Generalized Spatial Kernel based Fuzzy C-Means Clustering Algorithm for Image Segmentation

Transcription

1 Internatonal Journal of Scence and Research (IJSR, Inda Onlne ISSN: Generalzed Spatal Kernel based Fuzzy -Means lusterng Algorth for Iage Segentaton Pallav Thakur, helpa Lnga Departent of Inforaton Technology, PIIT, New Panvel, Inda School Departent of Inforaton Technology, PIIT, HO, Rasayanee, Inda Abstract: Iage segentaton plays an portant role n age analyss. It s one of the frst and ost portant tasks n age analyss and coputer vson. Ths proposed syste presents a varaton of fuzzy c- eans algorth that provdes age clusterng. Based on the Mercer kernel, the kernel fuzzy c-eans clusterng algorth (KFM s derved fro the fuzzy c-eans clusterng algorth (FM.The KFM algorth that provdes age clusterng and proves accuracy sgnfcantly copared wth classcal fuzzy -Means algorths. Ths proposed syste akes the use of the advantages of KFM and also ncorporates the local spatal nforaton and gray level nforaton n a novel fuzzy way. The new algorth s called Generalzed Spatal Kernel based Fuzzy - Means (GSKFM algorth. The aor characterstc of GSKFM s the use of a fuzzy local (both spatal and gray level slarty easure, ang to guarantee nose nsenstveness and age detal preservaton as well as t s paraeter ndependent. The purpose of desgnng ths syste s to produce better segentaton results for ages corrupted by nose, so that t can be useful n varous felds lke edcal age analyss, such as tuor detecton, study of anatocal structure, and treatent plannng. Keywords: Iage analyss, clusterng, FM, KFM, GSKFM.. Introducton Iage segentaton plays crucal role n any applcatons, such as age analyss and coprehenson, coputer vson, age codng, pattern recognton and edcal ages analyss. Many algorths and ethods have been proposed for obect segentaton and feature extracton []. In ths syste, a clusterng ethod for edcal and other age segentaton wll be consdered. lusterng s a process of parttonng or groupng a gven set of unlabelled obects nto a nuber of clusters such that slar obects are allocated to one cluster. There are two an approaches to clusterng []. One ethod s crsp clusterng (or hard clusterng, and the other one s fuzzy clusterng. A characterstc of the crsp clusterng ethod s that the boundary between clusters s fully defned. However, n any real cases, the boundares between clusters cannot be clearly defned. Soe patterns ay belong to ore than one cluster. In such cases, the fuzzy clusterng ethod provdes a better and ore useful ethod to classfy thesepatterns.the FM eploys fuzzy parttonng such that a data pxel can belong to all groups wth dfferent ebershp grades between0 and.fm s an teratve algorth. The a of FM s to fnd cluster centers (centrods that nze obectve functon. The KFM s derved fro the orgnal FM based on the 'kernel ethod' [3]. A coon phlosophy behnd these algorths s based on the followng kernel (substtuton trck. KFM algorth s extended whch ncorporates the neghbor ter nto ts obectve functon [4]. In the lterature, varous nubers of technques are descrbed for clusterng and age segentaton. Ever snce Zadeh presented the fuzzy set theory n hs senal paper n 965[5], fuzzy set theory also found applcatons [6] n clusterng. Fuzzy clusterng s a wdely appled ethod for acqurng fuzzy patterns fro data and becoe the an ethod of unsupervsed pattern recognton. It has been appled successfully n any felds, such as pattern analyss, extracton of fuzzy rules, age segentaton and so on.fuzzy clusterng ethod (FM was orgnally proposed by Dunn and later extended by Bezdek [7]. Recently, any researchers have odfed the orgnal FM algorth. Drawback for FM algorth s the senstvty to nose or outler. Drawbacks of FM were solved by ntroducng KFM. A nuber of powerful kernelbased ethods were proposed and have found successful applcatons n pattern recognton and functon approxaton.in Wu and Gao spaper[8],the Mercer kernel based ethod was nvestgated. They proposed the KFM algorth whch s extended fro FM algorth.it s shown to be ore robust than FM. N. A. Mohaed, M.N. Ahed et al.