Segmentation of Fluorescence Microscopy Cell Images Using Unsupervised Mining

Transcription

1 he Open Medical Infomaics Jounal, 00, 4, Open Access Segmenaion of Fluoescence Micoscopy Cell Images Using Unsupevised Mining Xian Du and Sumee Dua *,, Daa Mining Reseach Laboaoy, Depamen of Compue Science, College of Engineeing and Science, Louisiana ech Univesiy, Ruson, LA, USA School of Medicine, Louisiana Sae Healh Sciences Cene, New Oleans, LA, USA Absac: he accuae measuemen of cell and nuclei conous ae ciical fo he sensiive and specific deecion of changes in nomal cells in seveal medical infomaics disciplines. Wihin micoscopy, his ask is faciliaed using fluoescence cell sains, and segmenaion is ofen he fis sep in such appoaches. Due o he complex naue of cell issues and poblems inheen o micoscopy, unsupevised mining appoaches of cluseing can be incopoaed in he segmenaion of cells. In his sudy, we have developed and evaluaed he pefomance of muliple unsupevised daa mining echniques in cell image segmenaion. We adap fou disincive, ye complemenay, mehods fo unsupevised leaning, including hose based on k-means cluseing,, Osu s heshold, and. Validaion measues ae defined, and he pefomance of he echniques is evaluaed boh quaniaively and qualiaively using synheic and ecenly published eal daa. Expeimenal esuls demonsae ha k-means, Osu s heshold, and pefom similaly, and have moe pecise segmenaion esuls han. We epo ha has highe ecall values and lowe pecision esuls fom unde-segmenaion due o is Gaussian model assumpion. We also demonsae ha hese mehods need spaial infomaion o segmen complex eal cell images wih a high degee of efficacy, as expeced in many medical infomaics applicaions. Keywods: Fluoescence micoscope cell image, segmenaion, cluseing,, heshold,.. INRODUCION Micoscopic imaging is nealy ubiquious in seveal medical infomaics disciplines, including bu no limied o, cance infomaics, neuo-infomaics, and clinical decision suppo in ophhalmology. While fluoescence micoscopes pemi he collecion of lage, high-dimensional cell image daases, hei manual pocessing is inefficien, iepoducible, ime-consuming, and eo-pone, pomping he design and developmen of auomaed, efficien, and obus pocessing o allow analysis fo high-houghpu applicaions. he sensiive and specific deecion of pahological changes in cells equies he accuae measuemen of geomeic paamees. Pevious eseach has shown ha geomeic feaues, such as shape and aea, indicae cell mophological changes duing apoposis []. As a pecuso o geomeic analysis, segmenaion is ofen equied in he fis pocessing sep. Cell image segmenaion is challenging due o he complex mophological cells, illuminan eflecion, and inheen micoscopy noises. he chaaceisic poblems include poo conas beween cell gay levels and backgound, a high numbe of occluding cells in a single view, and excess homogeneiy in cell images due o iegula saining among cells and issues. ypically, image segmenaion algoihms ae based on local image infomaion, including edge o gadien, level se *Addess coespondence o his auho a he Daa Mining Reseach Laboaoy, Depamen of Compue Science, College of Engineeing and Science, Louisiana ech Univesiy, Ruson, LA 77, USA; el: ; Fax: ; sdua@laech.edu [], hisogam [3], cluses [4], and pio knowledge [5]. hese segmenaion mehods have been boadly implemened in medical imaging applicaions [6]. he cuen segmenaion algoihms used in cell images include seeded waeshed [7], Voonoi-based algoihm [8], hisogambased cluseing [9] o heshold [0] and acive conou []. Waeshed algoihms can spli he conneced cells bu can lead o ove-segmenaion. Hisogam-based image segmenaion is unpaameic and based on unsupevised cluseing. he hisogam is used o appoximae he pobabiliy densiy disibuion of he image inensiy. Pixels in one image ae paiioned ino seveal non-ovelapping