Tracking Appearances with Occlusions

Transcription

1 Tracking ppearances wih Occlusions Ying Wu, Ting Yu, Gang Hua Deparmen of Elecrical & Compuer Engineering Norhwesern Universiy 2145 Sheridan oad, Evanson, IL bsrac Occlusion is a difficul problem for appearance-based arge racking, especially when we need o rack muliple arges simulaneously and mainain he arge ideniies during racking. To cope wih he occlusion problem explicily, his paper proposes a dynamic ayesian nework which accommodaes an exra hidden process for occlusion and sipulaes he condiions on which he image observaion likelihood is calculaed. The saisical inference of such a hidden process can reveal he occlusion relaions among differen arges, which makes he racker more robus agains parial even complee occlusions. In addiion, considering he fac ha arge appearances change wih views, anoher generaive model for muliple view represenaion is proposed by adding a swiching variable o selec from differen view emplaes. The inegraion of he occlusion model and muliple view model resuls in a complex dynamic ayesian nework, where exra hidden processes describe he swich of arges emplaes, he arges dynamics, and he occlusions among differen arges. The racking and inferencing algorihms are implemened by he sampling-based sequenial Mone Carlo sraegies. Our experimens show he effeciveness of he proposed probabilisic models and he algorihms. 1 Inroducion Tracking arges based on heir appearances play an imporan role in many applicaions such as inelligen human compuer ineracion and video surveillance. For example, before he deailed facial moion can be recovered and before he human ideniies can be recognized, we need o locae and rack faces in video sequences. n effecive way is hrough maching and racking face appearances. Since image appearances provide more comprehensive visual informaion o represen he arges, e.g., he faces, appearancebased racking mehods receive more and more aenion. However, if a arge is parially or compleely occluded, is visual appearance would dramaically deviae from is appearance emplae as we se for racking. Thus, occlusion becomes a special and difficul problem for appearancebased racking. In addiion, if we are concerned abou muliple arges, explici handling of occlusion is indispensable for racking, since occlusion would probably occur when differen arges inerac. This paper addresses he occlusion problem in he muliple arge racking scenario. Differen from oher works on racking muliple arges, his paper aims a solving he occlusion relaionships besides keeping he rajecories. Our mehod is based on a dynamic ayesian nework which models he occlusion process explicily. This model consiss of muliple hidden Markov processes: he dynamics of each individual arge, and he process of he occlusion relaion. In addiion, he model describes he formaion (or generaion) of he image observaions, joinly condiioned on he arges saes and heir occlusion relaions. Then, racking is o infer he saes of all hese hidden Markov chains based on he sequence of image observaions. In addiion, we invesigae wo represenaions for he appearances: i.e., single view and muliple views. The single view appearance is represened by an appearance emplae associaed wih a ransformaion ha depics he moion and deformaion of he emplae. Since he appearances change wih views, we exend his view+ransformaion represenaion o he muliple view case, by swiching among a se of emplaes and ransformaions. This mechanism is also modelled by a generaive model which conains a hidden swiching process. The combinaion of he occlusion modelling and he muliple view represenaion resuls in a mulilevel dynamic ayesian nework. Due o he complexiy in he srucure of he generaive model, he inference of he model is approximaed by he sampling-based sequenial Mone Carlo sraegies. Various es sequences showed he effeciveness of his approach o handle he occlusion siuaions. The proposed approach accommodaes he inference of he occlusion relaions of muliple arges and he swich of muliple views ino a probabilisic racking framework. No limied o muliple face racking, he proposed generaive model is general and valid for many racking scenarios which need o handle occlusion explicily. The paper is organized as follows. Secion 3 presens he Proceedings of he 2003 IEEE Compuer Sociey Conference on Compuer Vision and Paern ecogniion (CVP 03)

