Using The ACO Algorithm in Image Segmentation for Optimal Thresholding 陳香伶財務金融系

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1 教專研 95P- Usg The ACO Algorthm Image Segmetato for Optmal Thresholdg Abstract Usg The ACO Algorthm Image Segmetato for Optmal Thresholdg 陳香伶財務金融系 Despte the fact that the problem of thresholdg has bee qute extesvely studed for may years, the automatc determato of a optmum threshold value cotues to be of great challege. For oe, tradtoal optmal thresholdg methods exhaustvely search the optmal thresholds to optmze the object fuctos therefore become very computatoally expesve whe dealg wth mult-level thresholdg. Hece, our study proposes a hybrd optmzato scheme usg at coloy optmzato algorthm to reder the optmal thresholdg techque more applcable ad effectve. We employed the propertes of dscrmate aalyss usg Otsu s method to aalyze the separablty amog the gray levels the mage. The ACO-Otsu algorthm, cosdered a o-parametrc ad usupervsed method of automatc threshold selecto for mage segmetato, has several desrable advatages. The expermetal results show that the ACO-Otsu effcetly speed up the Otsu s method to a great extet at mult-level thresholdg, ad that such method ca provde better effectveess at populato sze of for all gve mage types at mult-level thresholdg ths study. 1. Itroducto May applcatos such as documet mage aalyss, map processg, scee processg, computer vso, patter recogto, ad qualty specto of materals cosder the mage thresholdg techque a crucal operato because further process steps have to rely o the segmetato results. The wdely-used techque whch extracts the objects from the backgroud has both b-level ad multlevel types recogzed. For a mage wth clear objects the backgroud, the b-level thresholdg whch dvdes the object pxels at oe gray level whle the backgroud pxels at aother s wdely used. For rather complex mages, o the other had, the multlevel thresholdg segmets the pxels to several dstct groups whch the pxels of the same group have gray levels wth a specfc rage. I recet practces, the multlevel thresholdg has bee much accepted, yet the complexty of the thresholdg problem ad the computato tme to solve such problem stll mpose sgfcat challeges as the umber of levels requred creases. For ths reaso, may thresholdg techques have bee proposed ad classfed. Some techques are detfed as ether global or local thresholdgs based o the role of the testy value whle other methods have bee classfed as ether optmal or property-based. Kapur et al. [1985] used the cocept of the etropy of a hstogram ad developed a global thresholdg method separatg the hstogram of gray level probabltes to two dstrbutos of the mage. Such method was also cosdered a optmal-based thresholdg whch maxmzed the combed etropy of the thresholded classes to determe the optmal threshold value. Y [1993] proposed a property-based method whch frst developed a peak-fdg method based o symmetry; the, the dualty property was used to detfy the valleys of the hstogram. Perhaps, the most mportat ad wdely-accepted cocept s o the characterstcs of thresholdg techques. Sahoo et al. [1988] preseted a comprehesve survey of a 95-45

2 教專研 95P- Usg The ACO Algorthm Image Segmetato for Optmal Thresholdg varety of thresholdg techques ad Abutaleb [1989] classfed them to parametrc or o-parametrc approaches. Parametrc approaches assume each group havg the probablty desty fucto of a Gaussa dstrbuto ad fd a estmate of the parameters of such dstrbuto whch wll best ft the gve hstogram data [Tsa 1995]. Ufortuately, whe the desred umber of classes s much lower tha the umber of peaks the orgal hstogram, the computato tme to fd the solutos of threshold values ofte becomes expesve. Dfferet from parametrc approaches, o-parametrc methods fd the threshold level accordg to some dscrmatg crtera such as the betwee-class varace Otsu [1979] ad etropy Kapur et al. [1985] whch both separate the gray-level regos of a mage a optmum maer. As the result, the o-parametrc approaches are prove to be more computatoally effcet ad smpler to apply. Despte the fact that the problem of thresholdg has bee qute extesvely studed for may years, the automatc determato of a optmum threshold value cotues to be of great challege. For oe, tradtoal optmal thresholdg methods exhaustvely search the optmal thresholds to optmze the object fuctos therefore become very computatoally expesve whe dealg wth mult-level thresholdg. Tll recet years, several researchers attempt to usg heurstcs as alteratve ways to solve mult-level thresholdg. Y [1999] proposed a fast scheme for optmal thresholdg usg geetc algorthms. Hs method, a optmal thresholdg techque, has show better performace tha those of some property-based oes. Cheg et al. [] appled fuzzy etropy mage segmetato, used t to select the fuzzy rego of membershp fucto automatcally so that a mage ca be trasformed to fuzz doma wth maxmum fuzzy etropy, ad mplemeted geetc algorthm to fd the optmal combato of fuzzy parameters. Zahara et al. [5] preseted a hybrd optmzato scheme whch appled the Otsu s method wth Nelder-Mead smplex search ad partcal swarm optmato (the NM-PSO-Otsu method) ad prove to ot oly expedte the Otsu s method effcetly but also extet ts effectveess to a mult-level thresholdg problem. I ths paper, a fast scheme usg at coloy optmzato algorthm s proposed to reder the optmal thresholdg techque more applcable ad effectve. We employed the propertes of dscrmate aalyss usg Otsu s method to aalyze the separablty amog the gray levels the mage. Ths method, cosdered a o-parametrc ad usupervsed method of automatc threshold selecto for mage segmetato, has several desrable advatages. Frst, the Otsu s method s very smple ad straghtforward to the mult-thresholdg problems. Also, a optmal threshold ca be selected automatcally based o the global property of the hstogram (.e. the betwee-class varace). Secod of all, our study cosders the at coloy optmzato (ACO) algorthm to fd the optmal threshold values because the ACO algorthm tself mposes several valuable features. For examples, a stochastc compoet allows the 95-46

