Multiple View Discriminative Appearance Modeling with IMCMC for Distributed Tracking

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1 Muliple View Discriminaive ing wih IMCMC for Disribued Tracking Sanhoshkumar Sunderrajan, B.S. Manjunah Deparmen of Elecrical and Compuer Engineering Universiy of California, Sana Barbara Absrac This paper proposes a disribued muli-camera racking algorihm wih ineracing paricle filers. A robus muli-view appearance model is obained by sharing raining samples beween views. Moivaed by incremenal learning and [1], we creae an inermediae daa represenaion beween wo camera views wih generaive subspaces as poins on a Grassmann manifold, and sample along he geodesic beween raining daa from wo views o uncover he meaningful descripion due o viewpoin changes. Finally, a Boosed appearance model is rained using he projeced raining samples on o hese generaive subspaces. For each objec, a se of wo paricle filers i.e., local and global is used. The local paricle filer models he objec moion in he image plane. The global paricle filer models he objec moion in he ground plane. These paricle filers are inegraed ino a unified Ineracing Markov Chain Mone Carlo (IMCMC) framework. We show he manner in which we induce priors on scene specific informaion ino he global paricle filer o improve racking accuracy. The proposed algorihm is validaed wih exensive experimenaion in challenging camera nework daa, and compares favorably wih sae of he ar objec rackers. Keywords Disribued Camera Nework, Paricle Filers, Objec Tracking. Predic and Updae Local Paricle Filer wih local informaion. Predic and Updae Local Paricle Filer wih local ineracions. Predic and Updae Ineracion Global Paricle Filer wih Muli-camera informaion and Scene Priors. Updae Local and Global Appearance Camera 1 Camera N Predic and Updae Global Paricle Filer wih Muli-camera informaion and Scene Priors. Fig. 1: Proposed Muli-camera based racking algorihm: Boh local and global paricle filers operae in parallel. Local paricle filer ineracs wih he global paricle filer using IMCMC framework [6]. Local paricle filer akes only local informaion available wihin he camera view ino accoun. Global paricle akes muli-camera informaion (performs fusion) and scene priors ino accoun. Finally, a robus global appearance model is learn by sharing raining samples wih he neighboring camera views. Conribuions of his paper are highlighed in red. I. INTRODUCTION Proliferaion of cheap and nework enabled smar cameras has provided an enormous opporuniy for large scale deploymen of camera neworks in real-world applicaions. This paper proposes a novel racking algorihm o rack pedesrians using a se of cameras wih overlapping views by inegraing informaion from differen camera views. The ground plane homography is used o relae informaion obained from muliple cameras o esimae an objec s posiion in he ground plane. Furher, o enhance racking qualiy, scene priors such as crowd flow informaion from he pas hisorical daa is used. More imporanly, we propose a sraegy o learn a robus discriminaive appearance model by sampling raining examples from generaive subspaces beween wo views and his leads o significan improvemen in racking accuracy. Exising muli-camera racking algorihms assume ha he racking problem in individual cameras is solved, and focus on higher level asks such as aciviy recogniion, even analysis and camera-hand-off. Due o background disorions, complex illuminaion changes, varying objec shapes and packe losses in wireless communicaion, he performance of single camera racking is far from he ideal. Also, he racking algorihm is mos likely o fail due o improper appearance modeling. Muliple viewpoin changes are no explicily modeled in exising racking algorihms. More imporanly, informaion