Image Segmentation by Clustering Methods: Performance Analysis

Transcription

1 Volume 9 No., eptember Image egmentaton by Clusterng Methods: Performance Analyss B.athya Department of Appled cence Vveanandha Insttute of Engneerng and Technology for Women Thruchengode, Tamlnadu, Inda R.Manavalan Department of Computer cence (PG) K..R College of Arts and cence Thruchengode, Tamlnadu, Inda ABTRACT Image segmentaton plays a sgnfcant role n computer vson. It ams at extractng meanngful obects lyng n the mage. Generally there s no unque method or approach for mage segmentaton. Clusterng s a powerful technque that has been reached n mage segmentaton. The cluster analyss s to partton an mage data set nto a number of dsont groups or clusters. The clusterng methods such as means, mproved mean, fuzzy c mean (FCM) and mproved fuzzy c mean algorthm (IFCM) have been proposed. K means clusterng s one of the popular method because of ts smplcty and computatonal effcency. The number of teratons wll be reduced n mproved K compare to conventonal K means. FCM algorthm has addtonal flexblty for the pxels to belong to multple classes wth varyng degrees of membershp. Demert of conventonal FCM s tme consumng whch s overcome by mproved FCM. The expermental results exemplfy that the proposed algorthms yelds segmented gray scale mage of perfect accuracy and the requred computer tme reasonable and also reveal the mproved fuzzy c mean acheve better segmentaton compare to others. The qualty of segmented mage s measured by statstcal parameters: rand ndex (RI), global consstency error (GCE), varatons of nformaton (VOI) and boundary dsplacement error (BDE). Keywords K means, mproved means, fuzzy c means, mproved c means, rand ndex, global consstency error, varatons of nformaton. INTRODUCTION Image segmentaton can be defned as the classfcaton of all the pcture elements or pxels n an mage nto dfferent clusters that exhbt smlar features. egmentaton nvolves parttonng an mage nto groups of pxels whch are homogeneous wth respect to some crteron []. Dfferent groups must not ntersect each other and adacent groups must be heterogeneous. The groups are called segments. Image segmentaton s consdered as an mportant basc operaton for meanngful analyss and nterpretaton of mage acqured. It s a crtcal and essental component of an mage analyss and or pattern recognton system, and s one of the most dffcult tass n mage processng, whch determnes the qualty of the fnal segmentaton. Researchers have extensvely wored over ths fundamental problem and proposed varous methods for mage segmentaton. These methods can be broadly classfed nto seven groups: () Hstogram thresholdng, () Clusterng (Fuzzy and Hard), (3) Regon growng, regon splttng and mergng, (4) Edge-based, (5) Physcal model- based, (6) Fuzzy approaches, and (7) Neural networ and GA (Genetc algorthm) based approaches.[],[]. PROBLEM DECRIPTION An mage may be defned as a two dmensonal functon f(x, y), where x and y are spatal (plane) coordnates, and the ampltude of f at any par of co-ordnates (x, y) s called the ntensty or gray level of the mage at that pont. The regon of nterest n the mage can be degraded by the mpact of mperfect nstrument, the problem wth data acquston process and nterferng natural phenomena. Therefore the orgnal mage may not be sutable for analyss. Thus mage segmentaton technque s often necessary and should be taen as sgnfcant step durng mage s processed and analyzed. Repeatable experments wth publshed benchmars are requred for ths research feld to progress. The problem addressed n ths thess s that the mage s splt nto number of segmentaton []. Choosng an approprate model for segmentaton s dffcult tas that the modal has the better segmentaton wth reduced computatonal tme. The problem s reformed wth mnmzed computatonal tme and hgh qualty of the results. 3. IMAGE EGMENTATION BY CLUTERING METHOD Clusterng can be consdered the most mportant unsupervsed learnng problem; so, as every other problem of ths nd, t deals wth fndng a structure n a collecton of unlabeled data. A defnton of clusterng could be the process of organzng obects nto groups whose members are smlar n some way. A cluster s therefore a collecton of obects whch are smlar between them and are dssmlar to the obects belongng to other clusters. [3], [4], [5], [6] 3. K Means Clusterng K-means s one of the smplest unsupervsed learnng algorthms that solve the well nown clusterng problem [8], [4]. The procedure follows a smple and easy way to classfy a gven data set through a certan number of clusters (assume clusters) fxed a pror [5], [6]. Ths algorthm ams at mnmzng an obectve functon, n ths case a squared error functon. The obectve functon, x () J = x - c == 7

