A Parameter Based Modified Fuzzy Possibilistic C-Means Clustering Algorithm for Lung Image Segmentation

Transcription

1 Global Journal of Computer Scence and Technology Vol. 10 Issue 4 Ver. 1.0 June 010 P a g e 85 A Parameter Based Modfed Fuzzy Possblstc C-Means Clusterng Algorthm for Lung Image Segmentaton M.Gomath 1 Dr. P.Thangaraj GJCST Classfcaton ) I.5.1, I..3, I.4.M Abstract- Image processng s a technque necessary for modfyng an mage. The mportant part of mage processng s Image segmentaton. The dentcal medcal mages can be segmented manually. However the accurateness of mage segmentaton usng the segmentaton algorthms s more when compared wth the manual segmentaton. Medcal mage segmentaton s an ndspensable pace for the majorty of subsequent mage analyss tasks. In ths paper, FCM and dfferent extenson of FCM Algorthm s dscussed. The unque FCM algorthm yelds better results for segmentng nose free mages, but t fals to segment mages degraded by nose, outlers and other magng artfact. Ths paper presents an mage segmentaton approach usng Modfed Fuzzy Possblstc C-Means algorthm (MFPCM). Ths approach s a generalzed adaptaton of standard Fuzzy C-Means Clusterng (FCM) algorthm and Fuzzy Possblstc C-Means algorthm. The drawback of the conventonal FCM technque s elmnated n modfyng the standard technque. The Modfed FCM algorthm s formulated by modfyng the dstance measurement of the standard FCM algorthm to permt the labelng of a pxel to be nfluenced by other pxels and to restran the nose effect durng segmentaton. Instead of havng one term n the objectve functon, a second term s ncluded, forcng the membershp to be as hgh as possble wthout a maxmum fronter restrant of one. Experments are carred out on real mages to examne the performance of the proposed modfed Fuzzy Possblstc FCM technque n segmentng the medcal mages. Standard FCM, Modfed FCM, Possblstc C-Means algorthm (PCM), Fuzzy Possblstc C-Means algorthm (FPCM) and Modfed FPCM are compared to explore the accuracy of our proposed approach. Keywords-Fuzzy C-Means Clusterng Algorthm,Modfed FCM, Modfed Fuzzy Possblstc C-Means Clusterng Algorthm, Lung Nodule Detecton, Medcal Image Processng and Image Segmentaton. I I. INTRODUCTION mage segmentaton s a necessary task for mage understandng and analyss. A large varety of methods have been proposed n the lterature. Image segmentaton can be defned as a classfcaton problem where each pxel s assgned to a precse class. Image segmentaton s a sgnfcant process for successve mage analyss tasks. In general, a segmentaton problem nvolves the dvson a About 1 -Department of MCA Velalar College Of Engneerng and Technology, Thndal (PO)Erode, Inda (e- mal;mdgomath@gmal.com) About - Dean, School of Computer Technology and Applcatons Kongu Engneerng College, Perundura Erode, Inda (e- mal;ctptr@yahoo.co.n) gven mage nto a number of homogeneous segments, such that the unon of any two neghborng segments yelds a heterogeneous segment. Numerous segmentaton technques have been proposed earler n lterature. Some of them are hstogram based technque, edge based technques, regon based technques, hybrd methods whch combne both the edge based and regon based methods together, and so on [1]. In recent years mage segmentaton has been extensvely appled n medcal feld for dagnosng the dseases. Image segmentaton plays an mportant role n a varety of applcatons such as robot vson, object recognton, and medcal magng []. In the feld of medcal dagnoss an extensve dversty of magng technques s presently avalable, such as radography, computed tomography (CT) and magnetc resonance magng (MRI) [3, 4]. In recent tmes, Computed Tomography (CT) s the most effectvely used for dagnostc magng examnaton for chest dseases such as lung cancer, tuberculoss, pneumona and pulmonary emphysema. The volume and the sze of the medcal mages are progressvely ncreasng day by day. Therefore t becomes necessary to use computers n facltatng the processng and analyzng of those medcal mages. Even though the orgnal FCM