2 dynamic ayesian nework for occlusion. The sequenial Mone Carlo sraegy is described in Secion 4. Secion 5 presens he muliple view appearance model. The generaive model ha combines he occlusion model and muliple view swiching can also be found in Secion 5. Experimens are given in Secion 6 and conclusions are in Secion 7. 2 Previous Work The arge represenaions affec he effeciveness and efficiency of racking algorihms. Many approaches have been sudied based on differen arge represenaions, e.g., image appearances [2, 3, 6, 9, 17] and geomerical shapes [1, 7, 15]. Shape-based approaches are concerned abou he maching beween shape models and image feaures. They need o deal wih more ambiguiies in racking bu are less sensiive o lighing. On he oher hand, since massive image appearance daa conain very rich informaion for characerizing arges, appearance-based mehods would no be sensiive o image resoluions, bu special aenion needs o be aken for deformaion and lighing. Many differen ypes of appearance models have been invesigaed, such as color appearances [3], eigen appearances [2], exure appearances [9], layered image emplae appearances [17], and he appearances combining image emplae and lighing [6]. ll of hese models parameerize he appearances for arge represenaions. Tracking arges includes he esimaion of hese parameers. There are wo mehodologies o his problem: boom-up and op-down. The boom-up approaches generally formulae he problem as nonlinear opimizaion problems which minimize some error funcions, e.g., flow residue [2, 6] and color discrepancy [3]. On he oher hand, he op-down approaches adop he idea of analysis-by-synhesis, by direcly verifying pleny of hypoheses [7, 15]. Mos boom-up algorihms are compuaionally more efficien, bu hey are subjec o he validaion of he small moion assumpion, and i is hard for hem o cope wih occlusions unless he appearance model iself is robus agains occlusions. On he oher hand, mos op-down algorihms involve more compuaion, bu he moion esimaion ends o be more accurae and more robus. In addiion, occlusion can be modelled from op-down in he same framework. The generaive model approaches ake a op-down mehodology, by modelling he hidden facors ha would affec he observed daa [10]. Once he srucure and he parameers of he model are se, hose hidden facors can be inferred and he parameers can be learn from he daa. s a special case, dynamic ayesian neworks model dynamic sysems and emporal signals [16]. The inference of he neworks provides racking resuls direcly. To rack muliple appearances wih occlusions, his paper describes a class of dynamic ayesian neworks ha accommodaes he hidden process of occlusion and model he swiching of he appearance emplaes of muliple views. 3 Generaive Model for Occlusion We ake a view+ransformaion approach o represen he sae of a arge, which consis of an appearance emplae T and a ransformaion H. The emplae T can be any kind of emplaes, such as an image emplae, an edge map emplae, or a exure emplae. The ransformaion H can be an affine ransformaion or a homography ransformaion. To make he descripion clearer, we limi he descripion o he siuaion of racking wo arges (i.e., and ). We denoe he arge sae of arge k a ime by k. The racking ask is o infer and based on all he observed image evidence = { 1,, }, where is he image measuremen (or observaion) a ime, i.e., o esimae p( )=p((, ) ), where =(, ). We are concerned abou he occlusions beween hese arges, i.e., a arge is occluded by a known objec. This paper does no invesigae a more challenging siuaion where he arge is occluded by a compleely unknown objec, since no clue from he occluding objec can be used for occlusion deecion. u i will be par of our fuure work. The racking process can be viewed as he densiy propagaion [7] from p( 1 1 ) o p( ), and i is governed by he dynamic model p( +1 ) and he observaion model p( ), since we have p( ) p( ) p( 1 )p( 1 1 )d 1 In addiion, since he moion of wo arges are independen, we have p( 1 )=p( 1)p( 1). Then we have p( ) p(, ) p( 1) p( 1)p( 1 1 )d 1 If here is no occlusion beween and, he observaion likelihood p(, ) can be uniquely deermined. However, when one arge occludes he oher, he occlusion relaion has o be known before he likelihood can be uniquely calculaed, i.e., he likelihood should be condiioned on he occlusion relaions addiionally. Le {0, 1, 2} denoe he occlusion relaion, i.e., =0 indicaes no occlusion, =1indicaes, and =2 indicaes, where means occludes. Then based on he join likelihood p(,, ),wehave p(, ) p(,, ) p( 1) p( 1)p( 1 )p( 1, 1 1 )d 1 (1) where p( 1 ) describes he ransiion of occlusion relaion. Thus, based on Equaion 1, he probabilisic dynamic sysem can be illusraed by a facorized graphical model (a facorized dynamic ayesian nework) in Figure 1. Proceedings of he 2003 IEEE Compuer Sociey Conference on Compuer Vision and Paern ecogniion (CVP 03)