2 Volume 9 No., eptember ( ) x - c Where s a chosen dstance measure between a ( ) data pont x and the cluster centre c, s an ndcator of the dstance of the n data ponts from ther respectve cluster centers. The algorthm s composed of the followng steps:. Place K ponts nto the space represented by the obects that are beng clustered. These ponts represent ntal group centrods.. Assgn each obect to the group that has the closest centrod. 3. When all obects have been assgned, recalculate the postons of the K centrods. Repeat teps and 3 untl the centrods no longer move. Ths produces a separaton of the obects nto groups from whch the metrc to be mnmzed can be calculated. 3. Improved K means Clusterng Let () D = {d / =,..., n} be a data set havng K-Clusters, C= { c / =,..., } be a set of K centers and () () = {d d s member of cluster K} be the set of samples that belong to the th cluster [],[7]. The followng functon whch s defned as an obectve functon, n () Cost(D, C) = dst(d,c ) = Where dst (d (), c) measures the Eucldean dstance between a ponts d () and ts cluster center c. The algorthm has the followng steps..dvdng D nto K parts accordng to data patterns; K D = U =, = θ, ¹ I () x (), =,..., K. Let be ntal clusterng centers calculated by, () () x () = d, =,..., K. d () Î 3. Decde membershp of the patterns n each one of the K- clusters accordng to the mnmum dstance from cluster center crtera. 4. Calculate new centers by the followng teratve formula, () (+) d n x = () = d Î q q () () q = x - d. Where 5. Repeat steps 3 and 4 tll there s no change n cluster centers. 3.3 Fuzzy C-Means Clusterng Fuzzy c-means (FCM) s a method of clusterng whch allows one pece of data to belong to two or more clusters [],[7]. That s t allows the pxels belong to multple classes wth varyng degrees of membershp. It s based on mnmzaton of the followng obectve functon: c c n m J(U, c, c,...cc) = J = u d = = = Where, m s any real number greater than.u s the degree of membershp of x n the cluster x s the th of d-dmensonal measured data, c s the d-dmenson center of the cluster. The algorthm s composed of the followng steps:. Intalze U= [ u ] matrx, U (). At -step: calculate the centers vectors c()= [c] wth U() N m u x c = = N m u = () + 3. Update U, U 4. If. u = c = (+) () U - U < ε x - c x - c m - then TOP; otherwse return to step 3.4 Improved Fuzzy C-Means The mproved FCM algorthm s based on the concept of data compresson where the dmensonalty of the nput s hghly reduced []. The data compresson ncludes two steps: quantzaton and aggregaton. The quantzaton of the feature space s performed by masng the lower 'm' bts of the feature value. The quantzed output wll result n the common ntensty values for more than one feature vector. In the process of aggregaton, feature vectors whch share common ntensty values are grouped together. A representatve feature vector s chosen from each group and they 8