algorthm yelds good results for segmentng nose free mages, t fals to segment mages corrupted by nose, outlers and other magng artfact. Medcal mage segmentaton s an ndspensable step for most successve mage analyss tasks. Ths paper presents an mage segmentaton approach usng Modfed Fuzzy C- Means (FCM) and Fuzzy Possblstc C-Means (FPCM) algorthm. Recently, many researchers have brought forward new methods to mprove the FCM algorthm [5, 6]. Ths approach s a generalzed verson of standard Fuzzy C- Means Clusterng (FCM) algorthm. The lmtaton of the conventonal FCM technque s elmnated n modfyng the standard technque. The algorthm s formulated by modfyng the dstance measurement of the standard FCM algorthm to permt the labelng of a pxel to be nfluenced by other pxels and to restran the nose effect durng segmentaton. Possblstc C-Means (PCM) algorthm, nterprets clusterng as a Possblstc partton. Instead of havng one term n the objectve functon, a second term s ncluded, forcng the membershp to be as hgh as possble wthout a maxmum lmt constrant of one. Experments are conducted on real mages to nvestgate the performance of the proposed modfed FPCM technque n segmentng the medcal mages. Standard FCM, Modfed FCM, Fuzzy

2 P a g e 86 Vol. 10 Issue 4 Ver. 1.0 June 010 Possblstc C-Means and MFPCM algorthm are compared to explore the accuracy of our proposed approach. The remander of the paper s organzed as follows. Secton provdes an overvew on related research works n medcal mage segmentaton. Secton 3 explans ntally explans the standard FCM algorthm and latter t explans the proposed MFCM, FPCM and MFPCM algorthm. Secton 4 dscusses on expermental results for real mages. Secton 5 concludes the paper wth fewer dscussons. Related work A lot of research work has been carred on varous technques for mage segmentaton. In recent years, many researchers have brought forward new methods to mprove the FCM algorthm [5, 6]. Ths secton of the paper provdes an overvew on the related research work conducted on medcal mage processng. Kenj Suzu et al. n [7] presented an mage processng technque usng Massve Tranng Artfcal Neural Networks (MTANN). Ther approach resolve the problem faced by radologsts as well as computer-aded dagnostc (CAD) schemes to detect these nodules n case when the lung nodules overlaps wth the rbs or clavcles n chest radographs. An MTANN s extremely a non-lnear flter that can be traned by use of nput chest radographs and the equvalent teachng mages. They used a lnear-output back-propagaton (BP) algorthm that was derved for the lnear-output multlayer ANN model n order to tran the MTANN. The dual-energy subtracton s a technque used n [7] for separatng bones from soft tssues n chest radographs by usng the energy dependence of the x-ray attenuaton by dfferent materals. A robust statstcal estmaton and verfcaton framework was proposed by Kazunor Okada et al. n [8] for characterzng the ellpsodal geometrcal structure of pulmonary nodules n the Mult-slce X-ray computed tomography (CT) mages. They proposed a mult-scale jont segmentaton and model fttng soluton whch extends the robust mean shft-based analyss to the lnear scale-space theory. A quas-real-tme three-dmensonal nodule characterzaton system s developed usng ths framework and valdated wth two clncal data sets of thn-secton chest CT mages. Ther proposed framework s a combnaton of three dfferent but successve stages. They are model estmaton, model verfcaton and volumetrc measurements. The man ssue of the approach s a bas due to the ellpsodal approxmaton. Segmentaton-by-regstraton scheme was put forth by Ingrd Slumer et al. n [9]. In the scheme a scan wth normal lungs s elastcally regstered to a scan contanng pathology. Segmentaton-by-regstraton scheme make use of an elastc regstraton of nclusve scans usng mutual nformaton as a smlarty measure. They are compared the performance of four segmentaton algorthms namely Refned Segmentaton-by-Regstraton, Segmentaton by Rule-Based Regon growng, Segmentaton by Interactve