fusion algorihms do no ake scene priors ino accoun. There are a number of muli-camera racking algorihms [2], ye very lile aenion has been paid o disribued racking algorihms. Exising disribued racking algorihms [3], [4], [5] manifes as soluions o an informaion fusion problem and do no ake prior informaion abou he nework ino consideraion during he fusion. Also, no much aenion has been paid o robus muli-camera appearance modeling. We propose a novel sraegy o rain a discriminaive Boosed appearance model by sharing raining samples wih neighboring views by aking view-shif ino accoun. More imporanly, we induce he priors on scene informaion such as crowd flow ino a paricle filer framework and demonsrae ha his significanly improves he robusness of objec racking. For a synchronized nework wih M cameras, le {I c 1:} be a se of video frames from differen camera views where c {1... M}. A ime insance, he sae of he i h objec on he image plane of he c h camera is denoed by X c,i = [posiionx, posiiony, sizex, sizey ] where i {1,..., O} is he global objec index and O is he number of objecs iniialized by he objec deecor a he firs frame. [posiionx, posiiony ] is he cener of he objec s bounding

2 box on he image plane and [sizex, sizey ] is he size of he objec along he x and y direcions. Given he se of video frames, i.e. {I c 1:} from differen cameras, we infer he objec sae for he i h objec, {X c,i } = [X 1,i... X M,i ] by Maximum a Poseriori (MAP) formulaion: arg max p({x c,i {X c,i } {I c 1:}) (1) } where i is he objec index and c is he camera index. We propose a novel sraegy o rain a robus discriminaive muli-view appearance model p(y c,i X c,i ), by aking viewpoin changes ino accoun. Addiionally, we propose a unified Markov Chain Mone Carlo (MCMC) framework o combine local and global informaion ino he racker. Mos imporanly, we show he manner in which we induce he scene specific priors and mulicamera ineracion ino he global paricle filer o improve he racking accuracy. Figure 1 highlighs he conribuions of he proposed muli-camera racking algorihm. Following are he main conribuions of his paper: 1. A robus globally discriminaive appearance modeling by aking viewpoin shif ino accoun. 2. A unified MCMC approach o combine local and global models. Global paricle filer models he muli-camera informaion fusion and akes scene priors ino accoun. II. RELATED WORKS In [7], a disribued Kalman filering framework is used o rack he objecs on he global ground plane. There have been recen effors o perform acive collaboraion beween cameras. [8] proposed a Bayesian algorihm for disribued muli-arge racking using muliple collaboraive cameras and hey used 2D locaion insead of 3D. They do no ake higher level scene informaion ino accoun while performing he fusion. Especially in [9], a disribued fusion mechanism ha clusers paricles obained from muliple camera views is proposed. This mehod is highly vulnerable o ouliers in shared paricles. In conras, our disribued racking algorihm combines local and global moion models in a unified probabilisic framework. Also, scene priors are aken ino accoun while updaing he global moion model. There are a few single camera racking algorihms ha ake scene priors ino accoun o improve he racking accuracy, however, hese mehods are no sraighforward o exend o muli-camera disribued racking scenarios [10], [11]. Recenly, racking by deecion algorihms have been gaining populariy [12], [13], [14]. Exising muliple camera racking algorihms do no discriminaively model he muli-view appearance in an online manner. Roh e al. [15] proposed a muliple insance learning based co-raining sraegy for muliview appearance racking. In comparison, we propose a novel disribued sraegy o rain a discriminaive appearance model by aking viewpoin shif ino