverge to local miima. The basic iitializatio procedure radomly selects the ceters of the cluster from the iput data. This procedure does t elimiate the problem of covergig ad also the segmetatio results differet ay time whe the algorithm is applied to the iput data. I this paper, by extractig the most power colors from the color histogram by usig a differet approaches to select the cluster ceters. Whe this procedure is applied o the large images the this procedure proved very efficiet. Durig the processig, the algorithm does t cosider the coectios betwee the color compoets of each pixels d its eighbors this is the limitatio with the K-Meas. Because of this reaso this algorithm is restricted with some applicatios of the clusterig to complex color-textured images. By cosiderig to the sample the local color smoothess, The iput image is filtered by the gradiet operator for the local complex texture image while for filterig the image a adaptive diffusio scheme is used. So durig the space partitioig, algorithm tries to optimize the fit diffusio gradiet distributio i a local eighborhood (aroud the pixels) uder the aalysis with the color for each cluster. Util the process is reached to coverges, the method is cotiuously applied. This is applied to the clusterig algorithm o large images of complex texture ad o to test the data that have bee corrupted due to oise. 2.1 The Algorithm The procedure of the algorithm is easy ad simple that fallows some steps to classify a set of data though some umber of clusters (k clusters). For each cluster defie k cetroid the these cetroid placed i a differet way at differet locatios so that it ca produce differet results. Make these cetroids far from each other to take a better result. Associate each poit to the earest cetroid which belogs to a give data set, ow each object assiged a earest cluster group. Now we have to re-calculate k for ew cetroid from the previous steps so that bidig has to be doe betwee earest poits of cetroid ad same data set the a loop has bee geerated ow we otice that k cetroid chages their locatio ad the o more chages have bee see, meas ow cetroid do ot chage their locatio or does t move aymore. Σ ζ( ti;cj ) (1) i=1 Cj is the earest cluster cetroid of ti q =1/ Σ ζ( ti; Cj ) (2) i=1 This ca be computed from R as, k d q(r, W) = Σ Wj Σ Rij (3) j=1 i= Steps of the classical K-Meas clusterig algorithm Steps i the algorithm are as follows [11]: Step1. Defie the umber of cluster k ad radomly selects the cetroid of the clusters. Volume 4 Issue 4 April ISSN :

3 Ceter i 0 =GL mi + [(i-i/2) (GL max -GL mi )/k)] i =1, 2.k (4) Step2. Geerate k clusters ad determie the clusters Cetre. Distace i, j = abs (GL j Ceter i ) i= 1,2,., K; j = 1,2,., N. (5) Step3. Assig each pixel i the image to the clusters that miimize the distace betwee the pixel ad the cluster Cetre (Distace is the squared or absolute differece betwee a pixel ad a cluster Cetre). Ni Ceter i m = 1/Ni i=1 Σ GLj j=1, 2,..K. (6) Step4. Re-compute cluster Cetre by averagig all of the pixels i the cluster. Step5. Repeat steps 2 ad 3 util covergece is attaied (for example cluster Cetre remais uchaged). Threshold=1/2(ceter k + ceter k-1 ). (7) III. FUZZY CLUSTERING I Fuzzy clusterig meas methods, a piece of data ca be from oe or more umber of clusters. I patters recogitio this techique is used. Clusterig meas dividig data poits of cluster ito homogeous classes, so that similar data items ca be take ito same class ad dissimilar data ca be take ito differet class as possible. Data compressio ca be though as a clusterig where large data coverted ito a small umber of clusters. The formatio of cluster depeds o the data ad the applicatio, to idetify the classes differet similarity-dissimilarity measures ca be used. Areas of applicatio of fuzzy cluster aalysis iclude data aalysis, patter recogitio, ad image segmetatio [4]. 3.1The Usupervised Optimal Fuzzy C-Meas Clusterig There are two problems i Fuzzy C-Meas Clusterig algorithm, oe is clusters eeds to be specified i advace which is used, ad other is limitatio of FCM( restrictio to spherical clusters). Also there are several derivatives of FCM oe is the UFP-ONC algorithm [3], it is a two-step approach to fidig a good results of a clusterig. The core part of the algorithms is FCM. UFP-ONC algorithm is the improvemet i the FCM. 3.2The Optimal Fuzzy Clusterig Cosider a collectio of patters, x1,x2, xєrp. Form a iput data set X. c J(U,V;X)= (μ ik ) m {(1-g)*( x k -V i l ) l + g*( {( x k -V i ) s ij } 2 )}, l 1 (8) i=1 k=1 c is the umber of the clusters ad V i is the prototype of i th cluster. These r eigevectors, N E i = (μ ik ) m (x k -V i ) (x k -V i ) T (9) K=1 Volume 4 Issue 4 April ISSN :

