A Cluster Number Adaptive Fuzzy c-means Algorithm for Image Segmentation

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1 , pp A Cluster Number Adaptve Fuzzy c-means Algorthm for Image Segmentaton Shaopng Xu, Lngyan Hu, Xaohu Yang and Xaopng Lu,2 School of Informaton Engneerng, Nanchang Unversty, NanChang,, JangX, Chna, Department of Systems and Computer Engneerng, Carleton Unversty, Ottawa, ON Canada, KS 5B6. xushaopng@ncu.edu.cn Abstract Amng at parttonng an mage nto homogeneous and meanngful regons, automatc mage segmentaton s a fundamental but challengng problem n computer vson. It s well known that Fuzzy c-means (FCM) algorthm s one of the most popular methods for mage segmentaton. However, the FCM-based mage segmentaton algorthm must be manually estmated to determne cluster number by users. In ths paper, we propose a novel cluster number adaptve fuzzy c-means mage segmentaton algorthm (CNAFCM) for automatcally groupng the pxels of an mage nto dfferent homogeneous regons when the cluster number s not known beforehand. We utlze the Grey Level Co-occurrence Matrx (GLCM) feature extracted at the mage block level nstead of at the pxel level to estmate the cluster number, whch s used as ntalzaton parameter of the followng FCM clusterng to endow the novel segmentaton algorthm adaptvely. We cluster mage pxels accordng to ther correspondng Gabor feature vectors to mprove the compactness of the clusters and form fnal homogeneous regons. Expermental results show that proposed CNAFCM algorthm not only can spontaneously estmate the approprate number of clusters but also can get better segmentaton qualty, n compare wth those FCM-based segmentaton methods recently proposed n the lterature. Keywords: Image Segmentaton, Fuzzy c-means, Estmaton of Cluster Number, Composte Cluster Valdty. Introducton Image segmentaton s one of the most dffcult and challengng problems n a number of applcatons, and ths low-level vson task s also one of the most crucal steps toward computer vson [-3]. Classcally, mage segmentaton s defned as an nverse problem whch conssts of achevng a compact regon-based descrpton of the mage by decomposng t nto meanngful or spatally multple coherent regons, whch are homogeneous wth respect to one or more characterstcs such as color or texture. From an mplementaton pont of vew, mage segmentaton can be treated as a clusterng problem where the features descrbng a pxel correspond to a pattern, and each mage regon corresponds to a cluster. Therefore, many clusterng algorthms, especally the fuzzy c-means algorthm (FCM), have wdely been used to solve the segmentaton problem and such a success chefly attrbutes to ntroducton of fuzzness for the belongngness of each mage pxel, whch makes the clusterng methods able to retan more nformaton from the orgnal mage than the crsp or hard segmentaton ISSN: IJSIP Copyrght c 203 SERSC

2 methods (e.g., K-means). The advantages of the FCM are ts smply straghtforward mplementaton, farly robust behavor, applcablty to vector data and the ablty of uncertanty data modelng. Nevertheless, most of the FCM-based mage segmentaton algorthms assume a pror knowledge of the cluster (regon) number. Whle n many practcal stuatons, the approprate cluster number s unknown or mpossble to determne, whch has unneglectable mpacts on the mage segmentaton qualty. Therefore, how to automatcally and accurately determne the cluster number to avod over-segmentaton or under-segmentaton becomes a challengng task. To solve ths problem, L and Shen [4] proposed an algorthm called automatc modfed fuzzy c-means cluster segmentaton algorthm (AMFCM) that can automatcally determne the optmal cluster number. However, the AMFCM algorthm requres teratve executon of the standard FCM wth cluster number from 2 to maxmum possble value untl predefned optmal valdaton crtera s met, whch wll extremely ncrease the computatonal complexty. To mprove the performance, an ant colony fuzzy c-means hybrd