3 教專研 95P- Usg The ACO Algorthm Image Segmetato for Optmal Thresholdg artfcal ats to buld a wde varety of dfferet solutos ad hece explore a much larger umber of solutos. Also, the heurstc formato s appled to gude ad fluece the ats movg ad learg towards the most promsg solutos. As well as, the use of a coloy of ats acts as the collectve teracto of a populato of search agets whch crease the algorthm s robustess ad effcetly solve a problem. For these reasos, the ACO algorthm has bee successfully employed to solve varous combatoral optmzato problems. Nevertheless, t s also our curosty to apply ad evaluate the ACO algorthm the feld of mage segmetato.. Otsu s Method for Image Thresholdg The cocept of usg dscrmate aalyss for classfcato problems was frst troduced by Fsher [1936] ad was appled o mage thresholdg by Otsu [1979]. I Otsu s paper, the elemetary case of threshold selecto where oly the gray-level hstogram suffces wthout other a pror kowledge s dscussed, ad ther method s proposed from the vewpot of dscrmate aalyss. The feasblty of evaluatg the goodess of threshold s doe through exhaustve search to maxmze the betwee class varace betwee dark ad brght regos of the mage. Our study uses the exteded propertes of the dscrmate crtero to determe the umber of objects to whch the mage should be segmeted, ad descrbes the cocept of a automatc multlevel thresholdg method as follows. For mult-level thresholdg, a gray level mage f ( x, y) s trasformed to a mult-level mage g( x, y) by a threshold set T = t, t,.., t,..., t }, whch s composed of k thresholds. { 1 k Wth a gve gray level, deote the observed occurrece frequeces (hstogram) of pxels ad the total umber of pxels N = L where L s the umber of gray values the hstogram. The the gray-level hstogram s ormalzed ad regarded as a probablty dstrbuto havg a gve gray level : p =, N p, L = 1 p = 1 Suppose we segmet these pxels to a sutable umber of classes. Wth k deotg the umber of selected thresholds (.e. k L 1), the mage s the parttoed to k+1 classes whch ca be represeted by C =,1,..., },... C t + 1, t +,... t },... { t1 = { + 1 Ck = { tk + 1, tk +,... L 1}. Hece, the probabltes of class occurreces ( w ), the class-mea levels ( μ ), ad the class varaces ( ) are gve as follows, respectvely: 95-47

