Recognising Behaviours of Multiple People with Hierarchical Probabilistic Model and Statistical Data Association

Transcription

1 Recognising Behaviours of Muliple People wih Hierarchical Probabilisic Model and Saisical Daa Associaion Nam Nguyen, Sveha Venkaesh Curin Universiy of Technology, GPO Box U1987, Perh Wesern Ausralia, Hung Bui Arificial Inelligence Cener, SRI Inernaional, 333 Ravenswood Ave Menlo Park, CA 94025, USA, 1 Absrac Recognising behaviours of muliple people, especially high-level behaviours, is an imporan ask in surveillance sysems. When he reliable assignmen of people o he se of observaions is unavailable, his ask becomes complicaed. To solve his ask, we presen an approach, in which he hierarchical hidden Markov model (HHMM) is used for modeling he behaviour of each person and he join probabilisic daa associaion filers (JPDAF) is applied for daa associaion. The main conribuions of his paper lie in he inegraion of muliple HHMMs for recognising high-level behaviours of muliple people and he consrucion of he Rao-Blackwellised paricle filers (RBPF) for approximae inference. Preliminary experimenal resuls in a real environmen show he robusness of our inegraed mehod in behaviour recogniion and is advanage over he use of Kalman filer in racking people. 1 Inroducion Building smar surveillance sysems has araced much ineres recenly because of heir numerous applicaions [1, 9, 12]. Recognising people behaviours, especially high-level behaviours, is a fundamenal problem in many sysems. This ask is challenging because of noisy daa from cameras and complex paern of he high-level behaviours. Much research has focused on recognising he high-level behaviour of a single person [9, 13, 14, 15]. Hierarchical probabilisic models such as he sochasic conex free grammar (SCFG) [9], he absrac hidden Markov model (AHMM) [4], and he hierarchical hidden Markov model (HHMM) [3, 7] have been used recenly o model he high-level behaviour and deal wih uncerainy. Liao e al. [12] use he AHMM in a surveillance sysem in which GPS sensors are deployed o recognise a user s daily aciviies in large and complex environmens. The AHMM is used o represen he aciviy hierarchy and he expecaion and maximizaion (EM) algorihm is applied o learn he model s parameers. Nguyen e al. [14] use he HHMM o recognise a se of complex aciviies in indoor environmens. The problem of recognising behaviours of muliple people is more complicaed. Usually, he reliable assignmen of people o he se of observaions is unavailable. We have BMVC 2006 doi: /c

2 2 a daa associaion problem. An efficien mehod o resolve his problem is he join probabilisic daa associaion filer (JPDAF) [2, 5]. However, he resricion of he JPDAF is he underlying Gaussian assumpion, which has been relaxed in recen approaches ha inegrae paricle filers wih he JPDAF [10, 16, 17, 18]. This mehod has been applied wih grea success in non-gaussian and non-linear dynamic processes. Work of noe includes Schulz e al. s [16], which uses paricle filers o represen he arge saes and hen applies he JPDAF direcly o he sample se of paricle filers. The algorihm is implemened in a mobile robo o rack people in indoor environmens. The Markov chain Mone Carlo (MCMC) can be used o generae samples from he large discree space of he assignmens of arges o measuremens, reducing he compuaional cos of he racking algorihm [11, 17]. Mos research so far has no ackled he problem of recognising he high-level behaviours of muliple people in a unified probabilisic framework. Wilson and Akeson [19] propose a sysem for simulaneous racking and recognising behaviours of muliple people. However, heir model is fla and canno easily be exended o model high-level aciviies. We propose an inegraed approach for racking and recognising high-level behaviours of muliple people. We consider primiive and complex behaviours, where primiive behaviour is a single acion such as moving from one landmark owards anoher landmark, while complex behaviour is a sequence of primiive behaviours. Modeling he primiive and complex behaviours requires a hierarchical model. We use he HHMM [3, 7] an exension of he hidden Markov model in our framework because here are efficien learning and inference algorihms in his hierarchical model. We consruc a unified graphical model, which we call he HHMM-JPDAF, o incorporae a se of HHMMs wih daa associaion. Furher, we presen a Rao-Blackwellised paricle filer (RBPF) algorihm ha efficienly compues he filering disribuion of he model a each ime. We presen he experimenal resuls o demonsrae he robusness of our inegraed mehod in behaviour recogniion and is advanages over he use of he Kalman filers in racking people. The novely of his paper is wo-fold: 1) we propose an inegraed graphical model he HHMM-JPDAF o rack and recognise behaviours of muliple people and 2) we describe an efficien algorihm for approximae inference. Our work goes beyond he work of Wilson and Akeson [19] by providing a framework for recognising more expressive classes of behaviours. While he behaviour recogniion in Wilson and Akeson s work is limied o wheher or no a person is moving, our work deals wih a hierarchy of primiive and complex behaviours. The paper is organised as follows: Secion 2 describes he HHMM and is use in behaviour recogniion of a single person. Secion 3 discusses he HHMM-JPDAF for racking and recognising behaviours of muliple people. The sysem implemenaion and experimenal resuls in a real environmen are presened in Secion 4, followed by concluding remarks in Secion 5. 2 The HHMM for behaviour recogniion 2.1 The HHMM The hierarchical hidden Markov model (HHMM) [3, 7] is an exension of he hidden Markov model (HMM) o include a hierarchy of hidden saes. A HHMM is defined by a uple < ζ, Y, θ >, where ζ is he opological srucure, Y is he observaion alphabe, and θ is he parameer of he model. The opology ζ specifies he deph of he model, he