[9] descrbed the applcaton of fuzzy set theory n edcal agng. A odfed fuzzy c-eans classfcaton algorth s used to provde a fuzzy partton. Ruoyu Du and Hyo Jong Lee[0], [] have dscussed that the edcal age segentaton sees to be tedous and also a ore challengng task due to the ntrnsc nature of the ages. In ths paper, we propose a Generalzed Spatal Kernel based Fuzzy -Mean clusterng (GSKFM whch s extended fro KFM whch ncorporates the neghbor ter nto ts obectve functon. Ths algorth deals wth real and synthetc ages and resolves the ssues of nose and ntensty nhoogenety and also t s ndependent of paraeter selecton. However the ethods dscussed above are based on ntal paraeter selecton hence A nonparaetrc segentaton ethod s needed whch can deterne the paraeters lke no of clusters autoatcally to ake t ore effcent. Deng-Yaun Haung, Ta- We Ln, Wu-hh-Hu [] proposed an effectve ethod of hstogra-based valley estaton s presented for deternng the no of clusters for an age..thus, GSKFM has the followng attractve characterstcs: t s relatvely ndependent of the types of nose, and as a consequence, t s a better choce for clusterng n the absence of pror knowledge of the nose. The fuzzy local constrants ncorporate sultaneously both the kernel functon, spatal and the local gray level relatonshp n a fuzzy way. Ths syste can provde sgnfcant robustness to the nosy ages and partally prove the perforance of segentaton. Volue Issue 5, May 03 65

2 Internatonal Journal of Scence and Research (IJSR, Inda Onlne ISSN: Prelnary Theory. Kernel Method A coon phlosophy behnd the algorths usng kernel ethod s based on the followng kernel (substtuton trck, that s, frstly wth a (plct nonlnear ap, fro the data space to the apped feature space, Φ : X F (x Φ(x, a dataset { x,x n } X (an nput data space wth low denson s apped nto a potentally uch hgher densonal feature space or nner product F, whch as at turnng the orgnal nonlnear proble n the nput space nto potentally a lnear one n rather hgh densonal feature space so as to facltate proble solvng. Due to any successes n applyng kernel ethods such as support vector achnes (SVM, Mercer kernels have recently becoe ore popular to real world probles. Mercer Theore: Any contnuous, syetrc, postve se defnte kernel functon k(x, y can be expressed as a dot product n a hgh-densonal space. The saple S x, x,..., x ncludes exaples. The Kernel (Gra atrx K s an X Matrx ncludng nner products between all pars of exaples.e., K k(x, x. K s syetrc snce k(x, y k(y, x Φ (x. Φ (y [0]. A syetrc functon k (.,. s a kernel ff for any fnte saple S the kernel atrx for S s postve se-defnte. There the Mercer kernels are used to ake t practcal, n the followng, the age of a nput data X,,, N n the hgh densonal feature space s denoted by Φ (X,,, M, where Φ (.s nonlnear appng functon. Three coonly-used kernel functons n lterature are: K ( x, y ( + ( x, y Polynoal kernel: d Gaussan Radal bass functon (GRBF kernel: ( ( x y K x, y exp σ Sgod kernel : K ( x, y tanh( α ( x, y + β Where d, α, β are the adustable paraeters of the above kernel functons.. The Fuzzy Means lusterng Algorth (FM The fuzzy c-eans (FM algorth s one of the ost tradtonal and classcal age segentaton algorths. The FM algorth can be nzed by the followng obectve functon. onsder a set of unlabeled patterns X, let X{x,,x,...,x N }, x Rf, where N s the nuber of patterns and f s the denson of pattern vectors (features. The FM algorth focuses on nzng the value of an obectve functon. The obectve functon easures the qualty of the parttonng that dvdes a dataset nto c clusters. The algorth s an teratve clusterng ethod that produces an optal c partton by nzng the weghted wthn group su of