4 教專研 95P- Usg The ACO Algorthm Image Segmetato for Optmal Thresholdg t + 1 w =, p = t + 1 μ = t + 1 = t + 1 w p, ad = t + 1 = t + 1 p ( μ ) w The wth-class varace, deoted by The betwee-class varace, deoted by classes ad s expressed as, WC, of all segmeted classes of pxels s computed as, k WC = w =, s used to measure the separablty amog all k = w = ( μ μ ) The total varace T ad the overall mea μ T of pxel a gve gray level mage f ( x, y) are computed as, L 1 = T = ( μt ) p, ad μ = = T L 1 T p I order to evaluate the goodess of the threshold at level k, the followg dscrmate crtero measures are used: T λ =, κ =, ad η = WC WC T Amog these measures, the parameterη s the smplest oe wth respect to k, ad therefore the * optmal threshold k that maxmzesη, or equvaletly maxmzes s also followed as, max * * * ( k1, k,.., k L ) = ( k1, k,.. k 1 k < k < L 1 L ) 3. At Coloy Optmzato (ACO) Algorthm Just lke other meta-heurstcs spred by the atural process, the At Coloy Optmzato (ACO) algorthm s mtatg the behavor of real ats. I ACO, a coloy of smple agets, called artfcal ats, search for good solutos at every geerato. Every artfcal at of a geerato bulds up a soluto step by step. These ats, oce buld a soluto, wll evaluate the partal soluto ad depost some amout of pheromoe to mark ther paths. The followg ats of the ext geerato are attracted by the pheromoe so that they wll lkely search these areas earby. The ACO algorthm has ts geeral framework lke below

5 教專研 95P- Usg The ACO Algorthm Image Segmetato for Optmal Thresholdg Set all parameters ad talze the pheromoe trals Loop (o. of teratos) Sub-Loop (populato sze, popsze) Buld solutos based o the state trasto probablty Cotue utl all ats have bee geerated Evaluate all solutos durg the terato ad select the best oe Apply the pheromoe update rule Cotue utl the stoppg crtero s reached For actvty selecto, the state trasto probablty show below s used the soluto costructo process. p j α ( τj) = ( τl) l {1,,.., UB LB + α 1} j {1,,.., UB LB + 1} otherwse where deotes the dex of the threshold at mult-level (e.g. = 1 for b-level, = for tr-level, ad = 3 for four-level), j refers to the dex for the gray level ragg from the lower boud ad the upper boud of the th threshold, ad α deotes the parameter cotrollg the relatve weght of pheromoe. The pheromoe trals, deoted by accordg to the pheromoe updatg rule. τ ew j τ j are costatly updated The pheromoe update rule cossts of the offle updatg whch s formally expressed as = ρ τ + ) old j e ( 1 ρ Δτ, where a parameter ρ [,1 ] cotrols the pheromoe persstece e ad1 ρ represets the proporto of the pheromoe evaporated. Meawhle Δτ represets the amout of pheromoe tral added toτ by the eltst ats for all combatos (, j) belogg to e the best soluto foud so far, ad s determed by Δτ = Q the magtude of the pheromoe cotrbuto. j 4. Computatoal Results ad Aalyss where a costat Q cotrols I ths secto, the performace of the proposed ACO-Otsu algorthm s evaluated ad compared to the Otsu s method wth exhaustve search ad the NM-PSO-Otsu algorthm [Zahara 5]. Our study deals wth a bary mage whch s produced by thresholdg a grayscale mage at mult-levels. These test mages were take uder atural room lghtg 95-49

6 教專研 95P- Usg The ACO Algorthm Image Segmetato for Optmal Thresholdg wthout the support of ay specal lght source. As t s commoly uderstood, the mages are composed of a collecto of dscrete cells, kow as pxels, whch has gve values ragg from to 55, or 1 to 56. So at the begg of our expermets o the parameter settg for the ACO-Otsu method, we mplemeted three stadard mages wth rectagular objects of uform gray values (see Fgure 1-a, Fgure -a, ad Fgure 3-a). As well as, we employed aother three test mages Drago, Screws, ad Blocks (show Fgure -a to -c, respectvely) to aalyze ad evaluate the performace of our algorthm. The ACO-Otsu method s mplemeted o a Petum IV 3.GHz, 768 MB persoal computer usg C++ programmg laguage whle the Otsu method wth NM-PSO-Otsu methods [Zahara et al. 5] were mplemeted o a Athlo XP + (166 11) wth 1 GB RAM usg Matlab. A stoppg crtero used Zahara et al. [5] ad our studes are the maxmum umber of teratos reached whe solvg a N-dmesoal problem. Our prelmary expermets have show the followg set of all parameters to accout for both effcecy ad effectveess; therefore, we set up as follows: α = 1, τ =. 1, ρ =. 9, ad Q =.1τ for all expermetal rus. Table 1 lsts out dfferet parameter settgs our prelmary expermets. Table 1. Settgs of Dfferet Parameters Implemeted the ACO-Otsu algorthm Parameters Values α.5 1 ρ Q τ o The expermet starts wth three stadard test mages (show Fgures 1-a, -a, ad 3-a, respectvely) wth rectagular objects of uform gray values. The the resultg mages of the b-level, tr-level, ad four-level (show Fgure 1-b, -b, ad 3-b, respectvely) verfy that ACO-Otsu method ca provde a qualty performace mage segmetato. Comparso results (see Table ) for these three stadard test mages have reveal detcal optmal threshold values for both Otsu s ad NM-PSO-Otsu methods [Zahara et al. 5], but slghtly dfferet values for our ACO-Otsu method. The appealg dfferece optmal threshold values perhaps comes from usg dfferet gray-level scales: (, 55) [Zahara et al. 5] whle (1,56) ths study. I addto, for both Otsu s ad NM-PSO-Otsu methods [Zahara et al. 5], the optmal objectve values greatly dffers from our optmal objectve values ACO-Otsu method of ths study (show Table ). The reaso has bee that Zahara et al. [5] mmzed the wth-group varace the objectve fucto whle our study maxmzed the betwee-class varace. 95-5