3 sae space a each level, and he paren-child relaionship beween wo consecuive levels. Saes a he lowes level are called producion saes and saes a higher levels are called absrac saes. A each level, an end sae is inroduced o signal when he conrol of acivaion is reurned o he sae a he higher level. Only producion saes emi observaions. A represenaion of he HHMM as a dynamic Bayesian nework (DBN) is provided in [3]. 2.2 Recognising primiive and complex behaviours of a person The primiive behaviour represens a person s acion of going from one specific landmark o anoher specific landmark in he environmen. For example, consider an environmen ha has four landmarks door, cupboard, fridge, and dining able we can define he following primiive behaviours: (1) door o cupboard, (2) cupboard o fridge, (3) fridge o dining able, and (4) dining able o cupboard. The complex behaviour is defined from a se of primiive behaviours. A complex behaviour can be refined ino differen sequences of he primiive behaviours. For example, he sequence of primiive behaviours (1), (2), (3), and (4) can belong o he complex behaviour have meal. The HHMM for recognising he primiive and complex behaviours of a single person is discussed in Nguyen e al. [14]. A hree-level HHMM is used for modeling he behaviour hierarchy. The complex behaviour, primiive behaviour and discree posiion of a person are mapped ino he op, middle and boom levels of he HHMM, respecively. The parameers for he HHMM can be learned from a se of raining sequences using he asymmeric insideouside (AIO) [3] or juncion ree algorihm [8]. The filering disribuion of he HHMM for each new observaion arrival can be compued by a RBPF algorihm as in [14]. 3 Recognising behaviours of muliple people We consider he problem of recognising he primiive and complex behaviours of K people. We assume ha a each ime a person generaes a mos one observaion. An observaion can be noise and a person can generae no observaion. Because he reliable assignmen of people o observaions is unavailable, we have a daa associaion problem. We propose he HHMM-JPDAF an exension of he HHMM ha corporaes he JPDAF for racking and behaviour recogniion. A RBPF algorihm is adaped for he HHMM-JPDAF o provide an efficien approximae inference algorihm. 3.1 The HHMM-JPDAF We use K HHMMs o model he behaviours of K people in he environmen. Inegraing he K HHMMs wih he assignmen of people o observaions, we have a HHMM-JPDAF model. The represenaion of he HHMM-JPDAF as a DBN is shown in Figure 1. In Figure 1, u = (u 1,...,u K ), v = (v 1,...,v K ) and x = (x 1,...,x K ) are he complex behaviours, primiive behaviours, and posiions of he K people, respecively. e =(e 1,...,eK ) is he end saus of he primiive behaviours. e k represens wheher he primiive behaviour v k erminaes or no. The se of observaions a ime is o = (o 1,..., om ), where m is he number of observaions. We assume ha he posiion x and observaion o are discree. We also do no consider he problem of recognising a sequence of complex behaviours, hus a single complex behaviour is assumed o las from ime = 1 o = T. The assignmen of K people o observaions a ime is θ = (θ 1,,..., θ K, ), where θ k, {0,...,m }. If θ k, 0, he observaion o θ k, 3 originaes from person k. Oherwise