squared error obectve functon J. N J ( U, W d ( J Where: N: No of pattern n X : No of clusters Volue Issue 5, May 03 U : Degree of ebershp X of n the th cluster W : Prototype of the center of the cluster d ( X : a dstance easure between obect X and cluster center W ; : the weghtng exponent on each fuzzy ebershp. The FM algorth focuses on nzng J, subect to the followng constrants on U: U [ 0,],,...N, and,,... (,,,...N (3 0 < N U <,,... (4 Functon ( descrbes a constraned optzaton proble, whch can be converted to an unconstraned optzaton proble by usng the Lagrange ultpler technque. U,,...,N,..., (5 / d d l f d 0 then U and U 0 for (6 N X W,,..., (7 N J can be obtaned through an teratve process, whch s carred as follows. Step : Set values for, and ε. Step : Intalze the fuzzy partton atrx U (0. Step 3: Set the loop counter b 0. Step 4: alculate the cluster centers W (b wth U (b by usng functon (7 Step 5: alculate the ebershp atrx U (b+ by usng functon (5 Step 6: If {U (b U (b+ } < ε then stop, otherwse set bb+.3 The fuzzy kernel -eans (KFM algorth The KFM algorth adds kernel nforaton to the tradtonal fuzzy c-eans algorth and t overcoes the dsadvantage that FM algorth can t handle the sall dfferences between clusters. The an dea of fuzzy kernel c-eans algorth (KFM s descrbed as follows. The kernel ethod aps nonlnearly the nput data space nto a hgh densonal feature space. Fro the Mercer theore, t s known that a Mercer kernel nduces an plct functon space Rq. The Eucldan x k Fgure : Square Wndow NB(X k on Pxel X k dstance between exaples X and X n the feature space of the kernel K can be defnton as follow k 66

3 Internatonal Journal of Scence and Research (IJSR, Inda Onlne ISSN: ( φ( φ( X φ( φ( X d dst X, X (8 dstances can be coputed drectly fro kernel functon d Φ ( X Φ( X Φ( X Φ( X + Φ( X Φ( X K ( X K( X K( X, X + K( X K( X K ( X X (9 Based on the orgnal FM algorth, the obect functon J k s gong to be lke ths: ( ( N J k K X, W (0 Accordng to equaton (, (3 and (4, by nzng (0 usng Lagrangan optzaton as before, the followng new teratve center W and ebershp U update equatons ( K ( X, W ( U ( ( K ( X, W K ( k n K ( X, W X W n ( K ( X, W J k can be obtaned through an teratve process, whch s carred as follows. Step Set values for,, and ε. Step Intalze the fuzzy partton atrx U (0. Step 3 Set the loop counter b0. Step 4 alculate the cluster centers W (b wth U (b by usng functon ( Step 5 alculate the ebershp atrx U (b+ by usng functon ( Step 6 If {U (b - U (b+ }< ε then stop, otherwse, set bb+ The KFM algorth aps nonlnearly the nput data space nto a hgh densonal feature space. It s confred that perforance of KFM algorth s better than FM algorth n age segentaton..4 Spatal Relatonshp One of the portant characterstcs of an age s that neghbourng pxels are hghly correlated. In other words, these neghbourng pxels possess slar feature values, and the probablty that they belong to the sae cluster s great. Ths spatal relatonshp s portant n clusterng, but t s not utlzed n a standard FM and KFM algorth. Wth the proposed ethod, the spatal constrant s adaptvely taken nto consderaton by ncorporatng t n the ebershp functon. Where NB (x k represents the square wndow. Here 3X3 wndow s used. entre on the pxel x k n the spatal doan. The spatal functon s nothng but the suaton of the ebershp functon n the neghbourhood of each pxel that s taken under consderaton. 