Robust Visual Tracking for Multiple Targets

Transcription

1 Robus Visual Tracking for Muliple Targes Yizheng Cai, Nando de Freias, and James J. Lile Universiy of Briish Columbia, Vancouver, B.C., Canada, V6T 1Z4 {yizhengc, nando, Absrac. We address he problem of robus muli-arge racking wihin he applicaion of hockey player racking. The paricle filer echnique is adoped and modified o fi ino he muli-arge racking framework. A recificaion echnique is employed o find he correspondence beween he video frame coordinaes and he sandard hockey rink coordinaes so ha he sysem can compensae for camera moion and improve he dynamics of he players. A global neares neighbor daa associaion algorihm is inroduced o assign boosing deecions o he exising racks for he proposal disribuion in paricle filers. The meanshif algorihm is embedded ino he paricle filer framework o sabilize he rajecories of he arges for robus racking during muual occlusion. Experimenal resuls show ha our sysem is able o auomaically and robusly rack a variable number of arges and correcly mainain heir ideniies regardless of background cluer, camera moion and frequen muual occlusion beween arges. 1 Inroducion Tracking muliple arges, alhough has is roo in conrol heory, has been of broad ineres in many compuer vision applicaions for decades as well. A visualbased muli-arge racking sysem should be able o rack a variable number of objecs in a dynamic scene and mainain he correc ideniies of he arges regardless of occlusions and any oher visual perurbaions. As i is a very complicaed and challenging problem, exensive research work has been done. In his work, we address he problem of robus muli-arge racking wihin he applicaion of hockey player racking. Paricle filering was firs inroduced o visual racking by Isard and Blake in [1]. Pérez e al. [2, 3] exended he paricle filer framework o rack muliple arges. Okuma e al. [4] furher exended i [3] by incorporaing a boosing deecor [5] ino he paricle filer for auomaic iniializaion of a variable number of arges. However, as heir sysem did no have explici mechanisms o model muual occlusions beween arges, i loses he ideniies of he arges afer occlusions. On he oher hand, various approaches have been aken o solve he occlusion problem in racking. Kang e al. [6] ried o resolve he ambiguiy of he locaions of he arges by regisering video frames from muliple cameras. Zhao e al. [7] also recified video frames o he predefined ground plane and model he arges in he 3D space wih a body shape model. A saic camera was used and background subracion was applied as well in heir work. Explici A. Leonardis, H. Bischof, and A. Pinz (Eds.): ECCV 2006, Par IV, LNCS 3954, pp , c Springer-Verlag Berlin Heidelberg 2006

2 108 Y. Cai, N. de Freias, and J.J. Lile arge shape modelling can help resolving he likelihood modelling and daa associaion problems during occlusions. The approach is ofen used wihin saic scenes [8, 9, 10]. However, in our applicaion, camera moion makes i difficul o separae arge moion or perform background subracion. Players wih drasic pose changes are difficul o be capured by any explici shape models. In order o build a racking sysem ha can correcly rack muliple arges regardless of camera moion and muual occlusion, we propose four improvemens on he previous sysems. Firsly, a recificaion echnique is employed o compensae for camera moions. Secondly, a second order auoregression model is adoped as he dynamics model. Thirdly, a global neares neighbor daa associaion echnique is used o correcly associae boosing deecions wih he exising racks. Finally, he mean-shif algorihm is embedded ino he paricle filer framework o sabilize he rajecories of he arges for reliable moion predicion. Alhough similar work [11] has been done on combining mean-shif wih paricle filering, our work is he firs one ha describes in deail he heoreical formulaion of embedding mean-shif seamlessly ino he paricle filer framework for muli-arge racking. Consequenly, alhough our sysem performs comparably o he sysem in [4], i significanly improves upon ha sysem when occlusions happen, which is he main focus of his work. 2 Filering Paricle filering has been a successful numerical approximaion echnique for Bayesian sequenial esimaion wih non-linear, non-gaussian models. In our applicaion, he fas moion of hockey players and he color model we adop [12, 13] is highly non-linear and non-gaussian. Therefore, paricle filering is he ideal model o be he basic skeleon of our racking sysem. The basic Bayesian filering is a recursive process in which each ieraion consiss of a predicion sep and a filering sep. predicion sep: p(x y 0: 1 )= p(x x 1 )p(x 1 y 0: 1 )dx 1 filering sep: p(x y 0: )= p(y x)p(x y0: 1) p(y x )p(x y 0: 1)dx (1) where he process is iniialized by he prior disribuion p(x 0 y 0 ) = p(x 0 ), p(x x 1 ) is he arge dynamics model, and p(y x ) is he likelihood model. Paricle filering uses a se of weighed samples {x (i),w (i) } Ns i=1 o approximae he poserior disribuion in he filering. The sample se is propagaed by sampling from a designed proposal disribuion q(x x 1,y 0: ), which is called imporance sampling. The imporance weighs of he paricles are updaed in each ieraion as follows w (i) p(y x (i) )p(x (i) x (i) 1 ) q(x (i) x (i) 1,y 0:) Ns w (i) 1, i=1 w (i) =1. (2) Resampling of he paricles is necessary from ime o ime in each ieraion o avoid degeneracy of he imporance weighs.