Regon growng, and Segmentaton by Voxel Classfcaton. The comparson results revealed that refned regstraton scheme enjoys the addtonal beneft snce t s ndependent of a pathologcal (hand-segmented) tranng data. Global Journal of Computer Scence and Technology A genetc algorthm for segmentaton of medcal mages was proposed by Ghosh et al. n [10]. In ther paper, they presented a genetc algorthm for automatng the segmentaton of the prostate on two-dmensonal slces of pelvc computed tomography (CT) mages. In ther approach the segmentng curve s represented usng a level set functon, whch s evolved usng a genetc algorthm (GA). Shape and textural prors derved from manually segmented mages are used to constran the evoluton of the segmentng curve over successve generatons. They revewed some of the exstng medcal mage segmentaton technques. They also compared the results of ther algorthm wth those of a smple texture extracton algorthm (Laws texture measures) as well as wth another GA-based segmentaton tool called GENIE. Ther prelmnary tests on a small populaton of segmentng contours show promse by convergng on the prostate regon. They expected that further mprovements can be acheved by ncorporatng spatal relatonshps between anatomcal landmarks, and extendng the methodology to three dmensons. A novel approach for lung nodule detecton was descrbed by M. Antonell et al. n [11]. They descrbed a computeraded dagnoss (CAD) system for automated detecton of pulmonary nodules n computed-tomography (CT) mages. Combnatons of mage processng technques are used for extracton of pulmonary parenchyma. A regon growng method based on 3D geometrc features s appled to detect nodules after the extracton of pulmonary parenchyma. Expermental results show, that mplementaton of ths nodule detecton method, detects all malgnant nodules effectvely and a very low false-postve detecton rate was acheved. Xujong Ye et al. n [1] presented a new computer tomography (CT) lung nodule computer-aded detecton (CAD) method. The method can be mplemented for detectng both sold nodules and ground-glass opacty (GGO) nodules. Foremost step of the method s to segment the lung regon from the CT data usng a fuzzy thresholdng technque. The next step s the calculaton of the volumetrc shape ndex map and the dot map. The former mentoned map s based on local Gaussan and mean curvatures, and the later one s based on the Egen values of a Hessan matrx. They are calculated for each Voxel wthn the lungs to enhance objects of a specfc shape wth hgh sphercal elements. The combnaton of the shape ndex and dot features provdes a good structure descrptor for the ntal nodule canddate generaton. Certan advantages lke hgh detecton rate, fast computaton, and applcablty to dfferent magng condtons and nodule types make the method more relable for clncal applcatons. A robust medcal mage segmentaton algorthm was put forth by Wang et al. n [13]. Automated segmentaton of mages has been consdered an mportant ntermedate processng task to extract semantc meanng from pxels. In general, the fuzzy c-means approach (FCM) s hghly effectve for mage segmentaton. But for the conventonal FCM mage segmentaton algorthm, cluster assgnment s based exclusvely on the dstrbuton of pxel attrbutes n

3 Global Journal of Computer Scence and Technology Vol. 10 Issue 4 Ver. 1.0 June 010 P a g e 87 the feature space, and the spatal dstrbuton of pxels n an mage s not taken nto consderaton. In ther paper, they presented a novel FCM mage segmentaton scheme by utlzng local contextual nformaton and the hgh nterpxel correlaton nherent. Frstly, a local spatal smlarty measure model s establshed, and the ntal clusterng center and ntal membershp are determned adaptvely based on local spatal smlarty measure model. Secondly, the fuzzy membershp functon s modfed accordng to the hgh nter-pxel correlaton nherent. Fnally, the mage s segmented by usng the modfed FCM algorthm. Expermental results showed the proposed method acheves compettve segmentaton results