algorthm (AFHA) was proposed to overcome the FCM s senstveness to the ntalzaton condton of cluster number n [5]. Essentally, the AFHA ncorporated the ant system algorthm (AS) to the FCM to mprove the compactness of the clusterng results n the color feature space. However, ts effcency s stll low due to computatonal complexty of the AS algorthm. To ncrease the AFHA s effcency, an mproved ant colony fuzzy c- means hybrd algorthm (IAFHA) was also ntroduced n [5]. Specfcally, the IAFHA added an ant subsamplng-based method to modfy the AFHA. Although the IAFHA's effcency had been ncreased, t stll suffers from hgh computatonal complexty. Tan et al., [6] presented a hstogram thresholdng fuzzy c-means hybrd (HTFCM) approach whch appled the hstogram thresholdng technque to estmate optmal cluster number n an mage. Then, the standard FCM algorthm was utlzed to mprove the compactness of the clusters formng those unform regons based on color feature. The above algorthms assume that the nput mages mostly contan unformly colored objects, whch s typcally not true for natural mages. In fact, the texture feature reflectng the spatal patterns of pxels at mage block level has strong lnks wth the human percepton and n many practcal scenaros the color-alone feature at pxel level s not suffcently robust to accurately descrbe the mage content [7]. The cluster number estmaton of those FCM-based algorthms, such as AFHA, IAFHA and HTFCM, only consders color feature at pxel level whch means that they could not determne accurate cluster number for complex mages, especally natural mages. In ths paper, we focus on cluster number adaptve segmentaton for computer vson applcatons. To overcome the aforementoned dsadvantages of those FCM-based segmentaton algorthms, a novel cluster number estmaton module s added pror to the standard FCM algorthm to obtan optmal cluster number. In ths estmaton module, nstead of processng at pxel level, the mage s frst dvded nto many small rectangular mage blocks. We complete Gray Level Co-occurrence Matrx (GLCM) feature extracton and clusterng at the block level to estmate optmal cluster number. The novel estmaton module s based on the coarse mage, whch makes ts executon tme s very fast and could be gnored, bascally. Moreover, n contrast to the ntalzaton module of the IAFHA and HTFCM algorthm only employng color feature, GLCM texture feature allows us accurately to estmate cluster number. Then, n the FCM clusterng, n contrast to the algorthms lke FCM_S [8, 9] that ncorporate local spatal nformaton n the objectve functon, Gabor flters [7, 0] are utlzed for 92 Copyrght c 203 SERSC

3 feature extracton for each pxel. The parameters of the Gabor flter are specfed by the frequency, the orentaton of the snusod, and the scale of the Gaussan functon. Therefore, the feature vector extracted for each pxel mplctly ncorporate local orentatons and spatal frequences nformaton. The proposed algorthm consders spatal nformaton n the feature space nstead of n the objectve functon, whch makes the objectve functon qute smple. A large number of experments were carred out to assess performance of the proposed segmentaton algorthm, and expermental results have demonstrated that the CNAFCM algorthm could accurately determne cluster number and obtan better segmentaton results (produce meanngful segmentaton effectvely) than those approaches such as AMFCM, AFHA, IAFHA and HTFCM. 