7 教專研 95P- Usg The ACO Algorthm Image Segmetato for Optmal Thresholdg Table. Computatoal Results for the three stadard test mages at the mult-level thresholdg Optmal Thresholds Optmal Objectve Values Stadard (over 1 rus) Test Images Otsu ad NM-PSO-Otsu ACO-Otsu Otsu ad NM-PSO-Otsu ACO-Otsu B-level thresholdg Tr-level thresholdg 111, , Four-level thresholdg 71, 114, 15 7, 113, Orgal mage T= (a) (b) (c) Fgure 1. B-level thresholdg test mage: (a) orgal mage, (b) ACO-Otsu method, ad (c) hstogram of (b) Orgal mage T=11, (a) (b) (c) Fgure. Tr-level thresholdg test mage: (a) orgal mage, (b) ACO-Otsu method, ad (c) hstogram of (b) 95-51

8 教專研 95P- Usg The ACO Algorthm Image Segmetato for Optmal Thresholdg Orgal mage T=7, 113, (a) (b) (c) Fgure 3. Four-level thresholdg test mage: (a) orgal mage, (b) ACO-Otsu method, ad (c) hstogram of (b) Table 3. Result comparsos amog Otsu s, NM-PSO-Otsu ad ACO-Otsu methods over the three stadard test mages Stadard Test Images Otsu CPU Tmes (sec.) NM-PSO- Otsu ACO-Otsu Populato Szes (NA) Iterato (NI) Otsu ad NM-PSO-Otsu ACO-Otsu B-level thresholdg Tr-level thresholdg Four-level thresholdg From the computatoal results lsted Table 3, we ca geerally coclude that the CPU tme goes learly up wth the creasg level of thresholdg; furthermore, the hgher levels of thresholdg wll gve rse to the populato sze ad terato. We also see that as the hgher level of thresholdg leads to the creasg computatoal complexty, our CPU tme also creases from the lowest the lowest CPU tme of.9 secods at NA=1 ad NI=1 (.e. No. of evaluatos = 1) to the hghest CPU tme of.14 secods at NA= ad NI=6 (.e. No. of evaluatos = 1). Whe we compare wth the Otsu s method, our ACO-Otsu method takes relatvely less executo tmes to acheve 1% optmum but ot whe we compare wth NM-PSO-Otsu method. For evaluatg the performace of our proposed method, three mages (Drago, Screws, ad Blocks) are chose; the threshold selecto values ad computato tmes for these three tested mages are automatcally determed accordg to dfferet threshold levels. These results as lsted Table 4. Also Table 5 shows our comparso results of Screws mage wth the oes [Zahara et al. 5] ad the ACO-Otsu takes relatvely loger CPU tme tha the other two methods. However, we see that our method s capable of obtag qualty mage segmetato results for the tr-level thresholdg wth a sgfcatly short perod of tme ad (show Fgure 4 to Fgure 6). For the Screws ad Blocks test mages (show 95-5

9 教專研 95P- Usg The ACO Algorthm Image Segmetato for Optmal Thresholdg Fgures 5 ad 6 below), both pctoral results appear to be better at the tr-level thresholdg tha at the b-level thresholdg. Table 4. Computatoal results for mages of Drago, Screws, ad Blocks at mult-level thresholdgs Images Level Optmal Populato Szes Optmal CPU Tmes Objectve (NA) Iterato Thresholds (sec.) Values (NI) Drago Screws , Blocks , Table 5. Computatoal results for Test Images of Screws at b-level thresholdg Screws test mage Otsu [Zahara et al. 5] NM-PSO-Otsu [Zahara et al. 5] Opt. Thresholds Opt. Obj. Values CPU Tmes (sec.) Pop Szes (NA) Iterato (NI) ACO-Otsu [Ths study] Orgal mage T= (a) (b) (c) Fgure 4. Result of Orgal Image of Drago : (a) orgal mage, (b) ACO-Otsu method, ad (c) hstogram of (b) 95-53