3 Robus Visual Tracking for Muliple Targes 109 One of he criical issues in keeping paricle filering effecive is he design of he proposal disribuion. The proposal disribuion should be able o shif he paricles o he regions wih high likelihood if here is a big gap beween he mode of he prior disribuion and he mode of likelihood disribuion. The boosed paricle filer (BPF) [4] used a mixure of Gaussians model ha combines boh he dynamics prior and he Adaboos deecions [5] q B(x x 1,y 0: )=αq ada (x y )+(1 α)p(x x 1 ), (3) where α is he parameer ha is dynamically updaed according o he overlap beween he Gaussian disribuion of boosing deecion and he dynamics prior. The issue of daa associaion arises here. Deails abou how o correcly assign boosing deecions o he exising racks will be discussed laer. In addiion, he original BPF work by Okuma e al. [4] is based on he mixure of paricle filer srucure (MPF) [3], which has a fixed number of paricles for all he arges. As a resul, new arges have o seal paricles from exising racks and reduce he accuracy of he approximaion. The merge and spli of paricle clouds in he MPF srucure also cause he loss of he correc ideniies of he arges during occlusions. Therefore, we adop he boosed paricle filer as he basic filering framework in our applicaion. However, insead of using he MPF srucure, we use an independen paricle se for each arge o avoid he wo inheren disadvanages of MPF. 3 Targe Dynamics Modelling In visual racking sysems, accurae modelling of he arge dynamics can improve he predicion of he locaions of he arges while visual suppor is insufficien due o occlusion. However, because of he camera moion in our applicaion, he image coordinae sysem changes over ime wih respec o he hockey rink coordinaes. Therefore, arge moion modelling and predicion in he image coordinaes are difficul. We adop he approach by Okuma e al. [14] o map he locaions of he arges from he image coordinaes o he sandard hockey rink coordinae sysem which is consisen over ime. Therefore, according o he physical law of ineria, he moions of he players in hockey games are beer prediced wih a consan velociy auoregressive model. 3.1 Recificaion Homography is defined by Harley and Zisserman in [15] as an inverible mapping h beween wo planes. Images recorded by cameras are 2D projecions of he real world. For any plane in he world, is images from a camera, which can pan, il, zoom or even move, are exacly modelled by a homography as long as here is no noiceable lens disorion. As he hockey players are always moving in he plane formed by he hockey rink, heir locaions on he rink are in he same plane boh in he real world and he image space. Therefore, i is possible o projec heir locaions beween he wo planes.