accoun. The res of he paper is organized as follows. Secion III inroduces Bayesian Tracking formulaion wih Markov Chain and Mone Carlo. Secion IV formulaes he mulicamera racking algorihm. Secion IV-A proposes a novel mehod for muli-view appearance modeling and secion IV-B discusses muli-camera informaion fusion by inducing scene priors. Secion V demonsraes he efficacy of he proposed mehodology on some challenging muli-camera daases and finally we conclude he paper in secion VI. III. BAYESIAN TRACKING FORMULATION We explain he basics of paricle filer based objec racking [11]. The goal of objec racking is o find he bes objec configuraion X given he observaions Y 1: up o ime using he following Bayesian formulaion: p(x Y 1: ) p(y X ) p(x X 1 )p(x 1 Y 1: 1 ) dx 1, The opimal objec configuraion ˆX is obained by Maximum a Poseriori (MAP) esimaion: (2) ˆX = arg max X p(x Y 1: ) (3) The poserior a ime 1, is approximaed by a se of weighed paricles in Sequenial Imporance Resampling (SIR) paricle filers: p(x 1 Y 1 ) {X (p) 1, π(p) 1 }P p=1 (4) where p is he paricle index and P is he number of paricles. The weigh of he p h paricle is given by, π (p) = p(y X (p) ). The inegral in he equaion 2 can be approximaed by: p(x Y ) p(y X ) P p=1 π (p) 1 p(x X (p) 1 ) (5) We use MCMC sampling insead of he sandard imporance resampling. Compared o imporance resampling based paricle filer, he MCMC based paricle filer is very efficien [16]. The complexiy varies linearly wih respec o number of objecs compared o exponenially varying complexiy in SIR paricle filers. More imporanly, imporance resampling mehods suffer from paricle impoverishmen and degeneracy. In MCMC mehods, a Markov chain is defined over he space of configuraions X and he saionary disribuion of he chain is equal o he poserior disribuion, p(x Y). A se of un-weighed samples i.e., p(x Y ) {X (p) } P p=1 is used o represen he poserior in MCMC based paricle filer. IV. DISTRIBUTED MULTI-OBJECT TRACKING IN A CAMERA NETWORK For a camera nework wih M synchronized cameras, he primary ask is o joinly rack objecs wih acive collaboraion beween he views. The goal is o esimae he sae of objecs, i.e, {X c,i } given he se of image observaions {Y c,i 1: } on he se of video frames {I c 1:} from differen cameras and ground plane homography. We assume ha no raw image daa is ransferred beween nodes due o nework bandwidh consrains and esimae he following by approximaing equaion 1 on camera c = C for he i h objec as:

3 Updae Local Updae Global Share Training Samples Updae Global Updae Local Paricle Sae Predicion for local Filer from ime -1 Paricle Sae Predicion for global Filer from ime -1 nework channel Paricle Sae Predicion for global Filer from ime -1 Paricle Sae Predicion for local Filer from ime -1 Updae global paricle filer sae a ime Updae global paricle filer sae a ime Updae local paricle filer sae a ime Share Objec Measuremen INTERACTION Camera 1 Camera N INTERACTION Updae local paricle filer sae a ime Trajecory Daabase Trajecory Daabase Fig. 2: Ineracive MCMC based racking: A ime 1, he global appearance model is rained by sharing raining examples beween differen views. The local appearance model is rained using examples wihin he image view. Boh local and global paricle filers predic he sae from ime 1. The global paricle updaes is sae using he objec measuremen shared beween differen views. The local paricle filer ineracs wih he global paricle filer abou he bes configuraion of he objec. arg max p({x c,i {X c,i } I c=c 1: ), c = 1... M (6) } By assuming I c=c is condiionally independen of I c=c 1: 1 given he esimaes {X c,i } and expanding equaion 6 by Bayes rule, we have he following: p({x c,i } I c=c 1: ) p(i c=c {X c,i })p({x c,i } I1: 1) c=c (7) On furher facorizing he image likelihood erm }), we ge: p(i c=c {X c,i p({x c,i } I c=c 1: ) Appearance Likelihood p(y c=c,i X c=c,i ) P rior p({x c,i } I c=c 1: 1) Spaial Likelihood p({x c C,i } X c=c,i ) We propose a novel sraegy o model he appearance likelihood in a disribued manner by aking viewpoin shif ino accoun (explained in secion IV-A). Also, in secion IV-B we show he manner in which we combine local and global moion models using he ineracing Markov Chain Mone Carlo. Mos imporanly, we induce scene specific priors ino he global paricle filer. Figure 2 shows he proposed disribued racking mehodology. A. ing We use a discriminaive classifier o model he appearance of he objec. The likelihood of a pixel x belonging o he foreground label y = 1 is given by: 1 p(y = 1 x) = (9) 1 + e H(F(x)) where H is a discriminaive classifier learn wih online Boosing and F is he image feaure compued a pixel locaion x. Given a confidence map of he objec of ineres by esing appearance classifiers a ime, a mean-shif based [12] objec (8) sae esimae ν is obained. The appearance likelihood is given as follows: p(y X ) = p pos (ν X ) (10) where p pos (ν X ) is drawn from he Normal disribuion such ha p pos (ν X ) N (ν ; X, Σ pos ) and Σ pos is he covariance marix. In he res of his secion, we discuss in deail abou he manner in which we rain he local and global appearance classifiers, H (l) and H (g) respecively. 1) Local ing: For learning he local appearance classifier H (l), we use a combinaion of hisogram of oriened gradiens feaures (HOG) [17] and normalized color feaures. We use a 12 dimensional feaure vecor wih 9 bins for HOG and 3 for normalized pixel RGB color values. Similar o Ensemble Tracker [12], we rain a discriminaive online classifier a each ime insance by using samples wihin he objec bounding box as posiive examples and samples ouside he objec bounding box as negaive examples. 2) Global ing: Similar o local appearance modeling, we exrac an n-dimensional feaure vecor wih HOG and normalized pixel RGB color values (we used 36 bins for HOG and 3 for normalized pixel RGB color values). We propose a novel sraegy o exrac raining samples for learning he global discriminaive appearance model in a disribued manner. A each ime insance, each racker in every view (one racker per objec) shares heir raining examples o heir neighboring camera views. We firs formulae he problem for wo views and subsequenly exend o muliple views. Le X 1 R N1 n and X 2 R N2 n be he se of raining samples obained from wo views where N 1 and N 2 are he number of raining samples in each of he views. S 1 R N1 d and S 2 R N2 d represen generaive subspaces obained by performing Principal Componen Analysis (PCA) on X 1 and X 2 where d << n (in our experimens, we se d = 17). We now discuss he compuaion of inermediae subspaces S m, m R, 1 < m < 2 in order o model he appearance changes due o viewpoin variaions. The space of d-dimensional subspaces conaining he origin in R n can be idenified wih he Grassmann manifold G n,d where S 1 and S 2 are poins on G n,d. The Grassmann manifold is he space of d dimensional subspace in R n and a poin on Grassmann manifold represens a subspace. We use geodesic pahs ha are consan velociy curves on a manifold o obain inermediae subspaces. Viewing G n,d as quoien space of SO(n), he geodesic pah saring from S 1 is given by oneparameer exponenial flow ψ(m ) = Qexp(m B) [1], [18] where 0 < m < 1 and B is resriced o a skew-symmeric, block diagonal marix of he form: [ ] 0 A T B =, A R A 0 (n d) d. (11) where A specifies he direcion and he speed of [ geodesic ] flow. Q SO(n) such ha Q T Id S 1 = J and J =. I 0 d is n d,d a d d ideniy marix. By varying m beween 0 and 1, we ge a se of inermediae subspace S ha includes S 1 and S 2 (ineresed readers refer o [1] for more deails on calculaing A).