3 Volume 9 No., eptember are gven as nput for the conventonal FCM algorthm. Once the clusterng s complete, the representatve feature vector membershp values are dstrbuted dentcally to all members of the quantzaton level. nce the modfed FCM algorthm uses a reduced dataset, the convergence rate s hghly mproved when compared wth the conventonal FCM. The mproved FCM algorthm uses the same steps of conventonal FCM except for the change n the cluster updatng and membershp value updatng crterons. The modfed crterons are showed below, c = Where n = n = m u y m u d = y - c y = Reduced Dataset, u = c /(m-) d = d 4. EXPERIMENTAL REULT ANALYI AND DICUION The proposed algorthms have been mplemented usng MATLAB. The performance of varous mage segmentaton approaches are analyzed and dscussed. The measurement of mage segmentaton s dffcult to measure. There s no common algorthm for the mage segmentaton. The statstcal measurements could be used to measure the qualty of the mage segmentaton [], []. The rand ndex (RI), global consstency error (GCE), boundary dsplacement error (BDE), and varatons of nformaton (VOI) are used to evaluate the performance. The detaled descrpton wth formulae of RI, GCE, BDE, VOI parameters are explaned n detal as follows, 4. Rand Index (RI) The Rand ndex (RI) counts the fracton of pars of pxels whose labelng are consstent between the computed segmentaton and the ground truth averagng across multple ground truth segmentatons[]. The Rand ndex or Rand measure s a measure of the smlarty between two data clusters. Gven a set of n elements and two parttons of to compare, and, we defne the followng: a, the number of pars of elements n that are n the same set n X and n the same set n Y b, the number of pars of elements n that are n dfferent sets n X and n dfferent sets n Y c, the number of pars of elements n that are n the same set n X and n dfferent sets n Y d, the number of pars of elements n that are n dfferent sets n X and n the same set n Y The Rand ndex (R) s, a + b a + b R = = n a + b + c + d ( ) Where, a + b as the number of agreements between X and Y and c + d as the number of dsagreements between X and Y. The Rand ndex has a value between and, wth ndcatng that the two data clusters do not agree on any par of ponts and ndcatng that the data clusters are exactly the same. 4. Varaton of Informaton (VOI) The Varaton of Informaton (VOI) metrc defnes the dstance between two segmentatons as the average condtonal entropy of one segmentaton gven the other, and thus measures the amount of randomness n one segmentaton whch cannot be explaned by the other []. uppose we have two clusterng (a dvson of a set nto several subsets) X and Y where X = {X, X... X}, p = X / n, n = Σ X. Then the varaton of nformaton between two clusterng s: VI(X; Y) = H(X) + H(Y) I(X, Y) Where, H(X) s entropy of X and I(X, Y) s mutual nformaton between X and Y. The mutual nformaton of two clusterng s the loss of uncertanty of one clusterng f the other s gven. Thus, mutual nformaton s postve and bounded by {H(X), H(Y)}_log(n) 4.3 Global Consstency Error (GCE) The Global Consstency Error (GCE) measures the extent to whch one segmentaton can be vewed as a refnement of the other []. egmentatons whch are related are consdered to be consstent, snce they could represent the same mage segmented at dfferent scales. egmentaton s smply a dvson of the pxels of an mage nto sets. The segments are sets of pxels. If one segment s a proper subset of the other, then the pxel les n an area of refnement, and the error should be zero. If there s no subset relatonshp, then the two regons overlap n an nconsstent manner. The formula for GCE s as follows, { } GCE = mn E(s,s, p), E(s, s, p) n Where, segmentaton error measure taes two segmentatons and as nput, and produces a real valued output n the range [::] where zero sgnfes no error. For a gven pxel p consder the segments n and that contan that pxel Boundary Dsplacement Error (BDE) The Boundary Dsplacement Error (BDE) measures the average dsplacement error of one boundary pxels and the closest boundary pxels n the other segmentaton[]. u - v < u - v L µ LA (u, v) = L - u - v < Let LA( u, v) µ denotes the membershp functon that descrbes the fuzzy relaton. The experment s conducted over the fve mages usng the algorthms means, mproved means, FCM, mproved fuzzy c means and ther results shown n Fg. wth requred statstcal parameters and ther results are presented n Table. The average of results s shown n Table. If the value of RI s 9

4 Volume 9 No., eptember hgher and GCE, BDE, VOI are lower then the segmentaton approach s better. The Fg. average performance analyss chart reveals that the rand ndex of mproved fuzzy c-mean s hgher than others and also the global consstency error, varaton of nformaton, and boundary dsplacement error are lower than others. The detaled analyss of the ndvdual statstcal measure s gven n Fg.3. Table 3 show that the tme evaluaton of proposed algorthms. The average tme of each method proected n the chart Fg.4. It shows that the K means tae mnmum tme compare to others, however t provdes poor results. The output provded by the mproved s also ptable even though the number of teratons taen by mproved means. Comparatvely the FCM algorthm provdes good result but t acqure more tme than K means and mproved K means. The average tme taen for fve mages by IFCM s comparatvely lower to tradtonal FCM method. o t was observed that the proposed method IFCM performs better compare to others approaches. Table.Performance Evaluaton IMAGE METHOD RI GCE VOI BDE Improved K IMG FCM IFCM Improved K IMG FCM IFCM Improved K IMG 3 FCM IFCM Improved K IMG 4 FCM IFCM Improved K IMG 5 FCM IFCM Table.Average Calculaton of Performance Analyss METHOD IMPROVE D K RI GCE VOI BDE FCM IFCM Fg : segmentaton results usng clusterng PERFORMANCE ANALYI IMPROVED K FCM IFCM Table 3. Tme Evaluaton IMAGE K MEAN IMPROVED K FCM IFCM ONE TWO THREE FOUR FIVE RI GCE VOI BDE Fg. Performance Analyss Chart 3