3. Generalzed Spatal Kernel Based Fuzzy - Means lusterng Algorth(GSKFM Though the conventonal FM algorth works well on ost nose-free ages, and KFM algorths have excellent perforance n the applcatons by gven approprate kernel functon and reasonable paraeters. But, the KFM Volue Issue 5, May 03 algorth descrbed n prevous secton stll has one drawback: t s very senstve to nose and other agng artfacts, snce t does not consder any nforaton about neghbourhood ter. Usng the KFM algorth on age segentaton, the calculaton of J k only consder the pxels of X, n fact, the neghbour around of the X have the pled relatonshp to the X. As a consequence the KFM algorth s unsutable for ages corrupted by pulse nose. In order to overcoe ths proble, we propose a generalzed spatal kernel based fuzzy c eans (GSKFM algorth whch ncorporates local nforaton nto ts obectve functon, defned n ters of J GSKFM (U,W as follows: ( ( ( N R α U k N k N J GSKFM U, W U K X, W (3 N R Where N R s ts cardnalty and N stands for the set of neghbours fallng nto a wndow around pxel X. where the th pxel s the center of the local wndow(for exaple, 3 3 or 5 5.The paraeter α s used to control the effect of the neghbours ter whch s gettng hgher wth the ncrease of age nose(0<α<. Accordng to equaton (, (3 and (4, by nzng (3 usng Lagrangan optzaton, the followng new teratve center W and ebershp U update equatons [3]: N ( R α U l l ( (, N K X W N R (4 U N ( R α Ukl l ( (, N X W K k N R K ( X, W X W (5 N K ( X, W 3. Peak pont Analyss Algorth The segentaton ethod should be nonparaetrc, and should take the local and global feature dstrbuton nto consderaton. Ths s a nonparaetrc algorth that detects the peaks of lusters n the color hstogra of an age. The hstogra bns rather than the pxels theselves to fnd the peaks of clusters; thus, the algorth can fnd the peaks effcently. Then, the algorth assocates the pxels of a detected cluster based on the local structure of the cluster. The approxate no of clusters can be deterned based on followng algorth: step : Input color age s browsed and selected that needs segentaton. step: Selected nput age s dvded n to three channels whch s RGB.e. Red, Green and Blue. step3: Then wndowng technque s appled to each channel separately. Each channel s dvded nto no of blocks,.e. for each channel wndow s appled fro start of age to the end of age wth wndow ove on. We set No of bns No. of wndow. 67

4 Internatonal Journal of Scence and Research (IJSR, Inda Onlne ISSN: step4: The ntensty value of each pxel n to the wndow s copare wth the specfed range and f the ntensty values are nearer to the range n the wndow then we club t nto one wndow.e. Neghborng pxels that lead to the sae peak are grouped together. step5: Otherwse we keep the pxel n the other wndow. Output of ths algorth s age wth separated color values. step6: Hstogra of ths age s coputed.. step7: Then the peakfnder ( ethod s used to deterne the no of dstnct peaks n the hstogra whch deternes approxate no of clusterss (c (d (e Fgure.3: lusterng of a synthetc age. (a Orgnal age, (b the sae Iage wth Salt & pepper (5%, (c FM result, (d KFM result, (e GSKFM result Fgure : Fndng Peaks n Hstogra J GSKFM can be obtaned through an teratvee process, whch s carred as before. Step : Set values and ε. Step : Fnd the No. of clusters usng the peak pont analyss ethod. Step 3: Intalze the fuzzy partton atrx U (0. Step 4: Set the loop counter b0. (b Step 5: alculate the cluster centers W wth U (b by usng functon (5 Step 6: alculate the ebershp atrx U (b+ by usng functon (4 Step 7: If {U (b U (b+ }< ε then stop, otherwse set bb+ 4. Experents and Dscusson 4. Experent II We apply all the algorths to bran age (Fg.4.(a: bran age downloaded fro net. We frstly added 3% Gaussan nose to the orgnal age. The algorth for fndng no of clusters s appled and the output s acheved by applyng the algorths entoned n the table. (a (b 4. Experent I: We apply all the algorths to a synthetc test age (Fg..3 (a: 8 8 pxels, two classes wth two gray level values 0 and 5, We frstly added 5% salt and pepper nose to the orgnal age. The algorth for fndng no of clusters s appled and the output s acheved by applyng the algorths entoned n the table. (c (d Fgure 3 llustrates the clusterng results of a corrupted age. Orgnal age [Fg.3 (a], corrupted age [Fg3 (b], FM result [Fg. 3(c], KFM result [Fg3 (d], GSKKFM result [Fg3 (e]. (e Fgure 4: lusterng of a bran age. (a Orgnal age, (b the sae age wth Gaussan nose (3%, (c FM result, (d KFM result, (e GSKFM result (a (b 68