3 O T T T Figure 1: hidden process { } is accommodaed in he dynamic ayesian nework o presen he occlusion relaionships. The poserior densiy of occlusion can be obained hrough inegraing ou and from he join poserior probabiliy, i.e., p( )= p(,, )d d (2) s a generaive model, his dynamic ayesian nework models he forwarding process of image formaion. In he graphical model, here are hree hidden Markov processes, { }, { } and { }, which are o be inferred from he observaion daa, based on all he condiional probabiliies as illusraed by arrows in he graph. Specifically, o characerize he model, we need o model he dynamics of he wo arges p( 1) and p( 1), he ransiion model p( 1 ) of he occlusion process { }, and he observaion likelihood p(,, ). We employ a consan velociy model for he arge dynamics p( k k 1),k {, }. In addiion, he ransiion p( 1 ) of he occlusion process is described by a finie sae machine, i.e., T =[T (i, j)] = [p( = j 1 = i)]. The observaion likelihood p(,, ) is modelled based on he innovaions, i.e, he discrepancies beween he prediced appearance and he acual image observaions. Denoe he prediced region of he k-h arge a ime by k = ( k ). Then, he prediced region of is he union of wo arges, i.e., = ( )=((, )) = The acual image appearance observaion is colleced on he prediced region and denoed by I( ). Denoe he predicaed appearance by T = T (,, ) which depends on he value of. s illusraed in Figure 2, we denoe he overlapping region of he wo arges by O = O( )=O((, )) = which is independen of. Then, u, T ( (u)), u O T (u) = T ( (u)), u O T C ( C (u)), u O Figure 2: The occlusion relaions of =1. where u is a pixel locaion in a region, and C indicaes he occluding arge, i.e., φ, =0 C = C( )=, =1, =2 Then, he observaion likelihood is modelled by: [ ] u p(, ) exp D(T (u),i (u)) M( ) where M( ) is he number of pixels in he region, and D(T (u),i (u)) = T (u) I (u) 2. Specially aenion should be aken for he case where one arge is fully occluded by he oher one as illusraed in Figure 3, since no image evidence can be used o suppor he exisence of he fully occluded arge. Consequenly, he racker would no be able o follow he occluded arge again. Under his circumsance, he regain of racking he =O Figure 3: Targe is fully occluded by. fully occluded arge would depends on moion predicion of arge and he deecion around he border of he occluding arge. Such a mechanism can be implemened by reducing he likelihood of he full occlusion evens. Then, we have p(, ) exp [ H(,, )], where H(,, )= u T T (3) D(T (u),i (u)) + u D(T (u),i (u)) M( )+M( ) (4) 4 Sequenial Mone Carlo Tracking The densely-conneced srucure of he facorized graphical model as shown in Figure 1 is complex. The srucure variaional analysis can be aken o analyze he graphical model [11]. nalyical resuls of a se of fixed-poin equaions were obained based on some simplificaions such as Proceedings of he 2003 IEEE Compuer Sociey Conference on Compuer Vision and Paern ecogniion (CVP 03)

4 linear observaion likelihood [5, 11]. In addiion, he fixedpoin equaions reveal a co-inference phenomenon [19]. However, in general, he exac probabilisic inference of he hidden processes would be very difficul especially when he observaion likelihood is complicaed. On he oher hand, saisical sequenial Mone Carlo sraegies provide a compuaional approach o his problem [4, 13, 14], in which a probabiliy densiy is approximaed by a se of weighed paricles. The evoluion of he se of paricles according o he dynamic ayesian nework characerizes he behavior of he dynamic sysem, and he hidden processes can be recovered from he se of paricles. Many paricle-based algorihms have been sudied for visual racking [7, 15, 19]. We ake a sequenial Mone Carlo approach o inferencing he facorized dynamic ayesian nework in Figure 1. The poserior densiy p(,, ) is represened by a se of weighed paricles {x,(n),x,(n), (n), }. The sampling-based algorihm is summarized in Figure 4. Generae {x,(n) +1,x,(n) +1,(n) x,(n), (n), }. +1,π(n) e-sampling. esample he paricle se {x,(n) produce {x,(n),x,(n), (n) 2. Predicion. For each (x,(n) } from {x,(n), } o } based on { }.,x,(n), (n),x,(n), (n) ): (a) sample he densiy of he arge dynamics p(x +1 x ) o produce x,(n) +1 from x,(n) ; (b) sample he arge dynamics p(x +1 x ) o produce x,(n) +1 from x,(n) ; (c) sample he finie sae machine T of p( +1 ) o produce (n) +1 from (n). 