4 4 β 1 complex behaviour u 1 1 u 1 primiive behaviour end saus v 1 1 e 1 1 v 1 e 1 person 1 sae x 1 1 x 1 complex behaviour u 2 1 β 2 u 2 primiive behaviour end saus v 1 2 e 1 2 v 2 e 2 person 2 sae x 2 1 x 2 se of observaions o 1 o assignmen θ 1 θ ime 1 ime Figure 1: The DBN represenaion of he HHMM-JPDAF when here are wo HHMMs. person k has no observaion a ime. θ k1, θ k2, if k 1 k 2, θ k1, 0, and θ k2, 0. For example, we have wo people ha is, person 1 and person 2 and hree observaions o = (o 1,o2,o3 ). θ = (2,0) means ha person 1 generaes he observaion o 2 a ime, person 2 generaes no observaion, and he observaions o 1 and o 3 are noise. Le δ(θ ) denoe he vecor of deeced people: δ(θ ) = (δ 1 (θ ),...,δ K (θ )). δ k (θ ) = 1 if person k has a corresponding observaion ha is, θ k, 0 oherwise δ k (θ ) = 0. Le ω(θ ) = { j o j is a false observaion} and φ(θ ) denoe he number of false observaions. Given he assignmen θ, hen δ(θ ) and φ(θ ) are compleely defined. For example, if θ = (2,0), hen δ(θ ) = (1,0), ω(θ ) = {1,3}, and φ(θ ) = 2. In he case ha he assignmens up o ime ha is, θ = (θ 1,...,θ ) are given, he HHMM-JPDAF can be separaed ino K HHMMs and he sequence of observaions corresponding o each HHMM is compleely defined. Thus, he exac inference algorihms in he HHMM such as AIO [3] or juncion ree algorihm [8] can be applied o esimae he curren filering disribuion of each HHMM. 3.2 The RBPF in he HHMM-JPDAF Le β = Pr(u,v,x õ ) denoe he belief sae of he HHMM-JPDAF given he observaions up o ime. Le β k denoe he belief sae of each person k (1 k K) ha is, β k = Pr(u k,v k,x k õ ). For racking and recognising people behaviours a a specific ime, we need o compue he belief sae β. However, exac mehods o compue β are inracable because: β = Pr(u,v,x õ ) = Pr(u,v,x θ,õ ) Pr( θ õ ) θ and he number of possible values of θ is large when increases. Thus, we need an approximae inference algorihm such as he RBPF [6] o compue β. We represen β by a se of paricles and selec r = (θ,e ) as he Rao-Blackwellised (RB) variable. Wih each paricle i, he RBPF samples he RB variable r (i) = (θ (i),e (i) ) and updaes he belief sae