5 Internatonal Journal of Scence and Research (IJSR, Inda Onlne ISSN: Perforance Evaluaton: To evaluate the perforance of the clusterng algorths, lusterng Accuracy Rate ((AR s used whch s defned as: A AR X 00% Where s the nuber of clusters, A represents the set of pxels belongng to the th class found by the algorth, whle represents the set of pxels belongng to the th class n the reference segented age. AR [0, ], thus the clusterng perforance s gettng better when the value of AR s hgher. lusterng Accuracy Rate can also be calculated as forula below: AR Nuber of correctly classfed pxels / Total nuber of pxels Table : oparson of lusterng Accuracy Rate (AR% of Four algorths on Synthetc Iages Dgtal Iage FM KFM GSKFM Salt & Pepper [(5% Gaussan 3% (bran oncluson and Future Scope lusterng s one of the effcent technques n edcal and other age segentaton. The prary advantage of the proect work s that t ncludes the kernel ethod, the effect of neghbour pxel nforaton and gray level nforaton to prove the clusterng accuracy of an age, and to overcoe the dsadvantages of the known FM algorth whch s senstve to the type of noses. The proposed algorth Generalzed Spatal Kernel based Fuzzy -Means (GSKFM s ndependent of paraeter selecton. Due to the factor that the gray value of the neghbour pxels generally affect the result of segentaton; the new algorth puts kernel ethod and the effect of neghbours together. It provdes nose-unty and preserves age detals. It can be useful n varous felds lke edcal age analyss, such as tuor detecton, study of anatocal structure, and treatent plannng. For ths algorth, Gaussan kernel s selected as a kernel functon n used n clusterng algorths. However, other heurstcs or approaches for estatng the kernel paraeter ay be consdered n future for provng the result [4] Yang Y., Zheng h., and Ln P., "Fuzzy c-eans lusterng Algorth wth a Novel PenaltyTer for Iage Segentaton", Opto-Electroncs Revew, Vol.3, No.4, Pp , 005. [5] Lotf A. Zadeh. Fuzzy sets. Inforaton and ontrol, Vol8, Pp: , 965 [6] Bezdek J.. Pattern Recognton wth Fuzzy Obectve Functon Algorths.Plenu Press, New York, 98 [7] J.. Dunn, "A Fuzzy Relatve of the ISODATA Process and ts Use n Detectng opact, Well- Separated lusters," J. ybernetcs, Vol. 3, Pp. 3-57, 973 [8] Wu Z, Xe,W.X Yu J.P. Fuzzy -eans lusterng Algorth Based on Kernel Method In: Proceedngs of Ffth Internatonal onference on oputatonal Intellgence and Multeda Applcatons,Pp 49-56,003 [9] Lee Song Yeow, Spatal Kernel-Based Generalzed - ean lusterng for Medcal Iage Segentaton, School of oputer Scences, Unversty Sansalasa,Dec 00. [0] Ruoyu Du and Hyo Jong Lee, "A Modfed-FM Segentaton Algorth for Bran MR Iages", In : Proceedngs of AM Int. onf. on Hybrd Inforaton Technology, Pp.5-7, 009 [] Huynh Van Lung and Jong-Myon K, "A generalzed spatal fuzzy -eans algorth for [] Medcal age segentaton", In proc. 8th Int. onf. on Fuzzy Systes, pp , 009. [3] Deng-Yaun Haung, Ta- We Ln, Wu-hh-Hu, Autoatc Multlevel Threshold Based on Two Stage Otsu s Method Wth luster Deternaton Wth Valley Estaton, II 0 ISSN , pp [4] hun-yan Yu, Yng L, A-lan Lu, Jng-hong Lu, A Novel Modfed Kernel Fuzzy -Means lusterng Algorth on Iage Segentaton, IEEE Internatonal onference on oputatonal Scence and Engneerng SE/I-SPAN/IU 0. References [] X. Munoz, J. Frexenet, X. uf, and J. Mart, Strateges for IageSegentaton obnng Regon and Boundary Inforaton, PatternRecognton Letters, Vol. 4, No., Pp375 39, 003. [] StelosKrnds and Vassloshatzs, A Robust Fuzzy Local Inforaton -Means lusterng Algorth,IEEE Transactons on Iage Processng, Vol. 9, No. 5, MAY 00 [3] Ga M, Mercer kernel based clusterng n feature space, IEEE Transactons on Neural Networks, Vol. 3, No. 3, Pp , 00 Volue Issue 5, May 03 69