Hstogram based Evolutonary Dynamc Image Segmentaton Amya Halder Computer Scence & Engneerng Department St. Thomas College of Engneerng & Technology Kolkata, Inda amya_halder@ndatmes.com Arndam Kar and Soumajt Pramank Computer Scence & Engneerng Department St. Thomas College of Engneerng & Technology Kolkata, Inda {arndam04.kar, soumajt.pramank}@gmal.com Abstract Ths paper descrbes an evolutonary approach for unsupervsed gray-scale mage segmentaton that segments an mage nto ts consttuent parts automatcally. The am of ths algorthm s to produce precse segmentaton of mages usng ntensty nformaton along wth neghborhood relatonshps. The proposed technque automatcally determnes the number of clusters. The proposed algorthm s evaluated on well known natural mages and ts performance s compared to that of DCPSO, MAMA based segmentaton technques etc. The proposed algorthm s very smple n mplementaton. Expermental results shown that the algorthm generates good qualty segmented mage. Keywords- Clusterng; Segmentaton; Thresholdng; Hstogram Analyss; Genetc Algorthm. I. INTRODUCTION Segmentaton refers to the process of parttonng a dgtal mage nto multple segments or regons. The goal of segmentaton s to smplfy the representaton of an mage nto somethng that s more meanngful and easer to analyze. Image segmentaton s typcally used to locate objects and boundares n mages []. More precsely, mage segmentaton s the process of assgnng a label to every pxel n an mage such that pxels wth the same label share certan vsual characterstcs. Image segmentaton s a very mportant feld n mage analyss, objects recognton, mage codng and medcal magng. Segmentaton s very challengng because of the multplcty of objects n an mage and the large varaton between them. Image segmentaton s the process of dvson of the mage nto regons wth smlar attrbutes. In many object based mage segmentaton applcatons, the number of cluster s known a pror, but our proposed scheme automatcally determnes the number of cluster produced durng the segmentaton of mages. The proposed technque should be able to provde good results whereas K-means algorthm whch may get stuck at values whch are not optmal [6]. Some of the several unsupervsed clusterng algorthms developed nclude K-means [7,8], fuzzy K-means, ISODATA [2], self-organzng feature map (SOM) [0], Partcle Swarm Optmzaton (PSO) [9], learnng vector quantzers (LVQ) [], GA based Clusterng [5] etc. Ths paper presents automatc mage segmentaton of gray scale mages usng Hstogram Analyss and Genetc Algorthm based clusterng. One natural vew of segmentaton s that we are attemptng to determne whch components of a data set naturally belong together. Clusterng s a process whereby a data set s replaced by clusters, whch are collectons of data ponts that belong together. Thus, t s natural to thnk of mage segmentaton as mage clusterng.e. the representaton of an mage n terms of clusters of pxels that belong together. The specfc crteron to be used depends on the applcaton. Pxels may belong together because of the same color or smlarty measure. The result of ths algorthm produced a better result to compare wth other technques such as DCPSO [6] MAMA [5,7]. Varous segmentaton technques have been developed for mage segmentaton [2,3,4,5,7]. The rest of ths paper s organzed as follows: - Secton II, the concepts of clusterng s provded. Secton III descrbes the threshold method. Secton IV gves the concepts of Hstogram analyss and secton V gves the concepts of Genetc Algorthm and secton VI descrbes the Hstogram based Genetc Algorthm analyss and secton VII descrbes the proposed algorthm and secton VIII descrbes the expermental results and secton IX concludes the paper. II. CLUSTERING The process of groupng a set of physcal or abstract objects nto classes of smlar objects s called clusterng. A cluster s a collecton of data objects that are smlar to one another wthn the same cluster and are dssmlar to the objects n other clusters. By clusterng, one can dentfy dense and sparse regons and therefore, dscover overall dstrbuton patterns and nterestng correlatons among data