inensiy egions. and ae exensions of hisogam segmenaion. In [9], he disibuion of image inensiy is modeled as a andom vaiable, which is appoximaed by a mixue Gaussian model. Due o he lack of inensiy disibuion infomaion in an image, he model can lead o significan bias. of he model is compuaionally efficien and easy o implemen, bu pefoms pooly in finding he opimal heshold beween cluses in he hisogam. Osu s opimal heshold is obained by minimizing ina-class vaiance and has been applied in nucleus segmenaion []. Level se and acive conou ae applied wih abiay ineacion enegy in ode o spli he conneced cells in []. his mehod is no meaningful fo isolaed cells and makes he cell segmenaion dependen on cell sizes. In [8], cells ae segmened accoding o he defined meic, he Voonoi disance beween pixels and seeds. his meic includes he infomaion fom image edges and ine-pixel disance wihin he image. he paameic acive conou and /0 00 Benham Open

2 4 he Open Medical Infomaics Jounal, 00, Volume 4 Du and Dua epulsive foce ae incopoaed in [3]. Howeve, his meic is no suiable fo he segmenaion of a lage numbe of cells in one image. Unsupevised leaning can be adaped and developed fo nuclei and cell image segmenaion due o he inheen coheen deecion and decomposiion challenges in he deecion and sepaaion of segmens. Howeve, i is difficul o selec a obus and epoducible mehod due o he lack of he compaaive evaluaion of hose algoihms. his poblem aises paially due o he lack of benchmak daa o because of manually oulined gound uh. his pauciy of pefomance evaluaion elevaes he difficuly fo medical scieniss o selec a suiable segmenaion mehod in medical image applicaions. Someimes, mehods ae seleced based on inuiion and expeience; e.g., Osu s heshold is used boadly in nuclei image segmenaion. Moeove, no boadly accepable mehod can addess he nuclei and cell image segmenaion poblems in a divese ange of applicaions accuaely and obusly. Recenly, seveal synheic (e.g. [4]) and benchmak cellula image daa (e.g. [5]) have been made publicly available. In his pape, we pesen and evaluae he pefomance of seveal unsupevised daa mining echniques in cell image segmenaion. We adap fou disincive, ye complemenay, mehods fo unsupevised leaning, including hose based on k-means cluseing,, Osu s heshold, and. Validaion measues ae defined o compae and conas he pefomance of hese mehods using publicly available daa. I should be noed ha he segmenaion algoihms ae ypical epesenaives of mehods based on hisogam, model, heshold, and acive conou. We only focus on segmenaion mehods using low-level image infomaion, such as pixel inensiy and image gadien. epesens boh he snake and level se echnologies [4]. he esuls pesened in his pape can guide domain uses o selec suiable segmenaion mehods in medical imaging applicaions.. UNSUPERVISED MINING MEHODS FOR IMAGE SEGMENAION Le us conside an image I of size = M N pixels, whee each pixel can ake L possible gayscale-level values in he ange [0, L]. Le h(x) be he nomalized hisogam of he image I... Noaion h(x) p μ Inensiy value of pixel i [ ] Hisogam of he image I, x 0, L Image size in ems of pixel numbes ( I ) ansfomaion funcion of image I ( ; ) -h pobabiliy densiy funcion wih paamee se wihin beween Mean of cluse Vaiance of cluse Wihin-class vaiance, Beween-class vaiance. i ( ), Pobabiliies of he wo cluses sepaaed by heshold f ( x) Image expessed wih spaial em x, which efes o pixel locaion (in ) Scala ha conols he balance beween egulaizaion and daa.. K-Means Cluseing We use cluseing fo image segmenaion o find he opimal heshold, such ha he image feaue values of pixels on one side of he heshold ae close o hei feaue values mean han he disance beween hose feaue values and he means on he ohe side of he heshold. his mehod is pefomed using he hisogam of image inensiy. We assume ha