5 corresponding o ha paricle ha is, β (i) using exac inference. The RBPF in he HHMM-JPDAF is shown in Algorihm 1, which is deailed below. Algorihm 1 The RBPF algorihm in he HHMM-JPDAF. S 1 = {< β (i) (i) 1,θ 1,e(i) 1,w(i) 1 > i = 1,...,N}, observaion o Inpu Begin /* sampling sep */ For each sample i = 1,...,N Updae he weigh w (i) 1 = w(i) 1 Pr(o θ (i) 1,ẽ(i) Sample θ (i) and e (i) from Pr(θ (i),e (i) θ (i) 1,ẽ(i) 1,õ ) /* re-sampling sep*/ Normalise he weigh w (i) 1 = w(i) 1 / N i=1 w(i) 1 Re-sample he sample se according o w (i) 1 /* Exac sep */ For each sample i = 1,...,N Compue β (i) Se he weigh w (i) using exac inference in he HHMM = 1 N Compue β 1 N N i=1 β (i) End A se of paricles S = {< β (i) 1,õ 1),e (i),θ (i),w (i) > i = 1,...,N} is mainained a each ime is he weigh of each paricle. The belief sae β of he HHMM-JPDAF is, where w (i) obained from he se of paricles S. Assume ha he se of paricles a ime 1, ha is, S 1, is known, he se of paricles a ime ha is, S is compued as follows: Updaing weighs. The weigh w (i) 1 is updaed as: w (i) 1 = w (i) 1 Pr(o r (i) 1,õ 1) = w (i) 1 Pr(o θ (i) 1,ẽ(i) 1,õ 1) (1) where r (i) 1 = ( θ (i) 1,ẽ(i) 1 ), and ẽ(i) 1 and õ 1 are he end nodes and observaions up o ime 1, respecively. From now on, he upper indice (i) is omied for simpliciy. We have: Pr(o θ 1,ẽ 1,õ 1 ) = θ (Pr(o θ,ẽ 1,õ 1 ) Pr(θ θ 1,ẽ 1,õ 1 )) (2) The probabiliy Pr(o θ,ẽ 1,õ 1 ) is compued as follows. Noe ha, {o 1,...,o m } = {o j o j is no noise} {o j o j is noise} = {o θ k, θ k, 0,k = 1,...,K} {o j j ω(θ )}. Thus, Pr(o θ,ẽ 1,õ 1 ) can be facorised as: Pr(o θ,ẽ 1,õ 1 ) = = K Pr(o θ k, θ k, 1,ẽ 1,õ k 1 ) k=1,θ k, 0 m j=1, j ω(θ ) Pr(o j is noise) K Pr(o θ k, θ k, 1,ẽ 1 k,õ 1) V φ(θ ) k=1,θ k, 0 5 (3)

6 6 where V is he probabiliy ha an observaion is noise. Pr(o θ k, θ k, 1,ẽ 1 k,õ 1) is facorised as: Pr(o θ k, θ k, 1,ẽ 1,õ k 1 ) = (Pr(o θ k, x k ) Pr(x k θ k, 1,ẽ 1,õ k 1 )) (4) x k To compue he probabiliy Pr(x k θ k, 1,ẽ 1 k,õ 1), we firs obain he belief sae β k by projecing β 1 k from ime 1 o wih he value of he end node ek 1 available. Then, we marginalise β k over {u k,vk } o obain he probabiliy Pr(xk θ k, 1,ẽ 1 k,õ 1). These seps are carried ou in he HHMM corresponding o person k in a similar manner as in [4]. According o he DBN represenaion of he HHMM-JPDAF, θ and { θ 1,ẽ 1,õ 1 } are independen when he observaion o is unknown (see Figure 1). Thus, Pr(θ θ 1,ẽ 1,õ 1 ) = Pr(θ ) (5) Noe ha, given he assignmen θ, δ(θ ) and φ(θ ) are compleely defined. Thus, Pr(θ ) can be compued as: Pr(θ ) = Pr(θ,δ(θ ),φ(θ )) = Pr(θ δ(θ ),φ(θ )) Pr(δ(θ ),φ(θ )) = Pr(θ δ(θ ),φ(θ )) K k=1 (P δ k (θ ) D (1 P D ) 1 δ k (θ ) ) µ(φ(θ )) (6) where P D is he probabiliy ha person k is deeced, δ k (θ ) is he k h elemen of he vecor of deeced people δ(θ ), and µ(φ(θ )) is he probabiliy ha he number of false observaions a ime is φ(θ ). Assuming ha here is a uniform disribuion over he se of he assignmens θ given δ(θ ) and φ(θ ), we have: Pr(θ δ(θ ),φ(θ )) = φ(θ )! m!. From (5) and (6), we can obain he probabiliy Pr(θ θ 1,ẽ 1,õ 1 ). Afer obaining he probabiliies Pr(o θ,ẽ 1,õ 1 ) and Pr(θ θ 1,ẽ 1,õ 1 ), we sum he produc of hese wo probabiliies over all possible assignmens θ as in (2), hen compue he weigh w (i) 1 from (1). In he case ha he number of he assignmens θ is large, he Markov Chain Mone Carlo (MCMC) mehod can be applied for sampling he assignmen θ as in [17] o reduce he compuaion cos. Sampling he RB variable. The RB variable r = (θ,e ) is sampled from Pr(r r 1,õ ), which can be facorised as: Pr(r r 1,õ ) = Pr(θ,e θ 1,ẽ 1,õ ) = Pr(e θ,ẽ 1,õ ) Pr(θ θ 1,ẽ 1,õ ) (7) We firs sample θ from Pr(θ θ 1,ẽ 1,õ ), hen sample e from Pr(e θ,ẽ 1,õ ). Pr(θ θ 1,ẽ 1,õ ) Pr(θ,o θ 1,ẽ 1,õ 1 ) = Pr(o θ,ẽ 1,õ 1 ) Pr(θ θ 1,ẽ 1,õ 1 ) = Pr(o θ,ẽ 1,õ 1 ) Pr(θ ) (8) Mehods o compue Pr(o θ,ẽ 1,õ 1 ) and Pr(θ ) have been discussed in he sep of updaing he weigh w (i) 1. Thus, we can sample he assignmen θ from (8).