attrbutes. Clusterng may be found under dfferent names n dfferent contexts, such as unsupervsed learnng (n pattern recognton), numercal taxonomy (n bology, ecology), typology (n socal scences) and partton (n graph theory) [3]. By defnton, cluster analyss s the art of fndng groups n data, or clusterng s the classfcaton of smlar objects nto dfferent groups, or more precsely, the parttonng of a data nto subsets (clusters), so that the data n each subset (deally) share some common trat-often proxmty accordng to some defned dstance measure [4]. Clusterng s a challengng feld of research as t can be used as a stand-alone tool to gan nsght nto the dstrbuton of data, to observe the characterstcs of each cluster, and to focus on a partcular set of clusters for further analyss. Alternatvely, cluster analyss serves as a pre-processng step 978--4673-850-/2/$3.00 202 IEEE 585
for other algorthms, such as classfcaton, whch would then operate on detected clusters. Clusterng s a useful unsupervsed data mnng technque whch parttons the nput space nto K regons dependng on some smlarty/dssmlarty metrc where the value of K may or may not be known a pror. The man objectve of any clusterng technque s to produce a K n partton matrx U(X) of the gven data set X, consstng of n patterns, X ={x, x2... xn} [3]. III. THRESHOLDING Thresholdng refers to the selecton of a range such that f a pxel s wthn the threshold dstance from a known centrod then the pxel s sad to belong to that centrod s cluster. For any pxel x, the membershp to a cluster centrod, C s defned as C ={x:x f(x,y) and I(C ) I(x) <=T}, where C = th cluster centrod, x = pxel under consderaton, I(C ) = Intensty value of th centrod, I(x) = Intensty value of the pxel x, T = Threshold value, f(x,y) = Input mage. In the proposed algorthm the threshold value s taken to be 5. Now, a 5 5 mage wth pxel values as shown n gven below. Assume the three known centrods are 26, 80 and 34 respectvely. We denote ther cluster membershp as I, II and III respectvely. 26 30 34 38 82 26 30 30 36 83 25 26 29 35 80 24 26 29 35 80 23 29 32 33 8 The correspondng membershp pattern s as shown n below. The value of the threshold s selected as 5 for natural mages based on expermental results. IV. HISTOGRAM ANALYSIS In tradtonal k-means, the new centrod value s computed as the mean of the pxel values of all the pxels that belong to a partcular cluster. By hstogram analyss, the mode of the dstrbuton of the pxel values of a cluster s calculated nstead of the mean. The new centrod s taken as the pxel value that s repeated the hghest number of tmes n the cluster. The bass of hstogram analyss stems from the fact that the mode s a more robust representatve of the cluster than the mean and so a sngle very unrepresentatve pxel n a cluster wll not affect the mode value, whch wll affect the mean value sgnfcantly. Snce the mode value must actually be the value of the pxel occurrng the maxmum number of tmes n the cluster, the hstogram analyss does not create new unrealstc pxel values when there s wde varaton n pxel values. Thus new ntensty s never generated. Suppose, for a cluster of 000 pxels, the followng dstrbuton shown n Fg.. Fgure. -Hstogram (ntensty vs. frequency) Collect all the pxels of the each cluster whch s defned by threshold operaton. Fnd the pxel x that the occurrence s maxmum and correspondng ntensty I(x) s selected for the centrod s of that cluster. From Fg., the mode value s: 2 wth frequency of occurrence 298.e. 298 whch s the maxmum. The mean value s: 7.25 wth frequency of occurrence 33. For ths reason, mode s a better choce than mean. V. GENETIC ALGORITHM Genetc Algorthm (GA) s a populaton-based stochastc search procedure to fnd exact or approxmate solutons to optmzaton and search problems. Modeled on the mechansms of evoluton and natural genetcs, genetc algorthms provde an alternatve to tradtonal optmzaton technques by usng drected random searches to locate optmal solutons n multmodal landscapes [8,9]. Each chromosome n the populaton s a potental soluton to the problem. Genetc Algorthm creates a sequence of populatons