he image inensiies compose a veco space and y o find naual cluseing in i. he pixels ae cluseed aound cenoid c i, which ae obained by minimizing he obecive funcion c i := ag min( dis ( μ )). () he cenoid fo each cluse is ieaively obained as follows, μ i := { } { c i = }x i, () c i = whee is he image size in ems of pixel numbe, i ieaes ove all inensiies, ieaes ove all cenoids, and μ i ae he cenoid inensiies. Using inensiy value diecly in micoscopic cell image segmenaion will no lead o he desied segmenaion esul due o he dynamic anges, which vay in images. We popose a gay-level ansfomaion funcion in he fom ( I )= I fo he above algoihm o implemen k-means segmenaion in cell image I, whee is a posiive consancy..3. Expecaion Maximizaion Mehod he Expecaion Maximizaion () algoihm assumes ha an image consiss of a numbe of gay-level egions, which can be descibed by paameic daa models. When he hisogam of he gay levels is egaded as an esimae of he pobabiliy densiy funcion, he paamees of he funcion can be esimaed fo each gay-level egion using he hisogam. he obecive of he algoihm is o find he maximum likelihood esimaes of he paamees in he funcion. Coespondingly, consiss of wo seps: expecaion and maximizaion. Using he same noaions in Secion., he mixue of pobabiliy densiy funcions is as follows, K p( )= p ;. (3) = In he above, is he popoion of he -h densiy funcion in he mixue model, and p ; K = is he -h

3 Segmenaion of Fluoescence Micoscopy Cell Images Using Unsupevised Mining he Open Medical Infomaics Jounal, 00, Volume 4 43 densiy funcion wih paamee se. he Gaussian mixue model (GMM) is he mos employed in pacice, and has wo paamees, mean μ and covaiance, such ha = ( μ, ). We conside GMM in ou eseach. If we assume ha is he esimaed value of paamees = ( μ, ), obained a he -h sep, hen + can be obained ieaively. he algoihm famewok follows, + = i, (4) μ + = + = i i i i, (5) ( μ ) μ = p ; μ, K = i p ; μ,, (6). (7) hese equaions sae ha he esimaed paamees of he densiy funcion ae updaed accoding o he weighed aveage of he pixel values whee he weighs ae obained fom he E sep fo his paiion. he cycle sas a an iniial seing of 0 = μ 0 0 (, ) and updaes he paamees using Equaions ((4)-(7)) ieaively. he algoihm conveges unil is esimaed paamees canno change. hen, he final paamees, = μ (, ), ae applied in image segmenaion by labeling pixels using Maximum Likelihood (ML). Pixel is labeled using he following funcion, ag max ( ) exp 0.5( μ ) μ heshold-based Segmenaion heshold segmenaion is a mehod ha sepaaes an image ino a numbe of meaningful egions hough he seleced heshold values. If he image is a gey image, hesholds ae ineges in he ange of [0, L-], whee L- is he maximum inensiy value. Nomally, his mehod is used o segmen an image ino wo egions: backgound and obec, wih one heshold. he following is he equaion fo heshold segmenaion: I B, if I ( x, y)> ( x, y)= 0,if I ( x, y). (8). (9) In he above equaion, I B is he segmenaion esulan. he mos famous heshold mehod was poposed by Osu in []. he Osu s mehod finds he opimal heshold among all he inensiy values fom 0 o L- and chooses he value ha poduces he minimum wihin-class vaiance wihin as he opimal heshold value. Consequenly, he opimal value of Op is obained hough he following opimal compuaion, wihin ( op )= min wihin 0 L ( ). (0) In he whole image, vaiances ae made up of wo pas: = wihin ( )+ beween ( ). Osu shows ha min wihin 0 L is he same as max beween 0 L. heefoe, he opimal value of can also be obained hough he following alenaive opimizaion pocess: beween ( op )= max beween ( ). () 0 L Equaion () is ofen used o find he opimal heshold value fo simple calculaion. heoeically, beween ( )is expessed in he following, beween ( op )= ( ) ( )( μ ( ) μ ( )) () whee i ( )= hi () ae he pobabiliies of he wo cluses sepaaed by heshold, and