Enhancement of Particle Filter Resampling in Vehicle Tracking via Genetic Algorithm

Transcription

1 01 UKSm-AMSS 6h European Modellng Symposum Enhancemen of Parcle Fler Resamplng n Vehcle Trackng va Genec Algorhm We Leong Khong, We Yeang Ko, Y Kong Chn, Me Yeen Choong, Kenneh Tze Kn Teo Modellng, Smulaon & Compung Laboraory, Maeral & Mneral Research Un School of Engneerng and Informaon Technology Unvers Malaysa Sabah Koa Knabalu, Malaysa msclab@ums.edu.my, kkeo@eee.org Absrac Vehcle rackng s an essenal approach ha can help o mprove he raffc survellance or asss he road raffc conrol. Recenly, he developmen of vdeo survellance nfrasrucure has nced he researchers o focus on he vehcle rackng by usng vdeo sensors. Hoever, he amoun of he on-road vehcle has been ncreased dramacally and hence he congeson of he raffc has made he occluson scene become a challenge ask for vdeo sensor based rackng. Convenonal parcle fler ll encouner rackng error durng and afer occluson. Besdes ha, also requred more eraon o connuously rack he vehcle afer occluson. Thus, parcle fler h genec operaor resamplng has been proposed as he rackng algorhm o faser converge and keep rack on he arge vehcle under varous occluson ncdens. The expermenal resuls sho ha enhancemen of he parcle fler h genec algorhm manage o reduce he parcle sample sze. Keyords - Vehcle rackng; Parcle fler; Resamplng; Genec Algorhm I. ITRODUCTIO Recenly, he amoun of he on-road vehcles has been ncrease apparenly. Meanhle, he ncdens ha creaed by he users of he vehcle are also elevaed. Thus, vehcle rackng has dran he aenon among he researchers due o s numerous felds of applcaons such as raffc survellance and secury monorng sysem, advance drver asssan sysem (ADAS), road raffc conrol asssan sysem and navgaon sysem [1]. There s varous ypes of sensors have been mplemened n he vehcle rackng. In hs paper, he vdeo sensor has been chosen as he meda used for processng due o he developmen of he vdeo survellance nfrasrucure has been groh vasly n recen years. Moreover, vdeo sensors also can provde a de range of nformaon ha used o descrbe he vehcle. For nsance, he feaures vehcle such as colour, shape, edge and moon can be obaned by exrac he daa from he vdeo sensor va mage processng echnques. Besdes ha, due o he hgh congeson of he raffc flo [], he occluson and overlappng ll become he common scenaro. Furhermore, occluson and overlappng beeen vehcles s a challengng ask n survellance sysem va vdeo sensor. Thus, he complexy and dffcules cause by he occluson problems has become he drvng force o he researchers o sudy and develop an ecve and cen vehcle rackng algorhm. Vehcle rackng could lead o non-lnear and non- Gaussan suaons due o he dynamc changes of he vehcle flo. Thus, parcle fler has been chosen n hs research due o s ably o deal h non-lnear and non- Gaussan suaons. Alhough, parcle fler has he ably o overcome he dynamc changes problems. Hoever, parcle fler ll undergo parcle degeneracy afer a fe eraon of processng. everheless, parcle degeneracy problem can be solved by mplemen a huge amoun of parcles hoever s alays mpraccal due o he compuaonal complexy. Thus, an cen and ecve resamplng approach ll be requred o solve he parcle degeneracy problem. Therefore, an enhancemen of he parcle fler resamplng algorhm ll be mplemened o rack he arge vehcle under overlappng suaons. II. REVIEWS OF OBJECT TRACKIG Throughou he leraure, here are many dfferen algorhms have been developed for objec rackng purpose. For nsance, he echnques such as Kalman fler, Markov Chan Mone Carlo, opcal flo and parcle fler are he ell knon objec rackng echnques. Alhough here are many ype of objec rackng algorhm, each of he echnques have he pros and cons. For example, Kalman fler s a frameork for esmang he objec sae and usng he measuremens o updae he sae esmaon. Hence, Kalman fler s ac an esmaor ha predcs and correcs he saes of lnear process [3]. To solve he non-lnear case, he exended verson of Kalman fler can be mplemened o change he measuremen relaon of he curren esmae become lnear [4]. Hoever, hen he nonlneary s naccuraely approxmaed by he algorhm, he esmaed resuls ll be dverged and hence lead o an naccurae rackng resul. Moreover, Markov Chan Mone Carlo s one of he echnques ha mplemened for vehcle rackng purpose. Hoever, he sample sze mplemened n he algorhm as an ssue because a non-opmal sample sze ll affec he rackng accuracy [5]. Alhough he algorhm as able o rack he overlapped vehcle h adapve sample sze bu /1 $ IEEE DOI /EMS

2 he algorhm sll unsable and have some rackng resul errors. Besdes ha, opcal flo also s a ell knon echnque ha used for objec rackng. In research [6], he opcal flo as used o deec and rack he movng arge. Hoever, he opcal flo as reflecs o he moon feld of he capured mage. Thus, hen here as overlappng occurred, he opcal flo could hardly locae he arge objec or mslead by he obsacles. Hence, parcle fler has been chosen as he rackng algorhm n hs sudy because s a promsng echnque ha can deal h non-lnear suaons [7, 8]. In research [9], he convenonal parcle fler ll faced he parcle degeneracy durng he rackng process. The occurrence of parcle degeneracy s because he lo egh parcles ere seleced afer a fe eraons and hence blocks he furher mprovemen of he algorhm. In research [10], saes ha he parcle degeneracy can be solved by mplemen a huge amoun of parcles n he algorhm or by resamplng he parcles. Moreover, mplemen huge amoun of parcles s alays mpraccal due o he hgh compuaonal. Thus, resamplng he parcles becomes he suable soluon o deal h he degeneracy problem [11]. Besdes ha, he colour feaure as mplemened n research [10, 1] o rack he vehcle and non-rgd objecs. From he resuls shon, he algorhm h colour feaure can accuraely rack he vehcle because colour feaure as srong o deal h paral occluson, scale nvarans and roaon occurrence. Hoever, he colour feaure ll have he lmaon hen he background s cluered or he colour of he background smlar h he arge. Furhermore, n research [13] have been shos ha he rackng algorhm h mulple feaures ll provde a more accurae rackng resuls. Thus, n hs sudy a mulple feaures of parcle fler h genec operaor resamplng algorhm has been proposed. The expermenal resuls sho ha h hs genec operaor resamplng algorhm, he arge objec can be racked h more accurae under varous occluson ncdens. III. PARTICLE FILTER FRAMEWORK Parcle fler also knon as sequenal Mone Carlo s a mansream rackng echnque o represen he propagaon condonal densy dsrbuons hen he observaon probably densy dsrbuons nvolved n he process are non-lnear and non-gaussan. Moreover, parcle fler algorhm s developed based on approxmaes he curren sae of he arge vehcle by usng prevous observaons sae. In vsual rackng, he observaon sae of he arge s normally referred o he colour, edge, shape, exure and ec. hch can characerze he arge objec. In hs sudy, he colour feaure and he shape feaure has been seleced as he feaures o descrbe he arge vehcle model. In general, parcle fler approach s funconng based on hree mporan sages hch are predcon sage, measuremen sage and follo by resamplng sage. In he predcon sage, a se of parcles hch represen he sae ranson of he vehcle model ll be generaed. Moreover, he measuremen sage s he sage ha compues he egh for he parcles based on he lkelhood measuremen. In addon, resamplng sage s o avod he parcle degeneracy problems occur. In hs sudy, parcle fler as developed o rack vehcle n dynamc changes. Hence, he poseror probably densy funcon p( Z ) and he observaon probably densy funcon p( Z ) compued n parcle fler algorhm are ofen non-gaussan. From he poseror probably densy funcon, he sae vecor denoes sae space of he racked vehcle. Meanhle, Z denoes all he esmaons sae space. As saed earler, he man dea of parcle fler s o approxmae he poseror dsrbuon base on a fne se of random eghed