7 The probabiliy Pr(e θ,ẽ 1,õ ) which is used o sample e can be facorised as: 7 Pr(e θ,ẽ 1,õ ) = K k=1,θ k, 0 K k=1,θ k, =0 Pr(e k o θ k,, θ k, 1,ẽ 1 k,õ 1) Pr(e k θ k, 1,ẽ k 1,õ 1 ) (9) We sample e k, where θ k, 0, from Pr(e k o θ k,, θ k, 1,ẽ 1 k,õ 1) as follows. We firs projec he belief sae β 1 k from ime 1 o wih he value of ek 1 available o obain he belief sae β k. Then, we absorb he observaion o θ k, ino β k and sample he values of v k and x k from β k. The end node ek is sampled from he probabiliy Pr(e k v k,xk ). We sample e k, where θ k, = 0, from Pr(e k θ k, 1,ẽ 1 k,õ 1) in a similar manner bu wihou absorbing he observaion value. Re-sampling and exac sep. We re-sample he se of paricle filers S 1 according o he weighs w (i) 1. In he exac sep, we need o compue he belief sae of each person k a ime ha is, β k. We firs obain he corresponding observaion oθ k, of each person k (if person k generaes an observaion). The belief sae β k is compued by projecing he belief sae β 1 k from ime 1 o, hen absorbing he observaion oθ k, and he end node e k. These seps are carried ou by using exac inference algorihms in he HHMM. In he case ha person k has no corresponding observaion, he absorbing observaion sep is skipped. 4 Experimenal resuls 4.1 Implemenaion We se up he sysem o recognise he primiive and complex behaviours in an environmen as shown in Figure 2. The special landmarks in he environmen are he door, TV chair, fridge, sove, cupboard, and dining able. We use a op-down camera o obain he curren image of he environmen. A segmenaion algorihm is used o exrac moion blobs from he image, which are considered o be he observaions of people in he environmen. The feaures used o infer he people behaviours are he coordinaes of he cenroid of he moion blob. We do no use color in racking because he color of a moion blob varies significanly from ime o ime. The environmen is divided ino a grid of discree saes, ha are numbered 1, 2,..., 96. Each sae is a square region in he image. The observaion model is compued from a se of 1600 pairs (observaion, groundruh), ha are colleced manually. We define 13 primiive behaviours and hree complex behaviours in he environmen. The primiive behaviours are: (1) door o cupboard (5) fridge o dining able (9) door o sove (13) cupboard o sove (2) cupboard o dining able (6) door o TV chair (10) sove o fridge (3) dining able o cupboard (7) TV chair o sove (11) fridge o sove (4) dining able o fridge (8) sove o TV chair (12) sove o cupboard The srucure of he complex behaviours are shown in Figure 2. To learn he parameers for he primiive and complex behaviours, we obain en raining sequences for primiive behaviours and five sequences for complex behaviours. The primiive behaviours and complex behaviours are learned from hese raining sequences in a similar manner as in [14].