4 . HOG HOG View 1 View 2 G n,d ihog ihog p l (Y c=c,i X c=c,i ) = ψ(x c=c,i Appearance wih H (l) p(y c=c,i X c=c,i ) Ineracion { }}{ ψ(x c=c,i, X c=c,j ) j i (12), X c=c,j ) encodes he ineracion likelihood based on he sae of he oher objecs in he scene and i is based on he Magneic repulsion poenial: m' = 0.2 m' = 0.45 m' = 0.55 m' = 0.75 Fig. 3: Training Sample Generaion: Training samples for global appearance learning is obained by projecing samples from view 1 on o differen generaive subspaces obained by varying m. As highlighed in inverse HOG represenaion (ihog) obained using [19], body of he person is clearly discriminaive wih respec o viewpoin changes. Given he inermediae subspaces S, we propose a novel mehodology o exrac raining samples o learn he muliview discriminaive appearance model. Le N be he number of inermediae subspaces. We exrac raining samples by projecing X 1 on o hese inermediae subspaces. We rain our global discriminaive appearance model by gahering each of he raining samples projeced on o hese inermediae subspaces i.e., X 1 R N N1 d. For muliple views, we adop similar sraegy o exrac raining samples beween he curren view and every oher view using inermediae subspaces. Finally, we random sample raining examples o learn he global appearance classifier. B. Ineracing Markov Chain Mone Carlo Based Tracking We now presen a camera racking-by-deecion algorihm wih an ineracing MCMC framework. For every objec, we use wo kinds of paricle filers, local and global, wih MCMC sampling. For local paricle filers, he observaion likelihood is compued using he local appearance model and objec ineracion ha are local o he camera. For global paricle filers, he observaion likelihood is compued based on global appearance model, muli-camera informaion and scene priors. Similar o [20], each filer operaes eiher in parallel or ineracive mode. In he parallel mode, objec sae is compleely deermined by he local paricle filer. In he ineracing mode, he local paricle filer ineracs wih he global filer and deermines he objec sae a ha ime insance. By separaing he local and global models, we can easily accoun for higher level consrains ino he global model and reduce he complexiy of he local paricle filers significanly. C. MCMC based Local Paricle Filer The local paricle filer capures he local informaion wihin he image plane and i does no ake scene priors ino accoun for modeling he objec moion. The observaion model for he local paricle filer is given by: ψ(x c=c,i, X c=c,j ) = 1 1 exp( dis(xc=c,i β σ 2 i, X c=c,j ) ) (13) where β is he normalizaion consan and σi 2 characerizes he allowable maximum ineracion disance (in our experimens, we se β = 1 and σi 2 = 100). We approximae he local moion model wih he Normal disribuion such ha p l (X X 1 ) N (X ; X 1, Σ l ). The local paricle filer finds he MAP esimae defined in equaion 3 by sampling via Meropolis Hasings algorihm. The algorihm consiss of wo seps, a proposal sep and an accepance sep. In he proposal sep, he new sae is proposed wih he following proposal densiy: R l (X ; X ) = p l (X X ) (14) where R l denoes he proposal densiy funcion based on he local paricle filer s moion model and X represens he new sae proposed by R l a ime. Given he proposed sae, he local filer acceps he new sae wih he accepance raio given by: [ α parallel = min 1, p l(y X )R l (X ; X ) ] p l (Y X )R l (X ; X ) D. MCMC based Global Paricle Filer (15) The global paricle filer operaes wih he global appearance model and i akes scene priors and muli-camera informaion ino accoun. The observaion model, p g (Y c=c,i X c=c,i ), for he global paricle filer is given by: p g (Y c=c,i X c=c,i ) = Appearance wih H (g) p(y c=c,i X c=c,i ) Muli camera likelihood { }}{ Γ(X c=c,i, X c=k,i ) k C SceneP riors φ(x c=c,i ) (16) Γ(X c=c,i, X c=k,j ) encodes he muli-camera spaial likelihood and i is given by: Γ(X c=c,i, X c=k,i ) = 1 exp( dis(xc=c,i ρ σ 2 c, X c=k,i ) ) (17)