4 110 Y. Cai, N. de Freias, and J.J. Lile Fig. 1. This shows a projeced video frame blended wih he sandard hockey rink The work by Okuma e al. [14] is able o auomaically compue he homography beween video frames and he hockey rink. Figure 1 shows how he video frames are mapped o he sandard rink wih he homography. Wih his homography, he hidden saes of he arges are represened in he rink coordinaes and paricle filering is performed in he rink coordinaes as well. Hidden saes will be mapped o he image coordinaes when evaluaing he likelihood of he observaion. 3.2 Auoregressive Dynamics Model An auoregressive process is a ime series modelling sraegy which akes ino accoun he hisorical daa o predic he curren sae value. In his model, he curren sae x only depends on he previous saes wih a deerminisic mapping funcion and a sochasic disurbance. As he paricle filering process is performed in he sandard rink coordinaes, he moions of he players on he rink are separaed from he camera moion. Thus, he modelling is much easier. In hockey games, because of he effec of ineria, a consan velociy model is suiable o model he moion of he players. I is bes described by he following second order auoregressive model x = Ax 1 + Bx 2 + CN (0,Σ) (4) where {A, B, C} are he auoregression coefficiens, N (0,Σ) is a Gaussian noise wih zero mean and sandard deviaion of 1. 4 Daa Associaion In a sandard Bayesian filering framework, daa associaion is performed o pair he observaions and racks for he evaluaion of he likelihood funcion p(y m x n ). Wih proper esimaion of segmenaion and shape of he arges [10], he observaion can be assigned o racks in a globally opimal way. However, as we do no have an explici shape model for he arges, he paricle filer framework in our applicaion handles his level of daa associaion locally in

5 Robus Visual Tracking for Muliple Targes 111 an implici way. Because he boosing deecions are used o improve he proposal disribuion in paricle filers as in shown in Equaion 3, we perform daa associaion a his level o assign boosing deecions o he exising racks. 4.1 Linear Opimizaion The assignmen problem can be bes represened by an assignmen marix shown in Table 1. Each enry in he able is he cos or gain of pairing he corresponding rack and observaion. In our applicaion, he values of all he enries in he assignmen marix are defined o be he disance beween he observaions and he racks in he rink coordinaes. Assignmens ha are forbidden by gaing are denoed by in he corresponding enries. Observaions ha are forbidden by he gaing o be associaed o any rack are considered as a new rack in our applicaion. Table 1. Example of he assignmen marix for he assignmen problem Observaions Tracks O1 O2 O3 O4 T1 a 11 a 12 T2 a 21 a 24 T3 a 31 a 34 Such assignmen problems sem from economic heory and aucion heory as well. The objecive is o minimize he cos or maximize he gain subjec o a se of consrains. Given he assignmen marix shown in Table 1, he objecive is o find a se X = {x ij }, which are binary indicaors, ha maximizes or minimizes he objecive funcion C = n m i=1 j=1 a ijx ij subjec o some linear consrains. Linear programming was iniially used o solve his problem. Laer on, i was found ha he aucion algorihm [16] is he mos efficien mehod so far o reach he opimal soluion or sub-opimal one wihou any pracical difference. The exended aucion algorihm [17] is able o solve he recangular marix problems wih he consrain ha one observaion can only be assigned o one arge while a arge can have a leas one observaions. However, in our applicaion, i is very likely ha some racks do no have any observaion due o he mis-deecion of he boosing deecor. Therefore, even if here are some observaions wihin he gae of ha rack, i is sill possible ha none of he observaions belongs o he rack. Hence, he consrains are formalized as n i=1 x ij =1, j m j=1 x ij 0, i (5) and he soluion is x i j = { 1ifi =arg i min a ij 0 oherwise j (6)