8 8 TV chair fridge sove sar sar door sar door beh 1 door beh 9 cupboard beh 6 sove door beh 2 beh 3 TV chair beh 10 beh 11 dining_able beh 7 beh 8 beh 12 fridge beh 4 beh 5 sove beh 13 fridge cupboard dining Table cupboard have_meal have_snack cooking Figure 2: The room viewed from he op-down camera and he complex behaviours have meal, have snack and cooking. 4.2 Behaviour recogniion resuls We run he sysem o rack and recognise people behaviours in real scenarios. We evaluae he performance of he sysem by considering he winning complex behaviour and he correc duraion. The winning complex behaviour of each person in a scenario is defined as he complex behaviour ha is assigned he highes probabiliy a he end of he scenario. The sysem recognises he complex behaviour of a person correcly if he winning complex behaviour maches he groundruh. The correc duraion is defined as he oal of he ime periods, in which he primiive behaviour assigned he highes probabiliy maches he groundruh, over he lengh of he scenario. The correc duraion shows he performance of he sysem in recognising he primiive behaviour. We consider 12 scenarios. Each scenario has wo people and each execues a specific complex behaviour. Table 1 shows he resuls of recognising he behaviour of each person. Compared wih he groundruh, he sysem recognises correcly he complex behaviour execued by each person in all scenarios. The average correc duraion in all scenarios is 79%, showing ha he sysem is able o recognise he primiive behaviours reliably. We also compare he posiion of each person esimaed by he sysem wih he groundruh. The posiion error is he mean of he disance beween he cenroid of he person sae and he groundruh. The average posiion error of each person in each scenario is shown in Table 1. The average posiion error in all scenarios is 0.42 size o f sae, showing ha he sysem can rack muliple people reliably. 4.3 Compare he HHMM-JPDAF wih he Kalman filer We use he muliple Kalman filers and he JPDAF o rack people in a similar manner as in [2]. Then we compare he resuls wih he use of he HHMM-JPDAF. Consider Scenario 3 from ime 90 o 130. A ime 90, person 1 and person 2 are a he op-righ and boom-righ corners of he room, respecively (Figure 3(a)). Two people walk owards each oher and person 1 is occluded by person 2 a ime 110 (Figure 3(b)). Then, person 1 changes he direcion and heads o he op-lef corner of he room. Person 2 also changes direcion and heads o he boom-lef corner of he room. We obain he rajecory of each person by aking he mean of he cenroid of he person sae a each ime. Figure 3(d) shows he rajecories of person 1 and person 2 racked by he HHMM-JPDAF compared wih he groundruh. The HHMM-JPDAF can rack person 1 and person 2

9 9 Winning complex behaviour Correc duraion Average posiion error Scenario (uni = size of sae) Person 1 Person 2 Person 1 Person 2 Person 1 Person 2 1 have meal have snack 88% 97% cooking have meal 76% 40% have snack have meal 99% 79% cooking have meal 75% 77% have meal cooking 90% 81% have snack cooking 96% 75% have meal have meal 46% 74% have meal have snack 80% 96% have snack have meal 97% 94% cooking have meal 42% 63% have snack have meal 94% 94% have meal have meal 74% 75% Average 79% 0.42 Table 1: The winning complex behaviour, he correc duraion and he average posiion error in he 12 scenarios. (a) Time 90 (b) Time 110 (c) Time ime 130 ime ime 130 person 2 ime 90 peson 1 peson person ime 130 person 2 Ground Truh: Person 1 HHMM Person 1 Ground Truh Person 2 HHMM Person 2 person 2 ime person 1 Ground Truh: Person 1 Kalman Filer: Person 1 Ground Truh Person 2 Kalman Filer: Person 2 person 2 ime 130 ime (d) HHMM-JPDF vs. groundruh (e) Kalman filer vs. groundruh Figure 3: The racking resuls from ime 90 o 130 in Scenario 3. properly even when person 1 is occluded by person 2 and hen he wo persons change heir direcions. In conras, he Kalman filer mislabels hem in his case (Figure 3(e)). Under he same circumsance, he HHMM-JPDAF racks he wo people beer han he Kalman filer. Tha is because he HHMM-JPDAF can use informaion abou he behaviours of he wo people o solve he labelling confusion.

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