5 TABLE I: Mean Roo Mean Square Pixel Errors on differen daases. Daases OAB OAB-PF MS MIL MIL-PF Sruck Proposed Oudoor PETS Indoor TABLE II: Mean Pascal VOC deecion scores on differen daases. Daases OAB OAB-PF MS MIL MIL-PF Sruck Proposed Oudoor PETS Indoor where ρ is he normalizaion consan and σc 2 characerizes he allowable disance for muli-camera ineracion (in our experimens, we se ρ = 1 and σc 2 = 1000). We share objec s measuremen (mean-shif esimae obained by global appearance classifier) wih he neighboring camera views for mulicamera ineracion. φ(x c=c,i ) is based on he scene, i encodes he scene knowledge ino he observaion model. For modeling he scene specific priors, we used Kernel densiy esimaor o model he probabiliy densiy funcion on rajecories of he objecs ha moved over he scene for a period of ime [10]. We approximae he global moion model wih he Normal disribuion such ha p g (X X 1 ) N (X ; X 1, Σ g ). Similar o he local paricle filer, he global paricle filer uses he Meropolis Hasings algorihm based MCMC sampling. Algorihm 1: Muli-Objec Tracking wih IMCMC Inpu: X, γ Oupu: ˆX 1: rand() reurns a random number beween 0 and 1. 2: if rand() < γ hen Accep he new sae wih he probabiliy (18) else Propose he new sae using (14) Accep he new sae wih he probabiliy (15) end 3: Esimae he MAP sae ˆX using (3) E. IMCMC based Tracking Algorihm During he sampling process, a each ime sep, he local paricle filer ineracs wih he global paricle filer (illusraed in Fig.2). We make use of he IMCMC framework for he local paricle filer o communicae wih he global paricle filer [6], [11]. However, he global paricle filer operaes enirely in parallel mode. The proposed racking algorihm operaes in eiher parallel or ineracive mode [20]. The local and global paricle filers ac as he parallel Meropolis Hasings in he parallel mode. Whereas in he ineracion mode, he local paricle filer communicaes wih he global paricle filer and seeks a beer sae for he objec configuraion. The local paricle filer hen acceps he sae of he global paricle filer as is own sae wih he probabiliy as given by: α ineracing = p l (Y c=c,i p g (Y c=c,i X c=c,i X c=c,i ) ) + p g (Y c=c,i X c=c,i ) (18) F. Occlusion Handling In some scenarios, objecs migh no be deeced due o various reasons such as lighing changes, illuminaion effecs, and missing feaures. We assume ha an objec is occluded when ζ falls below a cerain hreshold (0.1 in our experimens), where ζ of he image pach posiioned a X is given by: ζ = sum of pixel likelihoods area of he pach posiioned a X For a given racker, if he objec is occluded, he global paricle filer proceeds wih he predicion sep and performs an updae wih muli-camera informaion and scene priors. On he oher hand, he local paricle filer operaes compleely in ineracive mode. The racker pauses is operaion afer a specified number of coninuously missed deecions beween frames (in our experimens, we se he hreshold o 20 frames). V. EXPERIMENTS We evaluaed he proposed mehod wih a wide area camera nework consising of six cameras on an oudoor environmen. Videos (640x480) are capured for several hours in an unconrolled environmen wih complex shape and appearance changes in human body, wireless packe losses and irregular illuminaion variaions (for example shadows, lighing changes due o sun rays and ohers). Also, we evaluaed he proposed algorihm in some of he publicly available muli-camera pedesrian daases [21] and [9]. Tables I and II show average VOC deecion scores and roo mean square pixel errors for various algorihms on hree differen daases (Oudoor, PETS2009, and Indoor). In all he experimens, we se he number of weak classifiers for he Ensemble raining o 12 and updaed 2 weak classifiers a every frame. We se he number of paricles P = 500. For boh local and global paricle filers, we used he Brownian moion model wih sandard deviaion σ x = 21, σ y = 3 and σ s = We se he IMCMC ineracion hreshold γ = 0.1. We assumed Σ pos o be a diagonal marix wih leading diagonals equal o [2, 2]. Finally, for generaing inermediae subspaces we se m = [0.25, 0.5, 0.75]. For comparison merics, we used Roo Mean Square Pixel error and pascal VOC deecion score (primarily used for comparing single camera appearance based rackers). VOC deecion scores capure compacness of he prediced bounding box is wih respec o he ground plane bounding box. Wih he prediced bounding box B p and he ground ruh bounding box B g, he pascal VOC deecion score is given by: Algorihm 1 explains he proposed muli-camera racking mehodology wih IMCMC framework. The MAP esimae is obained using he local paricle filer by communicaing wih he global paricle filer: V OC Deecion Score = area(b p B g ) area(b p B g ) (19)