4 V i t = (μ ik t-1 ) m x k / ( μ ik t-1 ) m (10) k=1 k=1 Where t is the iterative step umber, ad r μ ik t =1/{ δ ik t / δ t jk } (1 / (m-1)) (11) j=1 δ ik t = (1-g)* ( x k -V i t l ) l + g*( {(x k V i t ) s t ij} 2 (12) Explaatio of this equatio is i [15].Obliviously, these two values are the ecessary coditios for J to have a local miimum [15]. However, miimizatio of J with Eq. (8) forms a class of costraied oliear optimizatio problems whose solutio is ukow [12,15]. This problem arises by placig the l-orm i the objective Fuctio [15]. For the preset research, oly l=2 orm is cosidered for testig the UOFC algorithm while other orm measures will be studied i future work [15]. It ca be see that the two mai advatages of the UOFC algorithm are [ 15] (1) Its additioal liear i the geeralized objective fuctio; (2)The l-orm distace measure used The Algorithm The algorithm cosists of followig parts: (1) Choose iitial cluster cetroids Vi. (2) calculate the ceters vectors (3) Compute ew cetroids Vi_ew: (1/d^2(Xj, Vi))^ (1/ (q-1)) (13) u_ {ij}= Sum (k=1, K) (1/d^2(Xj, Vk)) ^ (1/ (q-1)) Sum (j=1, N) (u_ {ij}) ^q Xj Vi_ew = (14) Sum (j=1, N) (u_ {ij}) ^q (4) Whe the movemet of cetroids (relative chages) is less tha a predetermied threshold MOVETHRS, stop the iteratio. Otherwise go to step 2. IV. EXPERIMENTAL RESULTS We have cosidered three clusterig algorithms for the complete aalysis. these algorithms are kmeas clusterig, fcm clusterig ad desity based clusterig. Clusterig of color i oe stadard image is doe for all the three algorithms o MATLAB software tool. Fig 1 displays the stadard image. Fig 1 origial image Figure 2(a) displays the clusterig image after kmeas algorithm ad figure 2(b) displays the clusterig image after fcm. Volume 4 Issue 4 April ISSN :

5 (a) (b) Fig2 (a) kmeas result (b) fcm result Volume 4 Issue 4 April ISSN :

6 I figure 3 (a), (b) ad (c) color based separate clusters are show for kmeas, fcm ad desity based respectively Fig 3(a) Fig 3(b) Volume 4 Issue 4 April ISSN :

7 Fig 3(c) Fig 3 (a) kmeas color clusters (b) fcm color clusters (c) db color clusters Noise Salt & Pepper (0.05 level) Algorithm Accuracy (%) Kmeas Fcm Desity based Table 1 The accuracy of fcm is better tha the desity based ad kmeas clusterig algorithms as show i the table 1. Noise Salt & Pepper (0.15 level) Algorithm Accuracy (%) Kmeas Fcm Desity based Table 2 Noise Salt & Pepper (0..25 level) Algorithm Accuracy (%) Kmeas Fcm Desity based Table 3 Volume 4 Issue 4 April ISSN :