10 教專研 95P- Usg The ACO Algorthm Image Segmetato for Optmal Thresholdg Orgal mage T= (a) (b) (c) Orgal mage T=194, (a) (d) (e) Fgure 5. Thresholdg Results of Orgal Image of Screws : (a) orgal mage, (b) ACO-Otsu method at b-level, (c) hstogram of (b), (d) ACO-Otsu method at tr-level, ad (e) hstogram of (d). Orgal mage T= (a) (b) (c) Orgal mage T=196, (a) (d) (e) Fgure 6. Result of Orgal Image of Blocks : (a) orgal mage, (b) ACO-Otsu method at b-level, (c) hstogram of (b), (d) ACO-Otsu method at tr-level, ad (e) hstogram of (d)

11 教專研 95P- Usg The ACO Algorthm Image Segmetato for Optmal Thresholdg 5. Cocluso I ths study, we ca draw several geeral coclusos at the ed of ths aalyss. Frst of all, from our prelmary expermet, we have foud that NA ad NI have a verse relato for all levels of thresholdg. I other word, whe NA creases, NI decreases; whe NA decreases, NI creases. Secod of all, we also fd that whe the level of thresholdg creases, both NA ad NI wll crease. The, the computatoal results for most mages at b-, tr-, ad four-level thresholdgs have show umber of teratos (NI) appears to be rather effectve at populato sze (NA) of, NA regardless the complexty of the mages. From the above fdgs, whle the qualty of mage segmetato does ot get compromsed, we cosder the ACO-Otsu method to be a potetal method to accelerate the Otsu s method mult-level thresholdg for real-tme applcatos. Referece Abutaleb A.S. (1989). Automatc thresholdg of gray-level pctures usg two-dmesoal etropy, Computer Vso, Graphcs, ad Image Processg, 47, -3. Fsher R.A. (1936). The use of multple measuremets taxoomc problems, Aals of Eugecs, 7, Kapur J. N., Sahoo P. K., Wog A.K.C. (1985). A ew method for gray-level pcture thresholdg usg the etropy of the hstogram, Computer Vso graphcs Image Process, 9, Kttler J., Illgworth J. (1986). Mmum error thresholdg, Patter Recogto, 19, Lm Y. K., Lee S.U. (199). O the color mage segmetato algorthm based o the thresholdg ad the fuzzy c-meas techques, Patter Recogto, 3, Mtra A. (5). Restorato of osy documet mages wth a effcet b-level adaptve thresholdg, Iteratoal Joural of Computer Itellgece,, Otsu N. (1979). A threshold selecto method from gray-level hstograms, IEEE Tras. Systems. Ma Cyberet, SMC-9, Pu T. (198). A ew method of grey-level pcture thresholdg usg the etropy of the hstogram, Sgal Processg,, Pu T. (1981). Etropy thresholdg: a ew approach, Computer Vso Graphcs Image Process, 16, Tsa D.M., Che Y. H. (199). A fast hstogram-clusterg approach for mult-level thresholdg, Patter Recogto Letters, 13,

12 教專研 95P- Usg The ACO Algorthm Image Segmetato for Optmal Thresholdg Tsa D.M. (1995). A fast thresholdg selecto procedure for multmodal ad umodal hstograms, Patter Recogto Letter,16, Wag S. ad Haralck R. (1984). Automatc threshold selecto, Computer Vso Graphc Image Processg, 5, Y P.-Y., Che L.-H. (1993). New method for multlevel thresholdg usg the symmetry a dualty of the hstogram, Joural of Electroc Imagg,, Y P.-Y., Che L.-H. (1997). A fast teratve scheme for mult-level thresholdg methods, Sgal Processg, 6, Y P.-Y. (1999). A fast scheme for optmal thresholdg usg geetc algorthms, Sgal Processg, 7, Zahara E., Fa S.-K. S., Tsa D.M. (5). Optmal mult-thresholdg usg a hybrd optmzato approach, Patter Recogto Letters, 6,