samples or knon as parcles p. In addon, each eghed parcles are dran o represen he sae esmaon of he arge vehcle accordng o he poseror dsrbuon as shon n (1) here x denoes he sae of he arge vehcle and denoes he egh ha assocae o he parcle. Snce s he egh ha assgn o each parcle hence he lm for each egh of he parcle s [0,1]. The hole se of parcles egh should able normalzed and sum up o one as shon n ()., W 1,,3 p S,..., p 1 (1) 1 () A. Predcon Sage Predcon sage s he prmary sage ha naes sample parcles. Each parcle s represens he esmaed poseror poson ndvdually. Hoever, h he mplemen a large amoun of sample parcles, he accuracy o esmae he sae of he arge vehcle ll be ncrease. Unforunaely, by mplemen he large amoun of he sample parcles for esmaon process, he compuaonal cos ll be hghly expensve and vce versa for he leas amoun of parcles mplemen. In he predcon sage, he pror probably densy funcon can be obaned hrough (3). Based on he pror probably densy funcon obaned, he poseror probably densy funcon can be compued hrough he updaed sage by usng he Bayers rule as shon n (4). p (3) ( Z1 : 1) p( 1) p( 1 Z1: 1) d

3 p( Z ) p( Z1: 1) p ( Z1: ) (4) p( Z Z ) B. Measuremen Sage 1: 1 In measuremen sage, he egh of each parcle s compued based on he lkelhood probably from he feaures of arge vehcle. Hence, he observaon sae of he arge vehcle can be colour, shape, edge or exure ha exrac from he model of he arge vehcle. When he feaures of he arge vehcle have been exraced, he measuremen lkelhood needs o compue accordngly. In hs sudy, he egh of he parcles ll be compued based on shape and colour feaures lkelhood. I uses o compue he egh of he parcles based on he smlary hsogram of he arge vehcle and he reference vehcle model. The colour lkelhood s compued usng equaon n (5) and he shape lkelhood s compued usng equaon (6) here n (5) and (6) s he adjusable sandard devaon hch can be chosen expermenally. b 1 ds e. c (5) H 1 ds e s (6) The colour lkelhood s deermned by usng Bhaacharyya dsance, b ds [14] hereas shape lkelhood s deermned by usng Hausdorff dsance, H ds [15]. The value of dsance ll become smaller f he arge vehcle s smlar h he reference vehcle and vce versa. Boh of he lkelhood ll combne ogeher o compue he egh of he parcles as shon n (7) here s he egh consan. ) (1 )( ) (7) ( c s Afer lkelhood s compued, he egh for he parcle ll be updang as shon n (8) here q( 1, Z ) s he proposal dsrbuon. p( Z ) p( 1) 1 (8) q(, Z ) 1 Afer he egh for he parcle s updaed, he egh of he parcles ll undergo egh normalzaon as shon n (9) before he predcve poseror densy funcon s approxmaed. In he parcle fler algorhm, he poseror probably densy funcon compued from he pror densy funcon s represened by a se of eghed parcles. Furhermore, he egh of he parcles s compued n dscree naure. Hence, he poseror densy funcon can be obaned hrough (10). W p 1 p 1 (9) p( Z1 : ) W ( ( )) (10) When he predcve poseror dsrbuon for each parcle s obaned, he parcle fler algorhm ll ener he fnal sep. In he fnal sep, he poson of he arge vehcle ll be esmaed by akng he mean of he predced sae. For nsance, he mean sae of he arge vehcle can be calculaed by usng (11) here S s shon n (1). p 1 E( ) S (11) p 1 C. Resamplng Sage Alhough he poson of he arge vehcle can be predced hou he resamplng sage, hoever he resul obaned s no convncng afer a fe eraon. Ths s because parcle fler ll face an nheren problem hch s parcle degeneracy. When parcle degeneracy problem occur, one parcle ll experence neglgble egh because he varance of he mporan egh ll ncrease over me. The parcle degeneracy s denoes ha a huge compuaon or s needed o updae parcles hose he egh conrbue o he sae approxmaon s almos zero. Hence, he parcle degeneracy problem s canno avod bu can be solved by resamplng or mplemen a huge amoun of parcles. Implemen a huge amoun of parcles s alays mpraccal due o he hgh compuaonal. Hence, resamplng s he bes soluon o overcome