6 112 Y. Cai, N. de Freias, and J.J. Lile 5 Mean-Shif Embedded Paricle Filer The moivaion of embedding he mean-shif algorihm ino he paricle filer framework of our racking sysem is o sabilize he racking resul. I is imporan for he dynamics model because sabilizing rajecories improves he accuracy of he compued velociy of arges, which is criical for improving he predicion of he locaion of he arges. I is also imporan for he likelihood model because accurae predicion leads sampling o more promising areas so ha he influence from background cluer and muual occlusion will be reduced. 5.1 Color Model We adoped he color model in [13, 4] in our applicaion because i is successful in racking non-rigid objecs wih parial occlusion. The model is originally inroduced by Comaniciu e al. [18] for he mean-shif based objec racking. The observaion of he arge is represened by an N-bin color hisogram exraced from he region R(x ) cenered a he locaion x. I is denoed as Q(x )={q(n; x )} n=1,...,n, where q(n; x )=C k R(x ) δ[b(k) n] (7) where δ is he Kronecker dela funcion, C is a normalizaion consan, k is any pixel wihin he region R(x ). By normalizing he color hisogram, Q(x ) becomes a discree probabilisic disribuion. The similariy beween he curren observaion Q(x ) and he reference model Q, which is consruced a he iniializaion sep, is evaluaed based on he Bhaacharyya coefficien d(x, x 0 )= 1 ρ[q(x ),Q ],ρ[q(x ),Q ]= N q(n; x )q (n; x 0 ) (8) In order o encode he spaial informaion of he observaion, a muli-par color model [13, 4] is employed, which splis he arges verically ino wo pars. The color hisogram of he wo pars are consruced separaely and concaenaed in parallel as a new hisogram. The likelihood is hen evaluaed as n=1 p(y x ) e λd2 (x,x 0). (9) 5.2 Mean-Shif Mean-shif is a nonparameric saisical mehod ha seeks he mode of a densiy disribuion in an ieraive procedure. I was firs generalized and analyzed by Cheng in [19] and laer developed by Comaniciu e al. in [20]. The objecive of he mean-shif algorihm is o ieraively shif he curren locaion x o a new locaion x according o he following relaion ( M x i=1 a a iw(a i )k i x 2) h = ( M i=1 w(a a i)k i x 2) (10) h

7 Robus Visual Tracking for Muliple Targes 113 where {a i } M i=1 are normalized poins wihin he region R(x) around he curren locaion x, w(a i ) is he weigh associaed o each pixel a i,andk(x) is a kernel profile of kernel K ha can be wrien in erms of a profile funcion k :[0, ) R such ha K(x) =k( x 2 ). According o [19], he kernel profile k(x) should be nonnegaive, nonincreasing, piecewise coninuous, and k(r)dr <. 0 The heory guaranees ha he mean-shif offse a locaion x is in he opposie direcion of he gradien direcion of he convoluion surface C(x) = M G(a i x)w(a i ) (11) i=1 where kernel G is called he shadow of kernel K and profile k(x) is proporional o he derivaive of profile g(x). In order o uilize mean-shif o analyze a discree densiy disribuion, i.e., he color hisogram, an isoropic kernel G wih a convex and monoonically decreasing kernel profile g(x) is superimposed ono he candidae region R(x ) o consruc such a convoluion surface. Therefore, he new color model can be rewrien as M h q(n; x )=C h i=1 g ( a i x h 2) δ[b(a i ) n] (12) where C h is also a normalizaion consan ha depends on h, andh is he bandwidh ha deermines he scale of he arge candidae. I should be noed ha in our applicaion, scale of he arges is separaed from he sae space of he arges and smoohly updaed, on per paricle basis, using he adapive scaling sraegy in [12]. The weigh in he mean-shif updae for he color feaure is shown below. N q w(a i )= (n; x 0 ) q(n; x) δ[b(a i) n]. (13) n=1 The Epanechnikov profile [12] is chosen o be he kernel profile of kernel G in our applicaion. Because i is linear, he kernel K becomes a consan and he kernel erm in Equaion 13 can be omied. 5.3 Mean-Shif Embedded Paricle Filer Applying he mean-shif algorihm direcly o he racking oupu only gives one deerminisic offse a each sep. I migh no be able o capure he rue locaion of he arges due o background cluer or muual occlusion beween arges in he image. Embedding i ino he paricle filer framework brings uncerainy o he deerminisic mehod so ha he saisical propery can improve he robusness of he algorihm. In our applicaion, he mean-shif operaion biases all he paricles righ afer he sampling from he mixure of Gaussians proposal disribuion and before he resampling sep in he paricle filer framework. Alhough similar work [11] has been done for racking, i was only for single arge and he proper way of updaing he paricle weighs afer he mean-shif bias was no addressed clearly.