3. Correcion. e-weigh each paricle by calculaing he likelihood +1 = p( +1 x,(n) +1,x,(n) +1,(n) +1 ). Then normalize all he new weighs o 1. Figure 4: The sequenial Mone Carlo algorihm for he facorized dynamic ayesian nework in Figure 1. ased on he weighed paricle se a each ime insan, we obain he esimaion of he hidden saes: ˆ k = n ˆ = arg max x k,(n), k = {, }, (n) =, = {0, 1, 2}. 5 Swiching Muliple Views Mos appearance-based mehods are sensiive o view changes and large deformaions, since appearances are view-based. Subspace-based echniques can be employed o learn he appearance-based represenaions which are robus o views [12] and large appearance changes [2]. These represenaions are suiable for arge deecion and recogniion, bu he dimensionaliy of he subspace is high for he racking asks. To model view changes, we simplify he subspace-based approaches, and represen a arge by mainaining a finie se of examplar view emplaes, each of which is associaed wih a ransformaion, i.e.,{(t 1,H 1 ),,(T V,H V )}. Denoe an indicaor variable by {1,, V}. Our represenaion sipulaes ha he whole se of appearances under differen views can be divided ino a se of nonoverlapped subses represened by (T,H ). In oher words, for any appearance, a unique view emplae T and a suiable ransformaion exis. This mehod exends he view+ransoformaion approach o a swich view+ransformaion represenaion in he spiri of he Toyama and lake s examplar-based racking [18]. This represenaion is differen from subspace represenaions. In subspace mehods, since an appearance is modelled by a linear/nonlinear combinaion of a se of appearance basis, he mehods are global. On he oher hand, our swich view+ransformaion approach idenifies a specific mode (alhough i is a special case of linear combinaion), and i is local, like a piece-wise spline in he appearance space. Thus, our approach uses a swich o swich among differen modes or views emplaes Figure 5: discree hidden process { } is used o swich among differen views of he arge. ccommodaing his swiching view represenaion in he generaive model, he dynamic ayesian ne for a signal arge can be illusraed in Figure 5, where { } is he hidden process, and we have p( +1, +1, )=p( +1, +1)p( +1 ) where p( +1, +1) describes he swich of view emplaes and is dynamics, and p( +1 ) models he ransiion of he swich even which is sipulaed by a finie sae machine: +1 T =[T (i, j)] = [ p( = j 1 = i) ]. Proceedings of he 2003 IEEE Compuer Sociey Conference on Compuer Vision and Paern ecogniion (CVP 03)

5 lhough we can perform he srucure variaional analysis on his graphical model in Figure 5 (see [16]), a more flexible approach for inferencing is again he sequenial Mone Carlo sraegies. Similar o he mixed-sae CON- DENSTION [8], a paricle for he arge is represened as {x,(n),,(n), }. The evoluion of he se of paricles is generaed by he dynamic ayesian ne model. The esimae of he view is given by: ˆ = arg max ˆ = (n) = ˆ (n) = ; (5) x,(n). (6) Naurally, he combinaion of he occlusion model in Figure 1 and he model for swiching views in Figure 5 resuls in a new dynamic ayesian nework as illusraed in Figure 6, which models he occlusion of muliple arges as well as muliple views. Taking he sequenial Mone Carol Since he overlapping can be direcly calculaed once,(n) and,(n) are given, he uncerainy remained for occlusion variable is eiher =1or =2. Then he ransiion of { } is reduced o a wo-sae machine. In he experimen, we se T = p( j i )= [ ], i,j {1, 2}. (7) because we found he resuls were no sensiive o T. The racking resuls can be seen in occlusion.mpg 1. Some sample frames of he racking resuls are shown in Figure 7. In his experimen, he size of he paricle se was When he wo faces crossed, he racker proved o keep locking on he wo faces wih he righ ideniies, because he occlusion relaion was recovered during racking, which grealy helped o mainain he ideniies of differen arges. The occlusion was esimaed by maximizing he a poseriori in Equaion 5. The recovered occlusion process { } is shown in Figure 8. The esimaes of he occlusion Figure 6: hidden process { } conrols he occlusion relaions among differen arges and { k } swiches among differen views for he k-h arge, where k {, }. mehods similar as hose in previous secions, he inference of his dynamic ayesian ne is sraighforward. 