6 C2 C2 C2 C2 C1 C3 C6 O2 Proposed(Frame-45) OAB(Frame-45) MIL(Frame-45) Sruck(Frame-45) C4 C4 C4 C4 O2 Proposed(Frame-45) OAB(Frame-45) MIL(Frame-45) Sruck(Frame-45) Fig. 4: Experimen 1: On camera C2, objec is indisinguishable from he background and hence some of he discriminaive appearance model based rackers fail. Whereas in he proposed mehodology, raining samples are exraced from inermediae subspaces beween muliple views o learn he global appearance model. Addiionally, muli-camera informaion and scene priors are helpful in maneuvering he objec when appearance cues are misleading. Bes viewed in color. A. Global ing wih Global Filering In our firs se of experimens wih our own daase, we evaluaed he proposed mehodology wih six cameras in he nework, of which only wo of he cameras (C2 and C4) direcly sensed he objecs of ineres ( and O2). The objecs of ineres are iniialized using a background subracion based blob deecor. We compared he proposed mehodology wih some of he sae of he ar racking algorihms: on-line Adaboos (OAB) [22], on-line Adaboos wih paricle filer (OAB-PF), Muliple insance learning(mil) [13], Muliple insance learning wih paricle filer (MIL-PF), Sruck [23], and Mean-shif (MS) [24] rackers. From he oudoor scenario resuls in Tables I and II, we show ha he proposed mehodology ouperforms all he oher racking mehodologies in nework wide scenarios. Poor performance of some of he appearance based rackers is due o misaken ideniies and inadequae appearance modeling. In he case of he proposed algorihm, a robus global appearance classifier is learn by aking viewpoin shif ino accoun. Addiionally, he mulicamera likelihood and scene priors in global paricle filers are helpful in correcing he local paricle filers whenever he local paricle filer suffers from insufficien moion and appearance modeling. When he objec merges wih background (shown in Figure 4), scene priors in global paricle filers are helpful in maneuvering he objec using he prior informaion from previous objecs ha moved on he same locaion over he ime and also he muli-camera likelihood is helpful in correcing he objec sae esimae by exploiing muli-view redundancy. Mos imporanly, he global appearance model capures he missing feaures using he raining samples obained from neighboring camera views and helps he racker o recover iself in he subsequen frames by building a robus appearance model. B. Global ing wih Scene Priors For he second se of experimens wih PETS-2009 sequences, he objec of ineres () was iniialized in he firs (C1), hird (C3) and sixh (C6) views respecively. For his experimen, o sudy he efficacy of he global appearance modeling wih scene priors, he ineracive likelihood in local paricle filer was urned off. As seen in Tables I and II, he proposed algorihm ouperforms sae of he ar algorihms on VOC deecion scores and roo mean square pixel errors. The success of he proposed algorihm (as illusraed in Figure Fig. 5: Experimen 2: Tracking resuls from individual camera views are shown. Clearly, muli-camera informaion and scene priors help in avoiding failures due o parial occlusions. In his experimen, mos of he oher racking mehods failed due o he parial occlusion caused by he lamp pole. Objec of ineres is marked by he label. Bes viewed in color. 