2. The Standard FCM Algorthm The FCM clusterng algorthm was frst ntroduced by Dunn [] n 973 and later extended by Bezdek [2] n 98. Ths algorthm has been used as one of the popular clusterng technques for mage segmentaton n pattern recognton. In the FCM, each mage pxel has certan membershp degree assocated wth each cluster centrod. These membershp degrees have values n the range [0,], ndcatng the strength of the assocaton between that pxel and a partcular cluster centrod. The FCM algorthm attempts to partton every mage pxel nto a collecton of the K fuzzy cluster centrods by mnmzng the weghted sum of squared error objectve functon Jm( UC, ) [3]: N K m 2 m u jd j = j= J (U,C ) = () subject to K j= m j u =, < j< K N = m j u < N, N N K m uj = N (2) = j= where N s the total number of pxels n mage, u j s the membershp degree of th pxel x to j th cluster centrod c j, m s the exponental weght of membershp degree whch controls the fuzzness of the resultng partton, and d j = x c j s the dstance between x and c j. It needs to be ponted out that the standard FCM algorthm would degenerate to hard c-means algorthm when u j [0,] and m =.Let U = ( u, u,, u ) T be the set of membershp degree of x assocated wth each 2 K Copyrght c 203 SERSC 93

4 cluster centrods, then U = ( U, U2,, U N ) s the membershp degree matrx and C = ( c, c2,, c K ) s the set of cluster centrods. The degree of compactness and unformty of the cluster centrods greatly depend on the objectve functon of the FCM. In general, a smaller objectve functon of the FCM ndcates a more compact and unform cluster centrod set. Unfortunately, there s no close form soluton to produce mnmzaton of the objectve functon. To acheve the optmzaton of the objectve functon, an teraton process must be carred out by the FCM algorthm. The key steps of the FCM can be descrbed n Table. Table. The Standard FCM Algorthm Algorthm Descrpton Steps 0 Randomly ntalze the fuzzy partton matrxc, set the teraton termnatng threshold ε to a small : postve number n the range[0,] and the number of teraton q to 0. 2: q q CalculateU accordng to C wth Eq.(3) 3: q CalculateC + q accordng to U wth Eq.(4) 4: q Update U + q accordng to C + wth Eq.(3) q Compare U + q wth U. f q q U + U ε stop teraton. Otherwse, 5: q= q+, and repeat steps 3 to 4 untl q q U + U ε Fnally, we can get the optmal membershp matrx U. Based on U, we can get the fnal segmentaton mage. u = (3) j K 2/(m ) (d k j /d k ) = where j K and N. It should be noted that f d j = 0 then u j = and set others membershp degrees of ths pxel to 0. c N m u j X = j N m u j = = where j K and X s the multdmensonal feature vector of th pxel x. (4) 3. Proposed Algorthm 3.. Basc Idea As prevously mentoned, the performance of the FCM-based segmentaton algorthm s often affected by the cluster number whch s manually ntalzed. Therefore, n ths paper, 94 Copyrght c 203 SERSC

5 the core dea of our algorthm s to obtan a soluton to overcome the FCM's senstveness to the cluster number by ntroducng a novel cluster number estmaton module before the standard FCM clusterng. The most mportant object n ths estmaton module s to accurately determne cluster number wth mnmal computaton cost. Conventonally, feature vectors used n the FCM segmentaton algorthm are usually extracted for each pxel. For an mage wth a typcal sze, hundreds of thousands of vector data wll have to be processed f we drectly do clusterng at the pxel level. In fact, the noton of the regon s well defned at the level of our vsual percepton, and the human eyes and bran are able to delneate regons that exhbt common spatal patterns,.e., texture. In a certan sense, an mage can be roughly consdered as the composton of several dfferent regons. Therefore, the texture s useful for dentfyng object or regon of nterest, and the task to estmate the regon number can be performed at the coarse level,.e., the mage block level. In our work, the mage block s a rectangular regon wth s = r r pxels and the standard FCM algorthm s employed to determne the optmal cluster number wthn the range of 2 to predefned maxmum search value, whch best suts a gven mage accordng to cluster valdty ndex. Specfcally, the Gray Level Co-occurrence Matrx (GLCM) texture feature of each block s used to estmate all possble homogenous regons n the mage. Compared wth the large number of pxels n an mage, block-level representaton of an mage usually has only several hundreds of blocks. Therefore, we utlze the feature extracted at the block level nstead of the pxel