μ i cluse means. i ( ), and μ i using hisogam h(x) as follows, μ μ, ae he, can be esimaed ( )= hi () (3) L ( )= hi (), (4) ( )= ( )= i= + i=0 L i= + i h() i, (5) i h() i. (6) Using he above Equaions ()-(6), he opimal heshold is exhausively seached among [0, L-] o mee he obecive accoding o Equaion ()..5. Global Minimizaion of he Acive Conou Model () We choose he global minimizaion of he acive conou model () [6] o analyze he implemenaion of acive conou in cell-image segmenaion. his mehod has a simple iniializaion and fas compuaion, and i can avoid being suck a an undesied local minima. is based on Mumfod and Shah s (MS) funcion and he Chan and Vese s model of acive conous wihou edges (ACWE)

4 44 he Open Medical Infomaics Jounal, 00, Volume 4 Du and Dua [7]. impoves ACWE by using weighed oal vaiaion and dual fomulaion of he V fom, which peseves he advanage of ACWE. We define and elaed conceps below. min E ( μ,):= V g ( μ)+ μ, μ v L + ( x,c,c )μ + ( v)dx, (7) whee ( x,c,c )= (( c f ( x) ) ( c f ( x ) ) )dx, f ( x)is he given image, and c and c ae consans calculaed fo paiioning in ieaion; e.g., if μ* = ag min E [ μ,v,c,c ], c and c ae he means of pixels in wo paiions and can be obained using equaions, > 0 is chosen small enough, > 0 is a paamee conolling scale elaed o he scale of obsevaion of soluion, and is consan. V g ( μ)= g( x)μ dx (8) whee g(x) is an edge indicaion funcion which gives a link beween snake model and egion ems. he minimizaion Equaion (7) is solved using he following equaions ieaively unil convegence: c = c = f ( x) v( x)dx v( x)dx, (9) ( v( x) ) f x dx, (0) ( v( x) )dx, () p n+ = pn + divp n ( f v)/ + / g x divpn f v μ = v divp, () { } (3) v( x)= min max{ μ( x) ( x,c,c ),0}, In Equaion (), is he ime sep. 3. EXPERIMENAL RESULS In his secion, we pesen he expeimenal esuls fom he segmenaion of hee ypes of fluoescen cellula images: synheic cell images, nuclei images wih gound uh, and bain cell micoscopic images. he fis wo ypes of image daa ae used o evaluae he quaniaive pefomance of he fou segmenaion mehods and o compae he esuls o he gound uh. he bain cell images ae segmened wih qualiaive pefomance analysis due o he lack of gound uh. 3.. Quaniaive Measue We use he adiional pecision, ecall, and F-scoe as he quaniaive measues in pixel level. hese measues ae sandad echniques used o evaluae he qualiy of he segmenaion esuls agains he gound uh. hese measues quanify discepancy beween segmenaion esuls and binay gound uh mask as follows: # SR # SR G pecision = ecall = F scoe =, (4) # SR G, # G (5) pecision ecall, pecision + ecall (6) whee SR is he segmenaion esul and G is he gound uh of images. he symbol # efes o he pixel numbes in he ses Segmenaion of Synheic Daa Benchmak ses of synheic cell populaion images wih gound uh ae simulaed by P. Ruusuvuoi in [8]. We selec he second benchmak se which consiss of mulichannel cell images because we do no have suiable eal cell images wih gound uh fo evaluaion. In his se, nuclei, cyoplasm, and subcellula componens have been simulaed by uning paamees such as size, locaion, andomness of shape, and ohe backgound o fluoescence paamees (see deails in [8]). he image ses ae divided ino wo subses: high qualiy and low qualiy (examples shown in Fig. ), each consising of 0 cell images. he second se has ovelapping cells and a noisy backgound. Each image conains 50 cells. As each simulaed image has a coesponding binay mask as gound uh, binay opeaions can easily calculae he quaniaive measue defined above. a) b) c) d) Fig. (). Synheic cell images a) (low qualiy) wih noisy backgound and ovelapping cells, b) (high qualiy) wihou noise in backgound and ovelapping cells, c) gound uh of image a, d) gound uh of image b. Fig. () shows he segmenaion esul of fou mehods fo he low qualiy synheic image daa in Fig. (a).