for each successve generaton by usng a selecton mechansm and uses operators such as crossover and mutaton as prncpal search mechansms - the am of the algorthm beng to optmze a gven objectve or ftness functon. An encodng mechansm maps each potental soluton to a chromosome. An objectve functon or ftness functon s used to evaluate the ablty of each chromosome to provde a satsfactory soluton to the problem. The selecton procedure, modeled on nature s survval-of-thefttest mechansm, ensure that the ftter chromosomes have a greater number of offsprng n the subsequent generatons. For crossover, two chromosomes are randomly chosen from the populaton. Assumng the length of the chromosome to be l, ths process randomly chooses a pont between and l- 586
and swaps the content of the two chromosomes beyond the crossover pont to obtan the offsprng. A crossover between a par of chromosomes s affected only f they satsfy the crossover probablty. Mutaton s the second operator, after crossover, whch s used for randomzng the search. Mutaton nvolves alterng the content of the chromosomes at a randomly selected poston n the chromosome, after determnng f the chromosome satsfes the mutaton probablty. In order to termnate the executon of GA we specfy a stoppng crteron. Specfyng the number of teratons of the generatonal cycle s one common technque of achevng ths end. VI. HISTOGRAM BASED GA CLUSTERING In ths proposed scheme, we consder a gray level mage of sze m n. The basc steps of the GA-clusterng algorthm for clusterng mage data are as follows: A. Populaton ntalzaton After thresholdng and hstogram analyss we have a set of centrods. Let, that set s C={C,C 2,..C k } and all centrods belongng to that set are marked as ungrouped. Suppose µ s the mnmum of all the ungrouped centrod belongng to C.e. μ = mn( C ), where =,2,.. k () Create a group for µ and put all the ungrouped centrods whch have a dfference of value or less wth µ, nto that group (S ): S { ( ) = C C C and C μ θ ) } (2) Mark elements of S as grouped. Next tme, agan fnd the mnmum µ 2 of all ungrouped centrods n C and repeat ths process untl all centrods are grouped n ths manner. Each centrod of set S s consdered as chromosome of the populaton S. Now apply GA on centrods n each group S to fnd out the optmal centrod representng that group n fnal clusterng, B. Ftness value calculaton For each group S, segment the whole mage usng only the centrods belongng to S, usng any standard method (such as, K-means). The ftness value for each chromosome (centrod) s the no. of pxels n ts cluster. Let, S = {C,C 2..C n } and pxels of the cluster havng centrod C ={x,x 2..x m }. Then the ftness value of C s m: f ( C ) = m (3) In ths way, the ftness functon assgns a ftness value to each centrod belongng to S. C. Selecton Ths ftness level s used to assocate a probablty of selecton wth each ndvdual chromosome. We apply Roulette Wheel selecton, a proportonal selecton algorthm where the no of copes of a chromosome that go nto the matng pool for subsequent operatons s proportonal to ts ftness. If f(c ) s the ftness of ndvdual C n the populaton, ts probablty of beng selected s, p = n j= f ( C ), (4) f ( C ) j Where n s the number of ndvduals n the populaton. D. Crossover For crossover at frst the selected chromosomes are represented as 8bt bnary nos. Then we use sngle-pont crossover wth fxed crossover probablty μ c. Select a random no, rnd such that 0< rnd 2 < 8 and do crossover wth bts startng from rnd 2 th bt poston between centrods C p and Cp+ of Group S,where p=,3,5...[(no of members of Group S )- ] E. Mutaton Each chromosome undergoes mutaton wth a fxed probablty μ m. Select a random bt poston of C and nvert that wth probablty μ m. Here, the random bt poston s 2 and μ m =0.05.Then the 2nd bt poston of C 2 wll be nverted wth probablty 0.05. F. Termnal Crteron We execute the processes of ftness computaton, selecton, crossover, and mutaton for a predetermned number of teratons. In every generatonal cycle, the fttest chromosome tll the last generaton s preserved - eltsm. Thus on termnaton, ths chromosome gves us the best soluton encountered durng the search. That s, after ths process we get the best centrod for each group S. VII. PROPOSED ALGORITHM Step : Take a grayscale mage f(x,y) as nput. Step 2: Thresholdng: For each and every pxel of the mage, compare them to fnd smlarty (a maxmum devaton of (+/-5) 2.: If true, put them n the same group. 