level resultng n reducng the computatonal cost of the clusterng. The method provdes an attractve way to estmate cluster number wth mnmal tme cost n comparson wth those approaches such as AMFCM, AFHA, IAFHA and HTFCM GLCM Texture Feature Extracton Gray Level Co-occurrence Matrx was proposed n [4] by Haralck and s wdely used for texture analyss. It estmates the second-order statstcs related to mage propertes by consderng the spatal relatonshp of pxels [5, 6]. The GLCM s created by calculatng how often a pxel wth the ntensty value occurs n a specfc spatal relatonshp to a pxel wth the value j. The major two steps are as follow: The frst step s to determne co-occurrng probabltes of all parwse combnatons of quantzed grey levels (, j ) n the fxed-sze spatal wndow gven two parameters whch are the dstance between the pxel par d and ther angular relatonθ. θ s quantzed n four drectons ( 0, 45, 90, and 35 ). For rectangular r r mage segment Ixy (, ), gray levels and j, the non-normalzed GLCM P j 's are defned by: j r r 0 (5) x= y= P ( θ,d ) = C{(I( x,y) = ) I( x± d θ,y d θ ) = j} where C {} = f the argument s true and C {} = 0 otherwse. The ± and sgns n Eq.(5) mean that each pxel par s counted twce: once forward and once backward to make the GLCM dagonal symmetrc. For each drecton, θ 0 and θ are shown n Table 2. Copyrght c 203 SERSC 95

6 Table 2. θ Values for Dfferent Drectons θ θ0 0 θ 0 - The second step s to apply statstcs to the co-occurrng probabltes. Statstcs that dentfy some structural aspect of the arrangement of the co-occurrng probabltes, whch reflect some qualtatve characterstc of the local mage texture lke smoothness or roughness, are appled to generate the texture feature vector. In our work, we calculate fve GLCM texture features, whch are used to form a feature vector: ) contrast (CON); 2) homogenety (HOM); 3) angular second moment (ASM); 4) entropy (ENT); 5) correlaton (COR). Fnally, each mage block generates a feature vector to descrbe ts texture characterstcs Cluster Valdty For an unsupervsed clusterng scheme, the segmentaton qualty depends on determnng the cluster number accordng to cluster valdty ndex. Several well-known cluster valdty ndexes for evaluaton of the cluster qualty could be adopted. One of the most fundamental ndexes s the mean squared error (MSE) that could be descrbed as follows: K MSE = x c j (6) N j = S j It s qute clear from the concept of MSE that when cluster number s fxed, a good clusterng algorthm should always generate results wth small dstorton. In other words, cluster centrods should be placed n such a way that they reduce the dstances to data peces as much as possble. Another commonly used ndex s Bezdek's evaluaton functon V PC [7], whch s defned as follows: PC N K = j= 2 j V = u /N (7) Ths cluster valdty evaluaton functon essentally measures the fuzzness of a clusterng result, propertes of whch were studed n [8]. A smaller V PC value ndcates a fuzzer result. Contrary, the larger the V PC value, the better the clusterng result. For a crsp partton, V PC acheves maxmum value of. A more recent valdty evaluaton ndex s the Xe-Ben functon [9], whch s defned as follows: V XB N K = j= 2 j j u x c = N mn c c j k j k (8) 96 Copyrght c 203 SERSC

7 Accordng to Xe and Ben [9], V XB should decrease monotoncally when K s close to N. When V XB shows a smaller value, the result s presumably a better partton. In ths work, the determnaton of the cluster number K opt s carred out wth combnaton of cluster valdty ndex VPC and V XB FCM Clusterng Although the cluster number s approprately estmated n cluster number estmaton module, there stll exsts one problem to be resolved. For those FCM-based mage segmentaton algorthms such as AFHA, IAFHA and HTFCM, cluster assgnment s based solely on the dstrbuton of pxel attrbutes n the color feature space, and the spatal dstrbuton of pxels n an mage s not taken nto consderaton. The applcaton of the FCM to complex scenes such as natural