5 Segmenaion of Fluoescence Micoscopy Cell Images Using Unsupevised Mining he Open Medical Infomaics Jounal, 00, Volume 4 45 Segmened images in Fig. () ae compaed and evaluaed using he gound uh image in Fig. (c). Fig. (3) shows he segmenaion esul of fou mehods fo he high qualiy synheic image daa in Fig. (b). Segmened images in Fig. (3) ae compaed and evaluaed using he gound uh image in Fig. (d). a) b) values fo he segmenaion esuls using subcellula images wih high qualiy. We obseve ha he segmenaion esuls of lowe qualiy images, wih noisie backgounds and ovelapping cells, have wose esuls han hose in high qualiy images. K- means, Osu s heshold and obain simila segmenaion qualiy in boh ses of images, measued by F- scoe, pecision, and ecall. hei pefomance is moe obus agains noises han. Moeove, he algoihm has lowe pecision, while keeping much highe ecall values, especially fo cell images wih noisy backgounds. o fuhe undesand hese phenomena, eal nucleus images ae segmened in he nex secion. able. Aveage Measues of he Segmenaion Mehods Applied on Low Qualiy Synheic Cell Images c) d) F-Scoe Pecision Recall K-Means Osu s able. Aveage Measues of he Segmenaion Mehods Applied on High Qualiy Synheic Cell Images Fig. (). Segmenaion esul fo synheic cell images of low qualiy in Fig. (a). a) esul, b) esul, c) Osu s esul, d) esul. a) b) F-Scoe Pecision Recall K-Means Osu s c) d) F-Scoe Image Numbe Fig. (3). Segmenaion esul fo synheic cell image of high qualiy in Fig. (b). a) esul, b) esul, c) Osu s esul, d) esul. Figs. (4-6) and able ae he qualiy measue values fo he segmenaion esuls using subcellula images wih low qualiy. Figs. (7-9) and able ae he qualiy measue Fig. (4). F-scoe of he fou mehods applied on low qualiy simulaed cell images Segmenaion of Nucleus Images Sixeen nucleus images wee hand-oulined by an expe in he CellPofile poec [8, 5]. We use hese images o evaluae he segmenaion algoihms quaniaively. We obain simila esuls, as shown in Figs. (0-3), as hose we obained in Secion 3... We obseve in able 3 ha

6 46 he Open Medical Infomaics Jounal, 00, Volume 4 Du and Dua mainains highe ecall and lowe pecision values, even if is F-scoe values ae as high as he ohe segmenaion mehods in seveal images. Fom Fig. (0d), we can see ha he unde-segmens nucleus images songly, which induces he high ecall values. his unde-segmenaion is due o he pesumed dual Gaussian mixue models in he calculaion of. One model epesens backgound, and he ohe efes o obecs. When obecs have much smalle gayness egions han backgound (as shown in Fig. 0a), he dual Gaussian mixue model leads o unde-segmenaion. Pecision Pecision Image Numbe Fig. (5). Pecision of he fou mehods applied on low qualiy simulaed cell images. Recall Image Numbe Fig. (6). Recall of he fou mehods applied on low qualiy simulaed cell images. F-Scoe Image Numbe Fig. (7). F-scoe of he fou mehods applied on high qualiy simulaed cell images Image Numbe Fig. (8). Pecision of he fou mehods applied on high qualiy simulaed cell images. Recall Image Numbe Fig. (9). Recall of he fou mehods applied on high qualiy simulaed cell images. Osu s mehod also has dawbacks. Alhough i pefoms well fo nucleus segmenaions, due o is fasness and simpliciy in applicaion, i canno be poven he bes segmenaion mehod fo nucleus images. As shown in Secion 3.., Osu s mehod shows sable pecision and ecall values even when i encounes abiaily defined noises. Howeve, in he expeimen using eal nucleus images, he Osu s mehod ecall value is significanly lowe han is pecision values, which means i has ove-segmened he image. is moe obus and sable han he Osu s mehod in ou expeimens. depends on boh image inensiy disibuion infomaion (egion) and gadien (edge) infomaion. When he conas beween backgound and cells becomes ligh, and cells ae hidden by noises, he combinaion of gadien and inensiy infomaion ecods bee infomaion han inensiy alone does, e.g. in Osu s. In he k-means mehod, we choose k= o cluse some obecs ino one goup and ohe segmens ino a backgound goup. pefoms he bes in almos all expeimens. Is good pefomance is due o he applicaion of powe funcion fo he compensaion of inensiy ansfomaion bough in by he micoscopic device. In his eseach, we assume his powe funcion is known, and we obain i by choosing he opimal k-means esul (smalles eo beween