he parcle degeneracy problem. Resamplng sage should apply a he begnnng of eraon, by elmnang hose lo egh parcles and only concenrang on hose hgh egh parcles. The resamplng s normally appled by replacemen bass. Ths means ha a ne se of parcles ll be defned o replace hose elmnaed parcles. In order o deermne he occurrence of he parcle degeneracy problem, he ecve sample szes need o be compued by usng (1). From (1), he egh s referred as he rue egh as shon n (13). everheless, he rue egh s very hard o compue exacly. Thus, an esmae of ecve sample szes can be obaned hrough (14) here s he normalsed egh. 3 45

4 oce ha f * ^ p (1) * 1Var( ) p( x z1: ) (13) q( x x, z ) s ( ) s small or hres (14), hch means he parcle degeneracy problem s occurred and resamplng s requred. Hence, he parcle fler ll be recursvely repeang he predcon sage and measuremen sage unl he soppng crera as fulfl. As a resul, resamplng s akng an mporan role n he parcle fler algorhm n order o oban an accurae rackng resul. IV. PROPOSED GEETIC OPERATOR RESAMPLIG The convenonal resamplng sep can reduce he ec of parcle degeneracy bu unforunaely ll creae anoher praccal problem. The problem creaed as knon as sample mpovershmen. Sample mpovershmen ll occurred hen he parcles h heavy egh are sascally seleced many mes. Thus, he esmaed poseror sae ll conan many repeaed locaons and lead o loss of dversy among he parcles. Afer a fe eraons, all he parcles ll collapse o a sngle poson and hence he algorhm ll unable o connuously rack he arge vehcle. In order o avod he parcles dversy, genec operaor ll mplemen n he parcle fler resamplng algorhm. In order o generae a good qualy chldren soluon, he selecon of he parens for crossover as became an mporan sep. Selecon s used o mprove he qualy of he populaon by gvng ndvduals of hgher qualy o generae ne offsprng or knon as chldren. By mplemen rank selecon, he parcles ll be gven a rank accordng o he egh of he lkelhood compued. The mos heavy parcles ll assgn h hgher rank hle he lgher egh parcles ll assgn h loer rank. Afer all he parcles have been ranked, he algorhm ll be randomly selec o parcles as he frs paren and he second paren. Snce he heavy egh parcle has been assgned h hgher rank, and hence he chances for he heavy egh parcle beng seleced as he paren ll be hgher. In hs research, he paren as represens he poson of he arge vehcle. Afer performed he rank selecon, he nex sep ll be crossover process. In hs sudy, arhmec crossover ll be mplemened n he parcle fler resamplng algorhm. The advanage of arhmec crossover as alays produces feasble chldren by conanng boh parens characersc. The chldren generaed by usng arhmec crossover ere shon n (15) and (16). C 1 P1 P(1 ) (15) C P P1 (1 ) (16) here s a egh facor h a lm of zero o one, P1 and P as he paren soluons and C1 and C are he chldren soluons. The egh facor s used o deermne he fracon of characersc from paren soluons conrbue o he chldren soluons. In hs sudy, he egh facor as se as 0.7 hch means he frs chldren ll preserve mos of he frs paren characersc meanhle second chldren soluon ll preserve mos of he second paren characersc. By applyng arhmec crossover n he parcle fler resamplng algorhm, he lo egh parcles ll be elmnaed frs meanhle he heavy egh parcles ll be preserved. Hence, arhmec crossover operaor ll generae he chldren soluon o replace hose elmnaed lo egh parcles. By usng arhmec crossover he esmaed poson for he arge vehcle ll be converge o he real poson. Hence, a more accurae rackng resul can be compued. Afer he genec crossover process, he chldren soluons ll undergo muaon process. Muaon operaor s a process o manan he genec dversy from one generaon o he nex generaon. Besdes ha, he muaon operaor also acs as a fnal checkng sae o recover he good nformaon hch mgh be los durng selecon and crossover sages. Muaon as played an mporan par n he genec algorhm o preven he populaon sagnang a he opmal poson. Muaon occurs