compared to other FCMbased methods, and s n general faster. II. PROPOSED APPROACH A. Conventonal Fuzzy C-Means Algorthm Fuzzy C-Means (FCM) Clusterng algorthm s one of the accepted approaches for assgnng mult-subset membershp values to pxels for ether segmentaton or other type of mage processng [14]. Generally, FCM algorthm proceeds by teratng the two ndspensable condtons untl a soluton s reached. Each data pont wll be joned wth a membershp value for each class after FCM clusterng. The objectve of FCM s to determne the cluster centers and to produce the class membershp matrx. In other words, t assgns a class membershp to a data pont, dependng on the smlarty of the data pont to a scrupulous class relatve to all other classes. The class membershp matrx s a cxn matrx; n whch c s the number of groups and N s the number of samples. Let X={x1, xn} be the tranng set and c be an nteger. A fuzzy c-partton of X can be represented by a matrx, U = {k}rcxn. U can be used to descrbe the cluster structure of X, by evaluatng k, as a degree of membershp of xk to cluster. The codebook vectors are evaluated by mnmzng the dstorton measure gven by the followng equaton, Mnmze: J m (U, v) = N k1 c 1 ( ) m X k v where X={x 1, x, x N }R N n a dataset, c s the number of clusters n X: c < N, m s a weghtng exponent: 1 m <, U = { k } s the fuzzy c-partton of X, X k v A s an nduced a-norm of R N, and A s a postve-defnte (NXN) weght matrx. A conventonal FCM algorthm ncludes the followng steps, 1. Intally values are set for the parameters lke c, A, m, ε, and the loop counter t s set to 1,. As a next step t s necessary to create a random cxn membershp matrx U, 3. The cluster centers are then evaluated usng the followng equaton, A v N k 1 ( ) m X k N k 1 ( 4. The membershp matrx s updated perodcally wth the help of the followng equaton, ( t1) c j1 d d kj m1 Where d s gven by X v A ( t1) 5. If max go to step 3. k ) m 1 > ε, ncrement t and B. Modfed Fuzzy C-Means Clusterng Technque for mage segmentaton The most mportant shortcomng of standard FCM algorthm s that the objectve functon does not thnk about the spatal dependence therefore t deal wth mage as the same as separate ponts. In order to decrease the nose effect durng mage segmentaton, the proposed method ncorporates both the local spatal context and the non-local nformaton nto the standard FCM cluster algorthm usng a novel dssmlarty ndex n place of the usual dstance metrc. Therefore a modfed FCM algorthm s used to segment the mage n our proposed paper. The non-local means algorthm [15] [16] tres to take advantage of the hgh degree of redundancy n an mage. The membershp value decdes the segmentaton results and hence the membershp value s evaluated by the dstance measurement denoted as d. Therefore the approach modfes the dstance measurement parameter whch s readly nfluenced by local and non-local nformaton. d (x j, v )=(1-λ j ) d l ( x j, v )+λ j d nl ( x j, v ) where d l stands for the dstance measurement nfluenced by local nformaton, and d nl stands for the dstance measurement nfluenced by non-local nformaton, λ j wth the range from zero to one, s the weghtng factor controllng the tradeoff between them. The dstance measurement nfluenced by the local measurement d l s gven by, Where d (x j, v ) s the Eucldean dstance measurement, ωl (x k, x j ) s the weght of each pxel n N.

4 P a g e 88 Vol. 10 Issue 4 Ver. 1.0 June 010 The dstance measurement nfluenced by non-local nformaton d nl s computed as a weghted average of all the pxels n the gven mage I, Modfed FCM algorthm goes through the followng steps, 1. Set the number of clusters c and the ndex of fuzzness m. Also ntalze the fuzzy cluster Centrod vector v randomly and set ε>0 to a small value,. Set the neghborhood sze and the wndow sze ncludes the evaluaton of cluster centers and membershp matrx, 3. Evaluate the modfed dstance measurement usng the equaton mentoned as d (x j, v ), 4. Update the membershp matrx and the dstance measurement. C. Possblstc C-Means Algorthm (PCM) In order to overcome the lmtatons of conventonal FCM technque, Possblstc C-Means (PCM) has been proposed n ths paper for medcal mage segmentaton. The Possblstc C-Means algorthm uses a Possblstc type of membershp functon to llustrate the degree of belongng. It s advantageous that the membershps for representatve feature ponts be as hgh as possble and unrepresentatve ponts have low membershp. The ntenton functon, whch satsfes the requrements, s formulated as follows, Global Journal of Computer Scence and Technology usng the nverse of the varance-covarance matrx of data set whch could be defned as follows,, j p ( )( j j ) D = Aj x y x y, j1 Aj j j where, x and y are the mean values of two dfferent sets of parameters, X and Y. are the respectve varances, and ρ j s the coeffcent of correlaton between th and j th varants. D. Fuzzy Possblstc C-Means Algorthm (FPCM) FPCM algorthm was proposed by N.R.Pal, K.Pal, and J.C.Bezdek[18] and t ncludes both possblty and membershp values. FPCM model can be seen as below: subject to the constrants where, dj represents the dstance between the jth data and the th cluster center, j denotes the degree of belongng, m represents the degree of fuzzness, s the sutable postve number, c s the number of clusters, and N denotes the number of pxels. j can be obtaned usng the followng equaton, The value of determnes the dstance at whch the membershp values of a pont n a cluster becomes 0.5. The man advantage of ths PCM technque s that the value of can be fxed or can be changed n each teraton. Ths can be accomplshed by changng the values of d j and j. The PCM s more robust n the presence of nose, n fndng vald clusters, and n gvng a robust estmate of the centers. Updatng the membershp values depends on the dstance measurements [17].The Eucldean and Mahalanobs dstance are two common ones. The Eucldean dstance works well when a data set s compact or solated [18] and Mahalanobs dstance takes nto account the correlaton n the data by where U s membershp matrx, T s possblstc matrx, and V s the resultant cluster centers, c and n are cluster number and data pont number respectvely. The frst order necessary condtons for extreme of J m,η are: If for all and k,m,η > 1 and X contans at least c dstnct data ponts, then may mnmze J m,η only f

5 Global Journal of Computer Scence and Technology Vol. 10 Issue 4 Ver. 1.0 June 010 P a g e 89 parameter smlar to weght to each vector. The weght s evaluated as follows: The above equatons show that membershp u k s affected by all c cluster centers, whle possblty t k s affected only by the -th cluster center c. The possblstc term dstrbutes the t k wth respect to all n data ponts, but not wth respect to all c clusters. So, membershp can be called relatve typcalty, t measures the degree to whch a pont belongs to one cluster relatve to other clusters and s used to crsply label a data pont. And possblty can be vewed as absolute typcalty, t measures the degree to whch a pont belongs to one cluster relatve to all other data ponts, t can reduce the effect of outlers. Combnng both membershp and possblty can lead to better clusterng result. E. Parameter based Modfed Fuzzy Possblstc Clusterng Algorthm (MFPCM) The clusterng optmzaton s entrely dependent on objectve functon snce the choce of a sutable objectve functon s the key to the success of the cluster analyss and to obtan better cluster results [0]. The followng set of requrements s taken nto account n order to get hold of a sutable objectve functon. The dstance between the clusters must be maxmzed and n the same manner the dstance between the clusters and the data ponts assgned to them should be mnmzed. The attracton between the data and the clusters s governed by the followng objectve functon formula. Where U s membershp matrx, T s Possblstc matrx, and V s the resultant cluster centers, c and n are cluster number and data pont number respectvely. The learnng procedure of α s based on an exponental partton strength stuck between clusters and s