8 114 Y. Cai, N. de Freias, and J.J. Lile However, embedding he mean-shif algorihm seamlessly ino he paricle filer framework wihou inroducing bias is non-rivial. Direcly biasing sampled paricles from he old proposal disribuion will change he overall poserior disribuion. This makes updaing he weigh of he paricles wihou bias exremely difficul. Alhough he mean-shif bias is a deerminisic mapping so ha i can be seen as a change of variable, i is no applicable in pracice. On one hand, because he mean-shif bias is a muliple o one mapping, i is no inverible. On he oher hand, because i is difficul o wrie he mean-shif bias in an analyical expression for differeniaion even in a piecewise manner, i is difficul o compue he Jacobian marix in he variable change. We ake an alernaive approach in our applicaion. Mean-shif biases he } i=1,...,n ha are propagaed by he old proposal disribuion o a new paricle se { x (i) } i=1,...,n. We denoe mean-shif searching wih funcion ϕ( ) such ha x = ϕ(ˆx ). Finally, a Gaussian disribuion is superimposed on he biased paricles o sample new paricles. Therefore, he mean-shif bias wih a superimposed Gaussian disribuion combined wih he old proposal disribuion can be considered as a new proposal disribuion q(x x 1, y ). For he new proposal disribuion, he weigh is updaed as follows: samples {ˆx (i) w (i) p(y x (i) )p( x (i) x (i) 1 ) q( x (i) x (i) 1, y ) w (i) 1 (14) where q( x (i) x (i) 1, y )=N ( x (i) x (i),σ). Here, Σ is a diagonal 2 2 marix and he value of he wo enries are chosen o be he same, which is 0.3, in our applicaion. Noe ha we use a sample x (i) insead of he biased paricle x (i). This ensures ha he sequenial imporance sampler remains unbiased and valid. The following pseudo-code depics he overall srucure of our racking sysem, which includes all he conribuions in our work. Iniializaion: =0 Map boosing deecions o he rink coordinaes o ge {x k,0 } k=1,...,m0. Creae paricle se {x (i) k,0, 1 N }N i=1 by sampling from p(x k,0). For =1,..., T, 1. Targes addiion and removal Remove arges wih large paricle se variance. Map boosing deecions from he video frame o he rink. Daa associaion Creae a paricle se for each new arge. Associae boosing deecions o he exising racks o consruc Gaussian mixure proposal disribuion q(x k, x k, 1, z k, ), where z k, is boosing deecion. 2. For all paricles in each rack Imporance sampling For all paricles in each rack, sample ˆx (i) k, q(x k, x (i) k, 1, z k,).