7 Segmenaion of Fluoescence Micoscopy Cell Images Using Unsupevised Mining he Open Medical Infomaics Jounal, 00, Volume 4 47 k-means segmenaion esul and gound uh). I demonsaes ha he k-means mehod can obain obus and pecise segmenaion esuls wih he aid of powe funcion. a) b) cell, which has been sained wih Calcein AM, a vial dye ha sains only living cells. he es images ae pixels wih 8-bi gay-levels. As no manual oulining has been pefomed on he images, he pefomance of segmenaion mehods is qualiaively evaluaed. F-Scoe c) d) Image Numbe Fig. (). F-scoe of he fou mehods applied on nucleus images. e) f) Pecision Image Numbe Fig. (). Pecision of he fou mehods applied on nucleus images. Fig. (0). Segmenaion of nucleus images: a) Nucleus images, b) Gound uh, c) esul, d) esul, e) Osu s esul, and f) esul. able 3. Aveage Qualiy Measues of he Segmenaion Mehods on Nucleus Images F-Scoe Pecision Recall K-Means Osu s Qualiy Measue of Segmenaion of Bian Cell Images In his evaluaive sudy, bain cell images wee capued using a compue conolled Micoscope (Leica DMI 6000 Digial). he cell images ae of a nomal healhy asocyes Recall OSU Image Numbe Fig. (3). Recall of he fou mehods applied on nucleus images. As shown in Fig. (4a), bain cell images ae dak, and cell conous ae blued. he segmenaion esuls of k- means, Osu s, and (Fig. 4b, d, e) seem o be washed ou. Using he nucleus, ligh aeas, we can idenify he exising cells in he image. he segmenaion esul of GMM (Fig. 4c) is sill unde-segmened. In Fig. (5), we can see ha he backgound, denoed by he annoaed

8 48 he Open Medical Infomaics Jounal, 00, Volume 4 Du and Dua a) b) c) d) e) Fig. (4). a) Bain cell micoscopy image, b) cluseing esul, c) cluseing esul, d) Osu s segmenaion esul, e) segmenaion esul. line maked by *, has a naow esimaed inensiy disibuion while cells disibue in a wide inensiy levels, denoed by he ohe annoaed line maked by +. his pesenaion using sandad Gaussian disibuion leads o eos in he esimae of pobabiliy disibuion. As shown in Fig. (6), he individual inensiy disibuions ae summed o obain he mixed Gaussian disibuion, which is pesened by he annoaed line maked by squae. he eos in esimaion ae accumulaed in he sum pocedue, which can be pesened by he discepancy beween he aeas coveed by he esimaed disibuion and he ue inensiy disibuion denoed by he annoaed line maked by iangle. he ohe hee segmenaion esuls have cells spli wih he nucleus, alhough seveal cells ae ove-segmened. his ove-segmenaion can be explained as ha hese echniques conside image inensiy and exue infomaion in he segmenaion pocess, while he spaial elaion o some connecion beween pixels is missed. Moeove, compaed o he synheic images in Secion 3.., eal cell images ae moe complex and difficul o segmen. Esimaed pobabiliy of inensiy disibuion Inensiy disibuion of backgound Inensiy disibuion of cells Inensiy levels Fig. (5). Esimaed inensiy disibuion of image in Fig. (4a) using GMM model. 4. CONCLUSION We pesen fou unsupevised mining mehods in cell image segmenaion. he fou mehods ae compaed and conased o showcase efficacy senghs, as well as embedded limiaions. While no single mehod oupefoms he ohes in all ess, his analysis is expeced o assis image scieniss in impoving hese echniques fo he moe complex cell image segmenaion poblems encouneed in elaed disciplines. Inensiy disibuion ue image inesiy disibuion Esimaed image inensiy disibuion Inensiy levels Fig. (6). he gound uh and esimaion of he inensiy disibuion of image in Fig. (4a). he mehods ae evaluaed boh quaniaively and qualiaively using synheic simulaed and eal images. pefoms weakly in boh cases due o is pesumed Gaussian model. I needs a bee model assumpion in micoscopic imaging if applied in cell image segmenaion. Osu s mehod canno always guaanee a good segmenaion esul, especially when he conas beween he backgound and cells is poo. inegaes inensiy and gadien infomaion and keeps a sable pefomance in ou expeimens. can pefom obus segmenaion wih he aid of powe funcion. In fuue wok, spaial infomaion beween pixels mus be involved o impove he pefomance of hose echniques. he knowledge abou he cell images, such as inclusion of he powe disibuion funcion will be incopoaed in segmenaion. REFERENCES [] Jean RP, Gay DS, Speco AA, Chen CS. Chaaceizaion of he nuclea defomaion caused by changes in endohelial cell shape. J Biomed Eng 004; 6(5): [] Oshe S, Sehian JA. Fons popagaing wih cuvaue-dependen speed: Algoihms based on Hamilon-Jacobi fomulaions. J Compu Phys 988; 79: -49. [3] Ohlande R, Pice K, Reddy DR. Picue segmenaion using a ecusive egion spliing mehod. Compu Gaph Image Pocess 978; 8: [4] Jain AK. Daa Cluseing: 50 Yeas Beyond K-Means. echnical Repo R-CSE-09-. Paen Recogni Le 009; in pess.