updated at each teraton. The formula of ths parameter s: s chosen as a sample varable and t s a normalzed term. Therefore can be defned as follows: Ths secton proposes a new parameter that suppresses the common value of α and thereby replacng t by a new where w j s weght of the pont j n relaton to the class. ths weght s used to adapt the fuzzy and typcal partton. The objectve functon s posed of two expressons: the frst s the fuzzy functon and uses a fuzzness weghtng exponent, the second s Possblstc functon and uses a typcal weghtng exponent. The objectve functon of the MFPCM can be formulated as follows U = {μ j } represents a fuzzy partton matrx, s defned as: T = {t j } whch resembles a dstnctve partton matrx, s defned as: V = {v} represents c centers of the clusters, s defned as: III. EXPERIMENTAL RESULTS The proposed Modfed FCM algorthm, Fuzzy Possblstc C-Means and MFPCM algorthm s mplemented usng MATLAB and tested on real mages to explore the segmentaton accuracy of the proposed approach. The varous types of FCM technques that has been used are standard FCM, Modfed FCM, PCM, FPCM and MFPCM Clusterng algorthm and are compared. A. Real Image Dataset A real set of lung mages are used to evaluate the accuracy of the proposed algorthm n segmentng the medcal mages. The results obtaned are then compared wth the segmentaton results that were performed manually to

6 P a g e 90 Vol. 10 Issue 4 Ver. 1.0 June 010 Global Journal of Computer Scence and Technology explore the accuracy of the proposed algorthm. The segmentaton results of standard FCM, Modfed FCM, Possblstc C-Means Clusterng (PCM), Fuzzy Possblstc C-Means Clusterng (FPCM) and Modfed Fuzzy Possblstc C-Means Clusterng (MFPCM) are consdered to nvestgate the best algorthm that delvered better segmentaton results for real medcal mages. The three most mportant parameters used to determne the accuracy of the proposed algorthm are smlarty, false postve and the false negatve rato. From the results obtaned t can be concluded that our proposed algorthm performed well ahead of other technques n segmentng the real medcal mages. The three man attrbutes mentoned above.e. smlarty, false postve rato, and the false negatve ratos are lsted n Table 1, for all the mage segmentaton technques. Fgure 1 shows the segmentaton result of the dfferent technques Standard FCM Modfed FCM Smlarty Possblstc C-Means PCM Fgure Comparson of Smlarty False Postve Rato FPCM Modfed FPCM False Negatve Rato Smlarty (a) (b) 0 Standard FCM Modfed FCM PCM FPCM MFPCM (c) (d) Fgure 1 (a) Actual Image, Segmented Images (b) usng Standard FCM (c) usng FPCM (d) usng MFPCM Algorthm Smlarty False Postve Rato False Negatve Rato StandardFCM ModfedFCM PossblstcC- MeansClusterng Algorthm(PCM) FuzzyPossblstc CMeansClusterng (FPCM) Modfed Fuzzy Possblstc C- Means Clusterng (MFPCM) Table 1 Dfferent Indces for Dfferent Algorthms Fgure 3 Comparson of False Postve and False Negatve Rato for the three approaches The expermental results obtaned by employng the Modfed Fuzzy Possblstc C-Means (MFPCM) algorthm revealed that the proposed technque of mage segmentaton has a better performance over other FCM extenson methods. Furthermore, the proposed approach of mage segmentaton usng Modfed Fuzzy Possblstc C-Means algorthm elmnates the effect of nose greatly. Ths n turn ncreased the segmentaton accuracy of the proposed mage segmentaton technque. IV. CONCLUSION FCM s one of a conventonal clusterng method and has been generally appled for medcal mage segmentaton. On the other hand, conventonal FCM at all tmes suffers from nose n the mages. Even though the unque FCM algorthm yelds good results for segmentng nose free mages, t fals to segment mages corrupted by nose, outlers and other magng artfact. Though a lot of researchers have developed a dversty of extended algorthms based on FCM, not any of them are deal. A modfed FCM clusterng algorthm and Modfed Fuzzy Possblstc C-Means (MFPCM) algorthm s proposed n ths paper. In the proposed Modfed FCM algorthm, both local and non-local nformaton are ntegrated to control the tradeoff between them. The algorthm s put together by modfyng the dstance measurement of the standard FCM algorthm to authorze the labelng of a pxel to be nfluenced by other pxels and to hold back the nose effect durng segmentaton. The