2.2: Else, form a dfferent group. Step 3: Hstogram Analyss: For each and every group, fnd the mode of all the pxel values belongng to that group. Ths s the new centrod of the group. Step 4: Applyng GA: Form groups of centrods found n step 3 and from each and every group fnd the fttest centrod usng GA as dscussed n secton VI. Step 5: Replacng Pxel Values: Cluster the mage usng optmal centrods proposed by G.A. Replace the mage s pxel values wth the centrods of the clusters to whch they belong. 587
VIII. VALIDITY INDEX The cluster valdty measure used n the paper s the one proposed by Tur [2]. It ams at mnmzng the valdty ndex gven by the functon, ntra V = y (5) nter The term ntra s the average of all the dstances between each pxel x and ts cluster centrod z whch s defned as k 2 ntra = x z (6) N = x = C Where x z means the Eucldean dstance, and N s the total number of pxels, C s the cluster number, z s the centrods of cluster C, k s the total number of clusters. Intra cluster dependency s the sum of square of Eucldean dstance of every element from the centrods of the cluster to whch t belongs. On the other hand, nter s the nter cluster dependency whch gves the dea about the extent to whch each clusters are related. The hgher ths value the better clusterng s obtaned. It s represented as 2 nter = mn( z z j ), where =,2,.. k j = +, + 2,.. K (7) Where z and z j are the centrods. Intra cluster dependency s the mnmum of the square of Eucldean dstances of each centrods from the other. Lastly, y s gven as y = c N(2,) + Where c s a constant (selected value s 25), N(2,) s a Gaussan dstrbuton functon wth mean 2 and standard devaton.ths valdty measure serves the dual purpose of Mnmzng the ntra-cluster spread, and Maxmzng the nter-cluster dstance. Moreover t overcomes the tendency to select a smaller number of clusters (2 or 3) as optmal, whch s an nherent lmtaton of other valdty measures such as the Daves- Bouldn ndex or Dunne s ndex. IX. EXPERIMENTAL RESULTS The algorthm developed has been smulated usng MATLAB. The nput mages are consdered to be pgm mages. The precson s assumed to be 8.e. the no of bts per pxel s 8. All the mages fles that we have tested are natural mages. All the results have been reported n Fg.2, Fg.3 and Fg.4. These results have been compared to those of MAMA [5] and DCPSO [6]. The optmal range for the number of clusters for the mages of Lena, mandrll and peppers has also been coped from [2] whch are based on vsual analyss by a group of ten people. Number of cluster obtaned by ths proposed method always gves range between optmal ranges [5]. In ths paper we compare the valdty ndex wth other technques. Our algorthm gves the better results. X. CONCLUSIONS Ths paper presented a new approach for unsupervsed segmentaton for gray-scale mage that can successfully segment the mages. In ths paper, that the user does not need to predct the number of clusters, requred to partton the dataset, n advance. Comparson of the expermental results wth that of other unsupervsed clusterng methods, show that the technque gves satsfactory results when appled on well known natural mages. Moreover results of ts use on mages from other felds (MRI, Satellte Images) demonstrate ts wde applcablty. REFERENCES [] Rafael C. Gonzalez, Rchard E. Woods, Dgtal Image Processng, Pearson Educaton, 2002. [2] R. H. Tur, Clusterng-Based Color Image Segmentaton, PhD Thess, Monash Unversty, Australa, 200. 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(a) (b) (c) (d) Fgure.2: Expermental results of some natural mages, (a)-orgnal mage, usng (b) MAMA, (c) DCPSO and (d) Our proposed method. Fgure..3: Valdty ndex curve for MAMA, DCPSO and Proposed Method. Fgure.4: Number of clusters values for MAMA, DCPSO and Proposed Method. 589