9 Segmenaion of Fluoescence Micoscopy Cell Images Using Unsupevised Mining he Open Medical Infomaics Jounal, 00, Volume 4 49 [5] Cooes, aylo CJ, Coope DH, Gaham J. Acive shape models- hei aining and applicaion. CVGIP: Image Undesanding 995; 6: [6] Pham ZL, Xu C, Pince JL. Cuen mehods in medical image segmenaion. Ann Rev Biomed Eng 000; : [7] Wahlby C, Lindblad J, Vondus M, Bengsson E, Bokesen L. Algoihms fo cyoplasm segmenaion of fluoescence labelled cells. Anal Cell Pahol 00; 4(-3): 0-. [8] Jones R, Capene A, Golland P. Voonoi-based segmenaion of cells on image manifolds. Lec Noes Compu Sci 005; [9] Bazi Y, Ruzzone L, Melgani F. Image hesholding based on he algoihm and he genealized Gaussian disibuion. Paen Recogni Le 007; 40: [0] Osu N. A heshold selecion mehod fom Gay-level Hisogam. IEEE ans Sys Man Cybeneics 979; ; Vol. SMC-9. [] Yan PK, Zhou XB, Shah M, Wong SC. Auomaic segmenaion of high-houghpu nai fluescen cellula images. IEEE ans Inf echnol Biomed 008; (): [] Coulo L, Kischne H, Chebia A, e al. opology peseving SACS segmenaion of poein subcellula locaion images. In: Poc IEEE In Symp Biomed Imaging, Alingon, VA, Ap 006; pp [3] Zimme C, Labuyee E, Meas-Yedid V, Guillen N, Olivo Main J- C. Segmenaion and acking of migaing cells in Videomicoscopy wih paameic acive conous: a ool fo cell-based dug esing. IEEE ans Image Pocess 00; (0): -. [4] Benchmak se of synheic images fo validaiong cell image analysis algoihms: Benchmak images. Available fom: hp:// [Accessed: 0 Sepembe 009]. [5] Cell Pofile: Cell image analysis sofwae. Available fom: hp:// [Accessed: 0 Sepembe 009]. [6] Besson X, Esedoglu S, Vandegheyns P, hian J, Oshe S. Fas Global Minimizaion of he Acive Conou/Snake Model. J Mah Imaging Vis 007; 8(): [7] Chan F, Vese LA. Acive conous wihou edges. IEEE ans Image Pocess 00; 0(): [8] Ruusuvuoi P, Lehmussola A, Selinummi J, Raala, Huunen H, Yli-Haa O. Benchmak se of synheic images fo validaing cell image analysis algoihms. In: Poceedings of he 6h Euopean Signal Pocessing Confeence (EUSIPCO-008), Lausanne, Swizeland, 008. Received: Ocobe 0, 009 Revised: Novembe 5, 009 Acceped: Novembe 5, 009 Du and Dua; Licensee Benham Open. his is an open access aicle licensed unde he ems of he Ceaive Commons Aibuion Non-Commecial License (hp://ceaivecommons.og/licenses/bync/3.0/) which pemis unesiced, non-commecial use, disibuion and epoducion in any medium, povided he wok is popely cied.