7 Global Journal of Computer Scence and Technology Vol. 10 Issue 4 Ver. 1.0 June 010 P a g e 91 Modfed Fuzzy Possblstc C-Means (MFPCM) algorthm nterprets clusterng as a Possblstc partton and ncludes membershp functons. Experments are conducted on real medcal mages to estmate the performance of the proposed algorthm. The three most mportant parameters used to determne the accuracy of the proposed algorthm are smlarty, false postve and the false negatve rato. The expermental results suggested that the proposed algorthm performed well than other FCM extenson, segmentaton algorthms V. REFERENCES 1) K. Hars, Hybrd Image Segmentaton usng Watersheds and Fast Regon Mergng, IEEE Transactons on Image Processng, vol. 7, no. 1, pp , ) W. M. Wells, W. E. LGrmson, R. Kns and S. R. Arrdrge, Adaptve segmentaton of MRI data, IEEE Transactons on Medcal Imagng, vol. 15, pp , ) L. Pham, C. Y. Xu, and J. L. Prnce, A survey of current methods n medcal mage segmentaton, Annual Revew on Bomedcal Engneerng, vol., pp , 000 [Techncal report verson, JHU/ECE 99-01, Johns Hopns Unversty]. 4) Lew AW-C, and H. Yan, Current methods n the automatc tssue segmentaton of 3D magnetc resonance bran mages, Current Medcal Imagng Revews, vol., no. 1, pp , ) R. J. Hathaway, and J. C. Bezdek, Generalzed fuzzy c-means clusterng strateges usng Lp norm dstance, IEEE Transactons on Fuzzy Systems, vol. 8, pp , ) S. C. Chen, D. Q. Zhang, Robust mage segmentaton usng FCM wth spatal constrants based on new kernel-nduced dstance measure, IEEE Transactons Systems Man Cybernet, vol. 34, no. 4, pp , ) Kenj Suzu, Hroyu Abe, Heber MacMahon, and Kuno Do, Image-Processng Technque for Suppressng Rbs n Chest Radographs by Means of Massve Tranng Artfcal Neural Network (MTANN), IEEE Transactons on medcal magng, vol. 5, no. 4, pp , ) Kazunor Okada, Dorn Comancu, and Arun Krshnan, Robust Ansotropc Gaussan Fttng for Volumetrc Characterzaton of Pulmonary Nodules n Mult-slce CT, IEEE Transactons on Medcal Imagng, vol. 4, no. 3, pp , ) Ingrd Slumer, Mathas Prokop, and Bram van Gnneken, Toward Automated Segmentaton of the Pathologcal Lung n CT, IEEE Transactons on Medcal Imagng, vol. 4, no.8, pp , ) Payel Ghosh, and Melane Mtchell, Segmentaton of medcal mages usng a genetc algorthm, Proceedngs of the 8th annual conference on Genetc and evolutonary computaton, pp , ) M. Antonell, G. Frosn, B. Lazzern, and F. Marcellon, Lung Nodule Detecton n CT Scans, World Academy of Scence, Engneerng and Technology, ) Xujong Ye, Xnyu Ln, Jamshd Dehmesh, Greg Slabaugh, and Gareth Beddoe, Shape-Based Computer-Aded Detecton of Lung Nodules n Thoracc CT Images, IEEE Transactons on Bomedcal Engneerng, vol. 56, no. 7, pp , ) Xang-Yang Wang, and Juan Bu, A fast and robust mage segmentaton usng FCM wth spatal nformaton, Elsever, ) J. C. Bezdek, Pattern Recognton wth Fuzzy Objectve Functon algorthms, Plenum Press, New York, ) A Buades, B. Coll, and J. -M. Morel, A non-local algorthm for mage denosng, In CVPR, vol., pp , ) A Buades, B. Coll, and J. -M. Morel, On mage denosng methods, Techncal Report , CMLA, ) K. P. Detroja et al., A Possblstc Clusterng Approach to Novel Fault Detecton and Isolaton, Journal of Process Control, vol. 16, no. 10, pp , ) N.R.Pal, and J.C.Bezdek. A mxed c-means clusterng model. In IEEE Int.Conf.Fuzzy Systems, pages 11-1, Span, ) A K Jan, Data clusterng: A revew. ACM Computng Surveys, vol. 31, no. 3, pp , ) Y. Zhonghang, T. Yangang, S. Funchun and S. Zengq, Fuzzy Clusterng wth Novel Serable Crteron, Vol. 11, no. 1, pp 50-53, February ) M.Gomath, P.Thangaraj A New Approach to Lung Image Segmentaton usng Fuzzy Possblstc C-Means Algorthm, Internatonal Journal of Computer Scence and Informaton Securty, March 010.