5 Volume 9 No., eptember TIME CALCULATION K MEAN IMPROVED -K FCM IFCM Fg.4 Average Tme Calculaton 5. CONCLUION In ths paper, the unsupervsed method.e. cluster based algorthms were proposed for mage segmentaton. The clusterng technques such as means, mproved means, fuzzy c mean, mproved fuzzy c means were tested n dfferent mages. The performance of proposed algorthms s measured usng segmentaton parameters RI, GCE, VOI, and BDE. The computatonal results showed that the K means mage segmentaton consumes less tme but t provde poor result. The modfed means algorthm taes mnmum numbers of teratons compare to means. The conventonal FCM consume more tme and provde good result where as the mproved FCM algorthm consume less tme compare to tradtonal FCM and provde good result. Therefore form the computatonal results conclude that the proposed algorthms the mproved FCM algorthm performed better than others n terms of performance accuracy and better convergence rate 6. REFERENCE [] Krshna Kant ngh, Aansha ngh,a tudy Of Image egmentaton Algorthms For Dfferent Types Of Images IJCI Internatonal Journal of Computer cence Issues [] F. MarquCs B. Marcotenu, F. Zanoguera, parton based mage representaton as bass for user asssted mage segmentaton, [3] U.M. Fayyad, G. Patetsy-hapro, P. myth, R. Uthurusamy, Advances n Knowledge Dscovery and Data Mnng,AAAI/MIT Press (996) [4] M.N. Murty, A.K. Jan, P.J. Flynn, Data clusterng: a revew, ACM Comput. urv. 3(3) (999) [5] A.K. Jan, R.C. Dubes, Algorthms for Clusterng Data,Prentce Hall, Englewood Clffs, NJ(988) [6] R.T. Ng, J. Han, Effcent and effectve clusterng methods for spatal data mnng, n: Proceedngs of the Twenteth Internatonal Conference on Very Large Databases, antago,chle(994) [7] u, M.C., Chou, C.H., A modfed verson of the K-means algorthm wth a dstance based on cluster symmetry. IEEE Trans. Pattern Anal. Machne Intel, 3(6)() [8] Xuyun L, Je Yang, Qng Wang, Jnn Fan, Peng Lu, Research and Applcaton of Improved K-means Algorthm Based on Fuzzy Feature electon [9] Kuo-Lang Chung, Keng-heng Ln, An effcent lne symmetry-based K-means algorthm, Pattern Recognton Lett, 7(6) [] ugar,.a., James, G.M., Fndng the number of clusters n a dataset: an nformaton-theoretc approach. J. Amer. tat. Assoc. 98(3) [] Kanugo, T., Mount, D.M., Netanyahu, N.., Pato, C.D., lverman, R., Wu, A.Y., An effcent K-means algorthm: analyss and mplementaton. IEEE Trans. Pattern Anal.Mach. Intell. 4() [] Maro G.C.A. Cmno, Beatrce Lazzern and Francesco Marcellon, A novel approach to fuzzy clusterng based on a dssmlarty relaton extracted from data usng a T system, Pattern Recognton, 39()(6) 77-9 [3] Mela, M., Hecerman, D., An expermental comparson of several clusterng methods, Mcrosoft Research Report MR-TR-98-6, Redmond, WA.(998) [4] hehroz. Khan, Amr Ahmad,Cluster center ntalzaton algorthm for K-means clusterng, Pattern Recognton Letters 5 (4) 93-3 [5] Bradley, P.., Fayyad, U.M., Refnng ntal ponts for Kmeans clusterng. In: harl, J. (Ed.), Proc. 5th Internat. Conf. on Machne Learnng (ICML98). Morgan Kaufmann, an Francsco, CA,(998) [6] K..Ravchandran and B. Ananth, Color n egmentaton Usng K-Means Cluster Internatonal Journal of Computatonal and Appled Mathematcs IN Volume 4 Number (9), pp [7] Jude hemanth.d, D.elvath and J.Antha, Effectve Fuzzy Clusterng Algorthm for Abnormal MR Bran Image egmentaton, Internatonal/Advance Computng Conference (IACC 9), IEEE, 9. [8] orn Istral, An Overvew of Clusterng Methods, Wth Applcatons to Bonformatcs. [9] hahram Rahm, M. Zarghamy A. Tharez D. Chhllar, A Parallel Fuzzy C Mean algorthm for Image egmentaton. [] P. Vasuda et. al. / (IJCE) Internatonal Journal on Computer cence and Engneerng, Improved Fuzzy C-Means Algorthm for MR BranImage egmentaton [] R. Unnrshnan, C. Pantofaru, and M. Hebert, Toward obectve evaluaton of mage segmentaton algorthms, IEEE Trans. Pattern Anal. Mach. Intell., vol. 9, no. 6, pp , Jun. 7. [] F. Ge,.Wang, and T. Lu, New benachmar for mage segmentaton evaluaton, J. Elect. Imag., vol. 6, no. 3, Jul. ep. 7. 3

6 Volume 9 No., eptember RAND INDEX(RI) GLOBAL CONITENCY ERROR(GCE) (a) (b) VARIATION OF INFORMATION (VOI) BOUNDARY DIPLACEMENT ERROR (BDE) (c) (d) Fg.3 tatstcal Measures (a) RI (b) GCE (c) VOI, (d) BDE. 3