5) on his scenario could be aribued o he following: The proposed algorihm is robus o inermien racker failures due o he parial occlusions by learning a robus global appearance model. In his scenario, he lamp pole caused a parial occlusion in view C1 and mos of he racking algorihms failed compleely due o improper appearance modeling. Similar o he firs se of experimens, scene priors and muli-camera informaion is helpful in correcing he local paricle filers during insufficien moion modeling. C. Global ing wihou Scene Priors For he hird se of experimens, we used indoor video sequences from [9]. The camera nework consiss of five cameras along a long corridor. In order o increase he difficuly of he experimen, we used a par of he sequence where he corridor lighs were swiched off. Also, scene priors were no available for his nework. As seen in Tables I and II, he proposed algorihm ouperforms he res due o he following reasons: a) Objecs appeared similar due o he lighing condiions, he global appearance model is helpful in capuring discriminaive feaures using he raining samples from neighboring views. Oher mehods fail o capure hese variaions and hence lose rack of he objecs due o improper appearance based associaion, b) Also, he ineracive likelihood in he local paricle filer is helpful in mainaining spaial relaionship beween he objecs beween he frames. This helps in proper associaion in he presence of ouliers due o missing feaures beween he frames. Missing feaures are more likely o happen due o irregular lighing condiions. D. Comparison Wih Muliple Camera Trackers We compared he proposed algorihm wih sae of he ar muliple camera disribued filering based racking algorihms: Join Probabilisic Daa associaion wih Kalman consensus filer (JPDA-KCF) [25], [26], Informaion consensus filering wih neares-neighbor daa associaion (ICF-NN) [5], Informaion consensus filering wih ground ruh daa associaion (ICF-GT) and Muli-camera informaion consensus (MTIC) [3]. In ICF-NN, he neares observaion is associaed wih he exising rackle based on Hungarian algorihm. We used Sruck [23] (an appearance based racker) o generae image based observaions. Ground plane esimaes are obained using homographic ransformaion and hey serve as measuremens for ground disribued fusion algorihms. Tables III show mean error (in meers) and error sandard deviaion for differen algorihms in oudoor/indoor sequences respecively. For he indoor sequences, scene priors were no available. The proposed algorihm clearly ouperforms oher muli-camera racking algorihms due o he following: a)

7 TABLE III: Muliple Camera Tracking Comparison in Oudoor/Indoor Sequences (Muliple Objecs) Algorihm Mean Error (m) Error Sandard Deviaion (m) Proposed 0.27 / / 0.39 MTIC 6.40 / / 0.44 ICF-NN 25.7 / / 0.41 JPDA-KCF 52.5 / / 0.46 ICF-GT 12.8 / / 0.40 Muli-view appearance model effecively capures viewpoin variaions. b) Ground plane fusion in global paricle filers is efficienly fed back o he local paricle filers hrough an IMCMC approach. VI. CONCLUSION This paper presened a robus muli-camera racking algorihm using ineracing Markov Chain Mone Carlo. The racking algorihm is formulaed as a global Bayesian esimaion problem and solved in a disribued manner. We proposed a novel algorihm o learn a discriminaive muli-view appearance model by sharing samples across he views. We provided an efficien algorihm o combine local and global models ino one using a unified probabilisic framework. The disribued muli-camera racker akes approximaely one second perframe wih he Malab implemenaion on a machine wih 8 GB RAM and 2.67 GHZ processor. The proposed algorihm is esed on some challenging daases and validaed wih objecive resuls. As a fuure work, we plan o add complex crowd behavioral model ino he local objec ineracion likelihood and accoun for saic scene componens such as enry/exi locaions ino he scene priors. ACKNOWLEDGMENTS This work was suppored by ONR gran #N REFERENCES [1] R. Gopalan, R. Li, and R. Chellappa, Domain adapaion for objec recogniion: An unsupervised approach, in Compuer Vision (ICCV), 2011 IEEE Inernaional Conference on. IEEE, 2011, pp , 3 [2] F. Fleure, J. Berclaz, R. Lengagne, and P. Fua, Mulicamera People Tracking wih a Probabilisic Occupancy Map, IEEE Transacions on Paern Analysis and Machine Inelligence, vol. 30, no. 2, pp , [3] A. T. Kamal, J. A. Farrell, and A. K. 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