9 Robus Visual Tracking for Muliple Targes 115 Mean-shif biasing Bias he paricles as x (i) k, = ϕ(ˆx(i) k, ). Sample x (i) k, q(x k, x (i) k, ) Weigh updae Updae weighs w (i) k, according o Equaion 14 and normalize. 3. Deerminisic resampling For each rack, resample paricles o ge new sample se {x (i) k,, 1 N }N i=1. 4. Oupu For each rack, E(x k, )= N i=1 w(i) k, x(i) k,. 6 Experimenal Resuls Figure 2 shows he comparison beween he racking resuls of he sysem in [4] and our sysem. Subfigure (a) is he key frame in he same racking sequence ha shows he overall view of he racking resuls. Subfigures (b-e) and (f-i) are he close-up views of he recangular region labelled in (a). Each player has a unique color box assigned o i. The color of he same player may no necessarily he same across resuls of he wo sysems. According o he resuls, we can see from Subfigures (b-e) ha he rackers merge ogeher when hey ge close and a new rack is creaed when hey spli. Meanwhile, our sysem can mainain correc ideniies during occlusion. Subfigures (j-u) in Figure 2 shows he paricle represenaion of he racking resuls of our sysem. In he pseudo-code in Secion 5.3, he evoluion of paricle ses in each ieraion of propagaion can be divided ino hree seps: before he mean-shif bias, afer he bias, and afer he deerminisic resampling. The las hree rows in he figure compare he difference beween he paricle ses afer each sep. Generally, he mean-shif algorihm moves paricles from differen locaions around he arge o locaions in he neighborhood ha are mos similar o he reference model in he color space. Therefore, paricle ses appear more condensed afer he mean-shif bias. The difference beween Subfigure (p) and (q) in Figure 2 indicaes ha mean-shif migh move paricles o some oher arges because of he similariy beween he wo arges in he color space. However, such paricles will be assigned low weighs because of he regularizaion of he dynamics model. As a resul, hose paricles will have much fewer or no children afer he resampling sage. For he same reason, paricles ha are biased o regions wihou any arge, as are shown in Subfigure (n) and (o), will be penalized as well. In summary, boh he mean-shif algorihm and he dynamics model penalize erroneous paricle hypoheses and improve he robusness of he overall racking sysem. Figure 3 shows more racking resuls from hree differen sequences. All of hem are able o correcly mainain he ideniies of he players regardless of parial of complee occlusions.

10 116 Y. Cai, N. de Freias, and J.J. Lile (a) Frame 1 (b) Frame 30 (c) Frame 39 (d) Frame 50 (e) Frame 58 (f) Frame 30 (g) Frame 39 (h) Frame 50 (i) Frame 58 (j) Frame 30 (k) Frame 39 (l) Frame 50 (m) Frame 58 (n) Frame 30 (o) Frame 39 (p) Frame 50 (q) Frame 58 (r) Frame 30 (s) Frame 39 () Frame 50 (u) Frame 58 Fig. 2. Each row is a close-up view of he recangular region in (a). Subfigures (b-e) show he racking resuls of he sysem in [4]. Subfigures (f-i) show he racking resuls of our sysem. Subfigures (j-u) show he paricle represenaion of each arge during he racking process. Differen arges are labelled wih recangles of differen colors.

11 Robus Visual Tracking for Muliple Targes 117 (a) Frame 79 (b) Frame 83 (c) Frame 88 (d) Frame 98 (e) Frame 28 (f) Frame 34 (g) Frame 42 (h) Frame 59 (i) Frame 8 (j) Frame 12 (k) Frame 14 (l) Frame 20 Fig. 3. Each row in he figure shows he racking resuls of hree differen sequences where he op one is he same sequence as he one shown in Figure 2 7 Conclusions In his paper, we devoe our endeavors o building a racking sysem ha is able o robusly rack muliple arges and correcly mainain heir ideniies regardless of background cluer, camera moions and muual occlusion beween arges. The new paricle filer framework is more suiable for racking a variable number of arges. The recificaion echnique compensaes for he camera moion and make he moion of arges easier o predic by he second order auoregression model. The linear opimizaion algorihm achieves he global opimal soluion o correcly assign boosing deecions o he exising racks. Finally, he mean-shif embedded paricle filer is able o sabilize he rajecory of he arges and improve he dynamics model predicion. I biases paricles o new locaions wih high likelihood so ha he variance of paricle ses decreases significanly. Acknowledgemens This work has been suppored by grans from NSERC, he GEOIDE Nework of Cenres of Excellence and Honeywell Video Sysems.

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