durng evoluon accordng o he muaon rae defned by he user. Furhermore, he muaon rae needs o be se farly lo. In hs research, he muaon rae as se as 1 percen n order o avod he loss of f soluons and affec he convergence of soluons. If he muaon rae as h, a ne chldren ll be generaed h he poson esmaed add h a random number h he lm of zero o one. The developmen of genec operaor n parcle fler resamplng algorhm ll llusrae n Table I. V. RESULT AD DISCUSSIO In hs secon, he resul of vehcle rackng usng convenonal resamplng (Fg. 1) ll be compared o he resul of vehcle rackng usng a genec operaor resamplng algorhm (Fg. ). In boh cases, he parcle sze as nalzed as 00 parcles. As shon n Fg. 1 and Fg., he cross symbol s represens he esmaed poson of he vehcle. Meanhle he red colour sold boundary box s ndcaes he locaon of he arge vehcle. The arge localzaon as deermned by he mean value of he esmaed poson of he parcle. Referrng o Fg. 1 and Fg., he rackng can caegorze no four suaons, such as before occluson, parally occluson, fully occluson and afer occluson. From he sequence of resuls shon n Fg. 1 and Fg., he genec operaor resamplng provde a more promsng and accurae rackng resul

5 TABLE I. PROPOSED GEETIC OPERATOR RESAMPLIG ALGORITHM 1: MEASUREMET & WEIGHT UPDATE: : Compue he egh of he parcle 3: Summaon of parcle egh 4: ormalze he egh 5: Calculae 6: hres Resamplng hres Accepance 7: RESAMPLIG: 8: Performed Rank Selecon 9: Arhmec Crossover 10: Generae muaon rae 11: IF muaon < 1% 1: rand(0,1) 13: ELSE 14: 15: ED IF 16: LOCALIZATIO: 17: x, y) E( ) ( In case 1, he arge vehcle as free of occluson as shon a Frame 5 n Fg. 1 and Fg..The resuls obaned shos ha he arge vehcle as accuraely beng racked by he convenonal and genec operaor resamplng algorhm. Ths s because before occluson, he nformaon used o descrbe he arge vehcle as clear and hou nfluence by he obsacles. In case, he arge vehcle as parally occluded by anoher movng vehcle as shon a Frame 1 n Fg. 1 and Fg.. From he resuls shon, he convenonal resamplng as merely racks he arge vehcle. Ths s due o he nformaon of he arge vehcle has been nfluenced by he movng vehcle. Hoever, he arge vehcle sll able beng racked by usng genec operaor resamplng alhough here are appearance of anoher vehcle. In case 3, he arge vehcle as fully occluded by he movng vehcle as llusraed a Frame 33 n Fg. 1 and Fg.. From he resuls obaned, he convenonal resamplng as unable o esmae he locaon of he arge vehcle because he nformaon of he arge vehcle has been los. Meanhle, he genec operaor resamplng as able o locae he arge vehcle. In case 4, he arge vehcle as afer occluded by he movng vehcle. A Frame 41 and Frame 49 n Fg. 1 and Fg., he arge vehcle as reappeared afer occluson. The convenonal resamplng algorhm as merely rack he arge vehcle. Hoever, he genec operaor resamplng as accuraely resume he rackng process. The nformaon of he arge vehcle as nfluenced by he movng vehcle. Hence, he convenonal resamplng ll requre more me o gan back he nformaon of he arge vehcle. Hoever, (a) Frame 5 (b) Frame 1 (c) Frame 33 (d) Frame 41 (e) Frame 49 Fgure 1. Resul of vehcle rackng by usng convenonal resamplng. (a) Frame 5 (b) Frame 1 (c) Frame 33 (d) Frame 41 (e) Frame 49 Fgure. Resul of vehcle rackng by usng proposed genec operaor resamplng algorhm

6 he genec operaor resamplng as able recover he nformaon n shor duraon. The RMSE of he convenonal resamplng and he developed genec operaor resamplng s ploed as shon n Fg. 3. From he resuls obaned, as clearly shos ha he RMSE for he genec operaor resamplng as loer han he RMSE for he convenonal resamplng. Hence, can conclude ha he mproved resamplng as gvng a hgher accuracy n rackng vehcle under occluson suaons. VI. COCLUSIO As menoned earler, he accuracy of he parcle fler could dmnsh by parcle degeneracy. Thus, resamplng as played an mporan role n he algorhm. Alhough, he convenonal resamplng able o rack he arge