mages wll lead to over-segmented results snce the spatal contnuty s not enforced durng the space parttonng process. The man approach s to ntroduce spatal constrants nto the objectve functon of the FCM. Although the ntroducton of local spatal nformaton to the correspondng objectve functons solves the problem to some extent, t wll also make the objectve functon more complcated at the same tme, resultng n low effcency. As we know, a feature vector can be extracted at each pxel va computng ts local propertes. The feature of a pxel depends on a number of factors, such as the spatal relaton among pxels, ther scale, and orentaton. In contrast to many conventonal approaches, n ths work, the spatal connectvty nformaton between pxels s extracted and embedded n the mult-dmensonal feature vector of each pxel. Specfcally, Gabor flters wth a large number of orented band pass flters wth adaptve flter sze, orentaton, frequency and phase have been used to extract spatal features of the pxels. As such, spatal connectvty s guaranteed snce a defnte spatal connectvty constrant has been mposed durng feature extracton. For detals about Gabor feature extracton, please refer to [20, 2]. Brefly, the standard FCM algorthm s used to cluster Gabor feature vectors of the pxels wth the cluster number whch has been estmated by the cluster number estmaton module already, and then we label each pxel wth ts correspondng cluster to form fnal compact regons Pseudo Code The outlne of the proposed segmentaton algorthm, whch automatcally clusters the pxels of an mage nto dfferent homogeneous regons when the cluster number s not known beforehand, s llustrated n Table 3: 4. Expermental Results In ths secton, a large number of experments were carred out to assess the performance of the proposed cluster number adaptve FCM-based mage segmentaton algorthm (CNAFCM), and the results were summarzed. The am of these experments s to test the accuracy of the CNAFCM algorthm for mage segmentaton wth respect to the correct dentfcaton of perceptual regons n the synthetc and natural mages. Snce HTFCM developed by Tan and Isa [6] adopts smlar approach wth AMFCM, AFHA, IAFHA and outperforms them, we manly tested the performance by comparng the results returned by the proposed CNAFCM algorthm aganst those returned by the well-establshed HTFCM algorthm. Copyrght c 203 SERSC 97

8 4.. Experments Performed on Synthetc Images Snce the ground truth data assocated wth complex natural mages s dffcult to estmate and ts extracton s hghly nfluenced by the subjectvty of the human operator, we performed the experments on synthetc mages where the ground truth s unambguous. To evaluate whether segmentaton algorthm can accurately estmate the cluster (regon) number, we executed the CNAFCM and HTFCM algorthm on fve sets of synthetc mages from the VsTex database [22], respectvely. Each of the fve sets of mages contans 6 synthetc mages, and each synthetc mage has four or fve regons whch are flled wth texture mage accordng to layouts shown n Fgure. Some synthetc mages (.e., the frst set of synthetc mages) are gven n Fgure 2, the others were omtted due to space lmtaton. The expermental data summarzed n Table 4 and Table 5 ndcate that the proposed algorthm wth texture extracton and composte evaluaton ndex workng at mage block level offers more accurate estmaton of the regon number substantally, whle estmatons gven by color-based HTFCM algorthm are almost wrong. It means that our approach could obtan better segmentaton results by producng a fewer number of regons as well as provdng more homogeneous segmented regon. The man reason behnd ths was that, n some cases, regons n synthetc mages may be composed of two colors or even more resultng n over-estmaton of regon number when usng HTFCM algorthm. Table 3. Cluster Number Adaptve Fuzzy c-means Algorthm Steps Algorthm Descrpton Maxmal search cluster number K max Dvde the nput mage nto mage blocks wth heght r and wdth