RGB-D Object Tracking: A Particle Filter Approach on GPU

Transcription

1 RGB-D Objec Tracking: A Paricle Filer Approach on GPU Changhyun Choi and Henrik I. Chrisensen Cener for Roboics & Inelligen Machines College of Compuing Georgia Insiue of Technology Alana, GA 3332, USA {cchoi,hic}@cc.gaech.edu Absrac This paper presens a paricle filering approach for 6-DOF objec pose racking using an RGB-D camera. Our paricle filer is massively parallelized in a modern GPU so ha i exhibis real-ime performance even wih several housand paricles. Given an a priori 3D mesh model, he proposed approach renders he objec model ono exure buffers in he GPU, and he rendered resuls are direcly used by our parallelized likelihood evaluaion. Boh phoomeric (colors) and geomeric (3D poins and surface normals) feaures are employed o deermine he likelihood of each paricle wih respec o a given RGB-D scene. Our approach is compared wih a racker in he PCL boh quaniaively and qualiaively in synheic and real RGB-D sequences, respecively. I. INTRODUCTION As robos are geing gradually deployed away from srucured environmens o unsrucured environmens, he reliable ineracion wih he environmens is a key necessiy for he success of uilizing roboic sysems. Especially, a robus and efficien objec pose recogniion is an imporan requiremen for reliable roboic asks. In early sages of roboic objec percepion, i was ried o solve his problem by employing known 3D objec models [1]. The problem was ypically formulaed as esimaing a pose ha will bes fi he given 3D model of he objec o 2D image feaures: edges [2], [3] or line segmens fied from he edges [4]. The opimal pose or moion parameers were hen esimaed via efficien local opimizaions. Alhough edge-based racking was shown o be usable for video rae racking even in he early 9 s [2], i was no robus o complex backgrounds and occlusions. Since edges hemselves are no discriminaive enough o provide reliable edge daa associaions, here have been many effors o augmen he early work by fusion wih keypoin feaures [5], [6], [7] or mainaining muliple pose hypoheses on edge daa associaions [5], [8]. However, hese approaches were sill limied in he sense ha hey only considered a small number of pose hypoheses. A more advanced formulaion considering muliple pose hypoheses has appeared based on paricle filering. Paricle filer [9], [1] is a Bayesian filering mehod based on sequenial simulaion from poserior probabiliy disribuions. For he las wo decades, his mehod has become popular since i can handle nonlinear and non-gaussian dynamics, so i has ofen been regarded as a good alernaive o he filering mehods designed upon Gaussian probabiliy disribuions for Fig. 1. A racking example. An objec is racked via our paricle filer parallelized on a GPU. The objec rendering represens he mean of he paricles. he sae space. Isard and Blake [11] inroduced a paricle filer o he compuer vision communiy as a robus 2D conour racking approach. Since hen, a large number of varians have been applied o he problem of body pose esimaion [12], 3D objec racking [13], [14], [15], SLAM [16], ec. However, adoping he paricle filering approaches o roboic percepion has been limied mainly due o heir high compuaional cos. To ackle his problem, some researchers [13], [14], [17], [18] have noiced ha paricle filer algorihms are inherenly parallelizable. The main boleneck of paricle filers is in heir likelihood evaluaions. When N paricles are employed o approximae he rue poserior probabiliy disribuion, N independen and idenical likelihood evaluaions should be performed a each ime sep. Since one likelihood evaluaion for a paricle does no depend on he res of he paricles, he likelihood compuaion can be parallelized. Modern graphics processing uni (GPU) provides massive parallel power beyond rendering purposes, so i is a naural idea o design a paricle filer on he GPU for fas and robus objec pose racking. Monemayor e al. [17] showed a preliminary design of a paricle filer on he GPU for a simple 2D objec racking. Klein and Murray [13] presened