8 Table 1 2 ad 3 are displayig the algorithms performace aalysis at differet salt ad pepper oise. At 0.05 level where oise is almost egligible all the three are above 75 % accuracy level but as the oise level icreases the performace of the algorithm degrades. Ad at 0.25 level of oise the kmeas accuracy goes dow to 59% whereas FCM still shows 78.23%. hece fcm performs better i cotext with the oisy eviromet it fouds the cluster above 75% correct. V. CONCLUSION After performig the experimets o all the three algorithm s for image segmetatio ad clusterig. we have cocluded that the fcm clusterig algorithm is quite accurate i-terms of detectig the clusters as compared to desity based ad kmeas algorithm at differet level of salt ad pepper oise. REFERENCES [1] J.Bezdek, A Covergece Theorem for the Fuzzy ISODATA Clusterig Algorithm, IEEE Tras.Patter. Aal. Mach. Itel, 2:1-8, [2] GAO Xi-bo.Fuzzy cluster aalysis ad its applicatios [M].Xi a, Chia: House ofxidia Uiversity, (i Chiese) [3] Ahmed M N, Yamay S M, Mohamed N, etal. A modified fuzzy Cmeas algorithm for bias field estimatio ad segmetatio of MRIdata [J].IEEE Tras o MedicalImagig, 2002, 21(3): [4] DINGZhe, HU Zhog-sha, YANG Jig-yu, TANG Zhe-mi, WU Yog-ge.Afuzzy-clusterig-based approach to image 1997, 34(7): (i Chiese) [5] F.Meyer, Color image segmetatio, I IEEE Iteratioal Coferece o Image Processig ad its Applicatios, pages , May 1995.Maastricht, The Netherlads. [6] A.Moghaddamzadeh ad N. Bourbakis, A Fuzzy Regio Growig Approach for Segmetatio of Color Images,Patter Recogitio, 30(6): , [7] G.A. Ruz, P.A.Estevez, ad C.A. Perez, A Neurofuzzy Color Image Segmetatio Method for Wood Surface Defect Detectio, Forest Prod. J. 55 (4), 52-58, [8] A.A. Youes, I. Truck, ad H. Akdaj, Color Image Profilig Usig Fuzzy Sets, Turk J Elec Egi, vol.13, o.3, [9] Refael C.Gozalez ad Richard E.Woods, Digital Image processig (secod editio) Pearso Educatio Asia Limited ad Publishig House of Electroics Idustyt, [10] Pham DL ad Price JL, A adaptive fuzzy C-meas algorithm for image segmetatio i the presece of itesity ihomogeeities, Patter Recogit Lett, 1999, 20(1): [11] B. Zhag, Geeralized K-harmoic Meas boostig i Usupervised Learig, Techical report (HPL ), Hewlett-Packard Labs, [11] ZhogxiagZhu,Bo Zhao,Erog Mao ad Zheghe Sog, Image segmetatio based o At coloy optimizatio ad K-meas clusterig, Proceedigs of the IEEE iteratioal coferece o Automatio ad logistics, August 18-21,2007,jia,chia. [12] Gath,I. ad Geva A. B. (1989), Usupervised Optimal fuzzyclusterig,ieee Trasactio o Patter Aalysis Machie Itelligece, 11(7): [13] Moika Xess ad S.Akila Ages, Survey O Clusterig Based Color Image Segmetatio Ad Novel Approaches To Fcm Algorithm, IJRET: Iteratioal Joural of Research i Egieerig ad Techology eissn: pissn: [14] Muthukaa.K, Merli Moses.M, Color Image Segmetatio usig K-meas Clusterig ad Optimal Fuzzy C-Meas Clusterig, Iteratioal Coferece o Commuicatio ad Computatioal Itelligece 2010, Volume 4 Issue 4 April ISSN :