r. j Extract GLCM feature vector f B for each mage block and obtan data set { j Z FB = f B} j=, where Z s the number of mage blocks. For k = to K max Do the standard FCM clusterng on F B, and k calculate cluster valdty ndex VPC and k V XB. End for Accordng to k V PC and optmal cluster number K opt. k V XB, determne the Apply the Gabor flter to extract texture feature for each pxel and obtan set F { } N P= f P =, where N s the number of pxels. Do standard FCM clusterng on F P agan wth cluster number K opt. As we know n advance the layouts for synthetc mages, the segmentaton accuracy of the CNAFCM algorthm can be easly estmated by calculatng the followng quanttatve ndex: f P 98 Copyrght c 203 SERSC

9 QI = C = C = S S S S ref ref (9) where S represents the set of pxels belongng to the th regon found by the proposed ref algorthm and S represents the set of pxels belongng to the th regon n the segmented ground truth mage. In fact, QI s a fuzzy smlarty measure, ndcatng the degree of equalty between S and S ref, and the larger the QI, the better the segmentaton s. To evaluate the segmentaton errors between the ground truth and the segmented results numercally, we tabulate a quanttatve comparson n Table 6 for the thrd mage n the each set of synthetc mages (a total of fve mages). The expermental data depcted n Table 6 show that the quanttatve ndex errors are acceptable. Fgure. Segmentaton Layouts for Synthetc Images Fgure 2. The Frst Set of Synthetc Images used n our Experments Copyrght c 203 SERSC 99

10 Table 4. Number of Regons Estmated by HTFCM wth Hstogram Thresholdng Estmaton Set No Pattern No Ground Truth In order to verfy the dscrmnaton power of our segmentaton approach n the more general case, t was also appled to a synthetc test mage wth dfferent regons separated by rregular boundary. The result depcted n Fgure 3 s very satsfactory even n the case of dvded regon. Table 5. Number of Regons Estmated by CNAFCM Algorthm wth Composte Evaluaton Crteron Set No Pattern No Ground Truth Table 6. Comparson of Segmentaton Errors (%) Synthetc mage Set Set 2 Set 3 Set 4 Set 5 Accuracy(%) Fgure 3. The Synthetc Image wth Dfferent Textures Separated by Irregular Boundary and ts Segmentaton Result 200 Copyrght c 203 SERSC

11 4.2. Experments Performed on Natural Images In ths subsecton, the segmentaton results are evaluated vsually. As we know, although synthetc test mages are best for verfyng the possbltes and lmts of an algorthm, segmentaton of natural mages s a relable evaluaton ndcator for mage segmentaton algorthms. In order to evaluate CNAFCM's performance wth respect to the dentfcaton of perceptual homogenous regons, we have tested the proposed CNAFCM segmentaton algorthm on a large number of complex natural mages databases (.e., Berkeley [23]), whch ncludes mages characterzed by nonunform textures, fuzzy borders, and low mage contrast. For nstance, we have compared our segmentaton results wth the ones by the color-based segmentaton algorthm,.e., HTFCM. Fgure 4 llustrates the result, the same mage was always been used n other lterature, so the reader may compare to those methods. From the result, t can be observed that the dfferent regons produced by CNAFCM algorthm are well segmented and the shape of objects n the mages s preserved. However, t can also be observed that the regons produced by HTFCM algorthm are mxed together (caused by over-estmaton of regons), whch can not preserve the shape of objects n the mages and makes t dffcult to detect and recognze objects n the hgh-level vson applcatons. Fgure 4. Natural Image from the Berkeley Database and Segmentaton Results. a) Orgnal Image; b) Usng Proposed Algorthm; b) Usng HTFCM Algorthm 5. Concluson Automatc mage segmentaton s always a fundamental but challengng problem n computer vson. To segment the pxels n mage space, the most straghtforward dea s frst to obtan a coherent or robust clusterng result on the pxels' feature space, then each pxel