6 Experimens The proposed mehods have been applied o he ask of racking wo moving and occluding faces. We repor he experimens in hree racking scenarios including occlusion, view changes and he combinaion of he wo. Our firs experimen was concerned abou he inference of occlusions induced by he ineracion of wo arges, and he generaive model in Figure 1 applied. In his case, he appearance of a face was represened by a single pre-rained view emplae of he face and an affine ransformaion. The racking ask was o esimae he affine parameers for boh emplaes as well as he occlusion relaion when he wo faces crossed. We employed wo ypes of view emplaes: one was he image emplae, and he oher was he exure emplae based on wavele ransformaions Figure 8: The recovered occlusion process { }. relaions were quie accurae, excep for he frames where he occlusion was abou o occur or abou o finish. u his phenomenon was reasonable since he occlusion relaions were weak and uncerain a hose ime insans. Since a face wen back and forh in fron of he oher face in he sequence, he occlusion evens =1occurred in wo ime inervals. This is clearly indicaed in Figure 8. Figure 9: The hree view emplaes used for he muliple appearances swiching. The second experimen was abou he muliple view model, and he generaive model in Figure 5 applied. The ask was o rack a single face bu he moion of he face conains ou-plane roaions, which resuled in muliple disinguishable views. In his experimen, we exploied hree view emplaes: one fron view, and wo profile views, wih hree homography ransformaions associaed wih each 1 ll resuls can be accessed from hp:// yingwu Proceedings of he 2003 IEEE Compuer Sociey Conference on Compuer Vision and Paern ecogniion (CVP 03)

6 Figure 7: Two faces are racked (in red or green) during he occlusion. One becomes dark if occluded. Their occlusion relaions are inferred and he ideniies of he wo faces are mainained. (See occlusion.mpg for deail.) emplae. The hree emplaes are shown in Figure 9. Here, = 1/2/3 denoes lef profile, fron and righ profile views, respecively. The ransiion of he view swiching process { } was a hree-sae FSM: T = p( j i )= (8) The resul for he single face wih muliple views is shown in he sequence muliview.mpg. Some sample frames are shown in Figure 10. The size of he paricle se in he sequenial Mone Carlo inference was When he face urned, he correc view emplae was auomaically seleced and he racker swiched o his view emplae and kep racking. Since he paricle se represens he densiy, i implicily keeps all he view hypoheses and he priors of hese hypoheses are propagaed from previous ime insans. The calculaion of he likelihood of he image observaion given hese view hypoheses can srenghen or weaken hese hypoheses. The one wih he maximum poserior probabiliy was seleced as he esimaion of he view emplae mode a each ime insan. The recovered process of mode swiching is shown in Figure 11. We see Figure 11: The recovered swiching process { }. clearly from his figure ha he person urns his head around when he moves. In he hird experimen, we racked wo faces under occlusion and muliple views, and he mehod in Figure 6 applied. The same as he second experimen, we used a hreeview emplaes wih homography ransformaions. nd T used Equaion 7, and T and T used Equaion 8. The sequence occlu muliview.mpg demonsraes he racking resul for he wo faces wih muliple views. Some sample frames are shown in Figure 12. Due o he complexiy of he dynamic ayesian ne in Figure 6 used in his experimen, more paricles are needed for effecive Mone Carlo. We used 4000 paricles o obain he resul. y accommodaing he processes of occlusion and view swiching, he racker needs o infer more hidden facors based on he image observaions, hus more compuaion is involved. u he payoff is huge: he racker becomes more robus and he recovered hidden facors provide quaniaive clues for evaluaing he racking performance online. 7 Discussion and Conclusions ppearance-based racking is useful in many applicaions such as face racking, bu is confroned by he problem of occlusion, especially when muliple appearances are concerned. This paper presens a generaive model o accommodae a hidden process of occlusion relaions among muliple arges. The likelihood of he image observaion is condiioned on he configuraion of he saes of muliple appearances as well as an occlusion relaion among hem. Graphically, such a generaive model is a facorized dynamic ayesian nework wih muliple hidden Markov chains. In addiion, his paper also presens a muliple view represenaion for appearances by a swich view+ransformaion approach. ccommodaing muliple views in he dynamic ayesian nework resuls in a mode-swich model. The inference of he hidden processes is made possible hrough paricle-based sequenial Mone Carlo mehods, by which he he mode and ransformaions of differen appearances as well as heir occlusion relaions can be recovered. The generaive models explicily represen he hidden facors which affec he image observaions, hus he recovery of hese hidden facors would provide significan