vehcle hen before occluson. Unforunaely, as unable o connuously and accuraely rack he arge vehcle afer occluson. Thus, he mplemenaon of he genec operaor resamplng algorhm s capable o allevae he rackng dffcules under varous occluson suaons. From he resuls shon, he performance and robusness of he proposed resamplng algorhm as promsng and esed under dfferen rackng condons. Hence, can conclude ha he proposed resamplng algorhm has been mproved he accuracy of he rackng resuls. ACKOWLEDGEMET The auhors ould lke o acknoledge he fnancal asssance from Mnsry of Hgher Educaon of Malaysa (MoHE) under Exploraory Research Gran Scheme (ERGS) o. ERGS001-TK-1/01, Unvers Malaysa Sabah (UMS) under UMS Research Gran Scheme (SGPUMS) o. SBK006-TK-1/01, and he Unversy Posgraduae Research Scholarshp Scheme (PGD) by Mnsry of Scence, Technology and Innovaon of Malaysa (MOSTI). Fgure 3. Graph of RMSE vs frame ndex for convenonal resamplng and genec operaor resamplng. REFERECES [1] F. Gusafsson, F. Gunnarsson,. Bergman, U. Forsell, J. Jansson, R. Karlsson and P.J. ordlund. Parcle Flers for Posonng, avgaon, and Trackng. IEEE Transacon on Sgnal Processng, vol. 50, no.., pp , 00, do: / [] Y.K. Chn,. Bolong, A. Krng, S.S. Yang and K.T.K. Teo. Q- Learnng Based Traffc Opmzaon n Managemen of Sgnal Tmng Plan. Inernaonal Journal of Smulaon, Sysems, Scence & Technology, vol. 1, no. 3, pp. 9-35, 011, ISS: prn. [3]. L, K.Wang, W. Wang and Y. L. A Mulple Objec Trackng Mehod Usng Kalman Fler. In Proceedngs of Inernaonal Conference on Informaon and Auomaon, 010, pp , do: /ICIFA [4] M. abaee, A. Pooyafard and A. Olfa. Enhanced Objec Trackng h Receved Sgnal Srengh usng Kalman Fler n Sensor eorks. In Proceedns of Inernaonal Symposum on Telecommuncaons, 008, pp , do: /ISTEL [5] W.Y. Ko, W.L. Khong, Y.K Chn, I. Saad and K.T.K. Teo. CUSUM-Varance Rao Based Markov Chan Mone Carlo Algorhm n Overlapped Vehcle Trackng. In Proceedngs of Inernaonal Conference on Compuer Applcaons and Indusral Elecroncs, 011, pp , do: /ICCAIE [6] Y. Fang and B. Da. An Improved Movng Targe Deecng and Trackng Based on Opcal Flo Technque and Kalman Fler, In Proceedngs of 4 h Inernaonal Conference on Compuer Scence & Educaon, 009, pp , do: /ICCSE [7] M.S. Arulampalam, S. Maskell,. Gordon and T. Clapp. A Tuoral on Parcle Fler for Onlne onlnear/on-gaussan Bayesan Trackng, IEEE Transacon on Sgnal Processng, vol. 50, no., pp , 00, do: / [8] H.P. Lu, F.C. Sun, L.P. Yu and K.Z. He. Vehcle Trackng usng Sochasc Fuson-based Parcle Fler. In Proceedngs of IEEE/RSJ Inernaonal Conference on Inellgen Robos and Sysems, 007, pp , do: /IROS [9] H. L, Y. Wu and H. Lu. Vsual Trackng Usng Parcle Flers h Gaussan Process Regresson. Sprnger-Verlah Berln Hedelberg on Advances n Image and Vdeo Technology, PSIVT 009, LCS 5414, 009, pp , do: / _3. [10] W.L. Khong, W.Y. Ko, L. Angelne, I. Saad and K.T.K. Teo. Overlapped Vehcle Trackng va Enhancemen of Parcle Fler h Adapve Resamplng Algorhm. Inernaonal Journal of Smulaon, Sysems, Scence & Technology, vol. 1, no. 3, pp , 011, ISS: prn. [11]. Fu and Y. Ja. An Improvemen on Resamplng Algorhm of Parcle Fler, IEEE Transacon on Sgnal Processng, vol. 58, no.10, pp , 010, do: /TSP [1] K. ummaro, E. Koller-meer and L.V. Gool. Colour Feaures for Trackng on-rgd Objecs, Specal Issue on Vdeo Survellance Chnese Jornal of Auomaon, vol. 9, pp , 003. [13] W.L. Khong, W.Y. Ko, Y.K. Chn, I. Saad and K.T.K. Teo. Overlappng Vehcle Trackng va Adapve Parcle Fler h Mulple Cues. In Proceedngs of Inernaonal Conference on Conrol Sysem, Compung and Engneerng, 011, pp , do: /ICCSCE [14] M.S. Khald, M.U. Ilyas, M.S. Sarfaraz, and M.A. Ajaz. Bhaacharyya Cocen n Correlaon of Gray-Scale Objecs, Journal of Mulmeda, vol.1 no. 1, pp , 006. [15] S.C. Park, S.H. Lm, B.K. Sn, and S.W. Lee. Trackng non-rgd Objecs usng Probablsc Hausdorff Dsance Machng, Journal of Paern Recognon, vol. 38 no. 1, pp , 005, do: /j.pacog