s labeled wth the cluster that contans ts feature vector. It s well known that the standard FCM algorthm s one of the most popular clusterng-based methods for mage segmentaton. However, the cluster number must be known n advance when usng the FCM algorthm. The cluster number estmaton module of the prevous algorthms such as AFHA, IAFHA and HTFCM only consder color feature at pxel level whch means that they could not determne accurate cluster number for complex mages, especally for natural mages. In ths paper, we present a novel cluster number adaptve fuzzy c-means algorthm. The hghlght s the utlzaton of mage blocks nstead of pxels n the cluster number estmaton module. We extracted GLCM texture feature at the mage block level and employed the standard FCM algorthm for estmatng the cluster number. The method provdes an attractve way to estmate cluster number wth mnmal tme cost n comparson wth those algorthms such as AMFCM, AFHA, IAFHA and HTFCM. On the bass of Xe-Ben and Bezdek crterons, we proposed a combned valdty crteron to fnd the cluster number. Experments show that proposed algorthm based on GLCM feature extracton and composte cluster valdty crteron could be enough to effectvely estmate the cluster number of the mages n most cases. In fact, the texture feature reflectng the spatal patterns of pxels at mage block level Copyrght c 203 SERSC 20

12 has strong lnks wth the human percepton. Therefore our new approach s robust to accurately descrbe the mage content n many practcal scenaros. Nevertheless, future work should take other cluster valdty crterons nto account for specfc applcaton requrements. Besdes, we are consderng on how to standardze GLCM features used n ths paper, and ths could make t robust to estmate the cluster number. We try to make the proposed algorthm more sutable for segmentaton of natural mages wthout a pror knowledge about the content n the computer vson applcatons. Acknowledgements Ths work was supported by the Chnese Natonal 863 Program under Grant 203AA03804, the Natonal Natural Scence Foundaton of Chna under Grant and , and the Scence and Technology Department of Jangx Provnce of Chna under grant 204BAB2024. References [] G. P. Tellaeche, X. P. Burgos-Artzzu and A. Rbero, A computer vson approach for weeds dentfcaton through support vector machnes, Appled Soft Computng, vol., no., (20), pp [2] D. Wenland, R. Ronfard and E. Boyer, A survey of vson-based methods for acton representaton, segmentaton and recognton, Computer Vson and Image Understandng, vol. 5, no. 2, (20), pp [3] J. Blasco, N. Alexos and E. Molto, Computer vson detecton of peel defects n ctrus by means of a regon orented segmentaton algorthm, Journal of Food Engneerng, vol. 8, no. 3, (2007), pp [4] Y. L and Y. Shen, An automatc fuzzy c-means algorthm for mage segmentaton, Soft Computng, vol. 4, no. 2, (2009), pp [5] Z. Yu, O. C. Au, R. Zou, W. Yu and J. Tan, An adaptve unsupervsed approach toward pxel clusterng and color mage segmentaton, Pattern Recognton, vol. 43, no. 5, (200),pp [6] K. S. Tan and N. A. M. Isa, Color mage segmentaton usng hstogram thresholdng fuzzy c-means hybrd approach, Pattern Recognton, vol. 44, no., (20), pp. -5. [7] D. E. Ilea and P. F. Whelan, An adaptve unsupervsed segmentaton algorthm based on color-texture coherence, IEEE Trans. Image Process., vol. 7, no. 0, (2005), pp [8] M. Ahmed, S. Yamany, N. Mohamed, A. Farag and T. Morarty, A moded fuzzy c-means algorthm for bas feld estmaton and segmentaton of MRI data, IEEE Trans. Med. Imag., vol. 2, no. 3, (2002), pp [9] S. Chen and D. Zhang, Robust mage segmentaton usng FCM wth spatal constrants based on new kernel-nduced dstance measure, IEEE Trans. Syst., Man, Cybern., vol. 34, no. 4, (2004), pp [0] D. A. Claus and H. Deng, Desgn-based texture feature fuson usng Gabor flters and co-occurrence probabltes, IEEE Trans. Image Process, vol. 4, no. 7, (2005), pp [] J. C. Dunn, A fuzzy relatve of the sodata process and ts use n