inerpreaion of he image sequences besides racking. Since analyical resuls are in general hard o obain, when more facors are included in he generaive model, he compuaional complexiy ends o be more remendous. Thus, more efficien Mone Carlo mehods should be developed o ease hese compuaional issues. In addiion, insead of preseing he parameers in he models, learning hese parameers from raining daa would be more plausible. Our fuure work will include hese wo issues. cknowledgmens This work was suppored in par by Norhwesern sarup funds for YW and Murphy Fellowships for TY and GH. We also hank he anonymous reviewers for heir valuable commens. Proceedings of he 2003 IEEE Compuer Sociey Conference on Compuer Vision and Paern ecogniion (CVP 03)

7 Figure 10: Tracking one face wih ou-plane roaions wih he swiching muliple view model. suiable appearance emplae is seleced auomaically a each ime insan. (See muliview.mpg for deail.) Figure 12: Two faces move across inducing occlusion, and he moion of he faces conains ou-plane roaions. The occlusion (he occluded one is shown in dark) are inferred and he suiable view emplaes are swiched. (See occlu muliview.mpg for deail.) eferences [1] San irchfield. Elliical head racking using inensiy gradien and color hisograms. In Proc. IEEE Conf. on Compuer Vision and Paern ecogniion, pages , Sana arbara, California, June [2] Michael lack and llan Jepson. Eigenracking: obus maching and racking of ariculaed objec using a viewbased represenaion. In Proc. European Conf. Compuer Vision, volume 1, pages , Cambridge, UK, [3] Dorin Comaniciu, Visvanahan amesh, and Peer Meer. eal-ime racking of non-rigid objecs using mean shif. In Proc. IEEE Conf. on Compuer Vision and Paern ecogniion, volume II, pages , Hilon Head Island, Souh Carolina, [4] rnaud Douce, S. J. Godsill, and C. ndrieu. On sequenial Mone Carlo sampling mehods for ayesian filering. Saisics and Compuing, 10: , [5] oubin Ghahramani and Michael Jordan. Facorial hidden Markov models. Machine Learning, 29: , [6] Greg Hager and Peer elhumeur. Efficien region racking wih parameric models of geomery and illuminaion. IEEE Trans. on Paern nalysis and Machine Inelligence, 20: , [7] Michael Isard and ndrew lake. Conour racking by sochasic propagaion of condiional densiy. In Proc. of European Conf. on Compuer Vision, pages , Cambridge, UK, [8] Michael Isard and ndrew lake. mixed-sae condensaion racker wih auomaic model-swiching. In Proc. of IEEE In l Conf. on Compuer Vision, pages , India, [9] llan Jepson, David Flee, and Thomas El-Maraghi. obus online appearance models for visual racking. In Proc. IEEE Conf. on Compuer Vision and Paern ecogniion, volume I, pages , Kauai, Hawaii, Dec [10] Nebojsa Jojic, Nemanja Perovic, rendan Frey, and Thomas S. Huang. Transformed hidden Markov models: Esimaing mixure models and inferring spaial ransformaions in video sequences. In Proc. IEEE Conf. on Compuer Vision and Paern ecogniion, Hilon Head Island, SC, June [11] Micheal Jordan, oubin Ghahramani, Tommi Jaakkola, and Lawrence Saul. n inroducion o variaional mehods for graphical models. Machine Learning, 37: , [12] S.. Li, G. Lv, and H. J hang. View-based clusering of objec appearances based on independen subspace analysis. In Proc. IEEE In l Conf. on Compuer Vision, Vancouver, Canada, July [13] Jun Liu and ong Chen. Sequenial Mone Carlo mehods for dynamic sysems. J. mer. Sais. ssoc., 93: , [14] Jun Liu, ong Chen, and Tanya Logvinenko. heoreical framework for sequenial imporance sampling and resampling. In. Douce, N. de Freias, and N. Gordon, ediors, Sequenial Mone Carlo in Pracice. Springer-Verlag, New York, [15] John MacCormick and ndrew lake. probabilisic exclusion principle for racking muliple objecs. In Proc. IEEE In l Conf. on Compuer Vision, pages , Greece, [16] Vladimir Pavlovic, James ehg, Ta-Jen Cham, and Kevin Murphy. dynamic ayesian nework approach o figure racking using learned dynamic models. In Proc. IEEE In l Conf. on Compuer Vision, volume I, pages , Corfu, Greece, Sep [17] Hai Tao, Harpree Sawhney, and akesh Kumar. Dynamic layer represenaion wih applicaions o racking. In Proc. IEEE Conf. on Compuer Vision and Paern ecogniion, volume 2, pages , [18] Kenaro Toyama and ndrew lake. Probabilisic racking in a meric space. In Proc. IEEE In l Conf. on Compuer Vision, Vancouver, Canada, July [19] Ying Wu and Thomas S. Huang. obus visual racking by co-inference learning. In Proc. IEEE In l Conference on Compuer Vision, volume II, pages 26 33, Vancouver, July Proceedings of he 2003 IEEE Compuer Sociey Conference on Compuer Vision and Paern ecogniion (CVP 03)