detectng compact, well separated cluster, Cybernetcs, vol. 3, no. 3, (973), pp [2] Bezdek, Pattern Recognton wth Fuzzy Objectve Functon Algorthms, Plenum Press, New York, (98). [3] S. S. Redd, S. F. Rudn and H. R. Keshavan, An optmal multple threshold scheme for mage segmentaton, IEEE-SMC, vol. 4, no. 4, (984), pp [4] R. M. Haralck, K. Shanmugam and I. Dnsten, Textural features for mage classfcaton, IEEE Trans. Syst., Man, Cybern., vol. SMC-3, no. 6, (973), pp [5] L. K. Soh and C. Tsatsouls, Texture analyss of SAR sea ce magery usng gray level co-occurrence matrces, IEEE Trans. Geosc. Remote Sens., vol. 37, no. 2, (999), pp [6] Claus and B. Yue, Comparng co-occurrence probabltes and markov random Felds for texture analyss, IEEE Trans. Geosc. Remote Sens., vol. 42, no., (2004), pp [7] J. C. Bezdek, Cluster valdty wth fuzzy sets, Cybernet. Syst., vol. 3, no. 3, (974), pp [8] N. R. Pal and J. C. Bezdek, On cluster valdty for the fuzzy c-means model, IEEE Trans. Fuzzy Syst., vol. 3, no. 3, (995), pp [9] X. L. Xe and G. A. Ben, Valdty measure for fuzzy clusterng, IEEE Trans. Pattern Anal. Mach. Intell., vol. 3, no. 4, (99), pp [20] J. F. Khan, R. R. Adham and S. M. A. Bhuyan, A customzed Gabor flter for unsupervsed color mage segmentaton, IEEE Trans. Geosc. Remote Sens., vol. 27, no. 4, (2009), pp Copyrght c 203 SERSC

13 [2] J. Daugman, Uncertanty relatons for resoluton n space, spatal frequency, and orentaton optmzed by two-dmensonal vsual cortcal flters, Journal of the Optcal Socety of Amerca, vol. 2, no. 7, (985), pp [22] Meda Lab., Mass. Inst. Technol., Cambrdge, MA. Vson Texture (Vstex)Database.Avalable: [23] D. Martn, C. Fowlkes, D. Tal and J. Malk, A database of human segmented natural mages and ts applcaton to evaluatng segmentaton algorthms and measurng ecologcal statstcs, Proceedngs of the Eghth Internatonal Conference On Computer Vson, Vancouver, Canada, (200) July 7-4, pp Authors Shaopng Xu receved the M.S. degree n Computer Applcaton from the Chna Unversty of Geoscences, Wuhan, Chna, n 2004 and the Ph.D. degree n Mechatroncs Engneerng from the Nanchang Unversty, Nanchang, Chna n 200. He s currently an Assocate Professor n the Department of Computer Scence and Technology, School of Informaton Engneerng, at the Nanchang Unversty. As the applcant and key nvestgator of projects, hs applcatons were approved by the Natonal Natural Scence Foundaton of Chna under Grant and n the year 20, respectvely. As the key nvestgator of project, hs applcaton was also approved by Chnese Natonal 863 Program under Grant 203AA03804 n the year 202. Dr. Xu has publshed more than 30 research artcles and serves as a revewer for several journals ncludng IEEE Transactons on Instrumentaton and Measurement, Sgnal, Image and Vdeo Processng, and Internatonal Journal of Robotcs and Automaton. Hs current research nterests nclude dgtal mage processng and analyss, computer graphcs, vrtual realty, surgery smulaton, n many practcal scenaros etc. Xaopng Lu receved hs Ph.D. degree from the Unversty of Alberta n He has been wth the Department of Systems and Computer Engneerng, Carleton Unversty, Canada snce July 2002 and he s currently a Canada Research Char. He s also wth the School of Informaton Engneerng, Nanchang Unversty as an Adjunct Professor. Dr. Lu has publshed more than 50 research artcles and serves as an Assocate Edtor for several journals ncludng IEEE/ASME Transactons on Mechatroncs and IEEE Transactons on Automaton Scence and Engneerng. He receved a 2007 Carleton Research Achevement Award, a 2006 Provnce of Ontaro Early Researcher Award, a 2006 Carty Research Fellowshp, the Best Conference Paper Award of the 2006 IEEE Internatonal Conference on Mechatroncs and Automaton, and a 2003 Provnce of Ontaro Dstngushed Researcher Award. Dr. Lu s a lcensed member of the Professonal Engneers of Ontaro (P.Eng) and a senor member of IEEE. Copyrght c 203 SERSC 203

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