2 a paricle filer which racks an arbirarily shaped objec in real-ime. To mainain he high frame rae, he OpenGL occlusion query exension was employed o calculae he paricle likelihood efficienly from a given edge image. While he work simply relied on an OpenGL exension, several approaches [14], [18] adoped a more advanced echnique o exploi he GPU, NVIDIA CUDA TM echnology, so ha hey render an objec model o he GPU and a CUDA kernel direcly accesses he rendering resuls, and hen he imporance weighs of he paricles are calculaed from he differences beween he rendered resuls and an inpu scene. Mos of he previous work have mainly used a monocular camera, so he visual feaures employed so far have been limied o edges [13], [14] or inensiy differences [17], [18]. However, as RGB-D sensors were recenly inroduced, no only color bu also deph informaion is readily available in real-ime. This deph informaion enables us o use various geomeric feaures, such as 3D poin coordinaes, surface normals, edges from deph disconinuiies, high curvaure regions, ec. Recenly, his addiional deph daa has acively been used in many roboic and vision applicaions, such as human pose esimaion [19], bin-picking problem [2], [21], [22], SLAM [23], [24], and objec racking [25]. The paricle filer-based racking in he PCL [26] is probably he closes sysem o our proposed soluion. Given an objec poin cloud as a reference model, i can rack he 6-DOF pose of he reference model over a sequence of RGB-D images. Is ime consuming rouines were parallelized in CPU, ye i does no achieve real-ime performance wih a sufficien number of paricles (see Secion VI). A brief descripion of he approach can be found in [27]. II. CONTRIBUTIONS We propose a robus paricle filer parallelized on a GPU which can rack a known 3D objec model over a sequence of RGB-D images. Unlike he PCL racking [27], we render he 3D objec model o be used in he likelihood evaluaion so ha our approach can rack he objec in spie of significan pose variaions. Our key conribuions are as follows: We employ exended feaures o evaluae he likelihood of each paricle sae. While mos of he previous work has mainly relied on 2D edges [13], [14] or inensiy differences [17], [18] o calculae he imporance weighs of paricles, we use boh phoomeric (colors) and geomeric feaures (3D poins and surface normals) available from boh RGB-D images and OpenGL rendering. We use he framebuffer objec exension (FBO) in OpenGL and he CUDA OpenGL ineroperabiliy o reduce he mapping ime of he rendering resul o CUDA s memory space. As [14] menioned, he mapping beween OpenGL framebuffer and he memory space of CUDA akes as much as copying he rendered resul o he memory space of CPU. To avoid his problem, our rendering is performed in he FBO so ha he mapping ime is nearly negligible. We devised an hierarchical approach o consider muliple renderings of he objec. While he PCL racking [26] mainains only one reference objec cloud, we render he objec o muliple viewpors wih differen poses. I would be ideal if we draw all paricle poses o he render buffers in he GPU, bu i is no possible due o he memory limiaion of he buffers. Insead, our approach renders he objec o V viewpors, and each paricle searches he closes rendering from V viewpors so ha each likelihood evaluaion is performed by ransforming he closes rendered resul wih he curren paricle sae (see Fig. 2). To he bes of our knowledge, our proposed soluion is he firs real-ime paricle filer for 6-DOF objec pose racking using rich visual feaures from he RGB-D sensor. Fig. 1 shows an example frame of our racking where a arge objec is racked in background cluer. The rendered 3D mesh model represens he mean of he paricles for visualizaion purpose. This paper is organized as follows. A paricle filer for 6- DOF objec pose racking is briefly menioned in Secion III, and he likelihood funcion employing poins, colors, and normals is inroduced in Secion IV. Afer he furher explanaion on he OpenGL and he CUDA implemenaion in Secion V, our approach is compared wih a baseline in boh synheic and real RGB-D image sequences in Secion VI. III. PARTICLE FILTER In he 6-DOF pose racking problem, a paricle filer is employed o sample he rajecory of an objec of ineres over ime. In a paricle filering framework, he poserior probabiliy densiy funcion of he objec pose p(x Z 1: ) a he curren ime is represened as a se of weighed paricles by S = {(X (1), π (1) ),..., (X (N), π (N) )} (1) where he paricles X (n) SE(3) represen samples, he normalized imporance weighs π (n) are proporional o he likelihood funcion p(z X (n) ), and N is he oal number of he paricles. A each ime, he paricle filer performs he sequenial imporance sampling wih resampling [1]. The curren sae X could be esimaed by he weighed paricle mean: X = E[S ] = N n=1 π (n) X (n). (2) As we already showed in [15], when we esimae he mean, we need o obain a valid roaion R SO(3) as he arihmeic mean R = 1 N N n=1 R(n) is no usually on he SO(3) group. From [28], he desired mean roaion can be calculaed via he orhogonal projecion of he arihmeic mean as { VU R = T when de(r T ) > (3) VHU T oherwise, where U and V are esimaed via he singular value decomposiion of R T (i.e. R T = UΣV T ) and H = diag[1, 1, 1].

3 Fig. 2. Muliple renderings for he likelihood evaluaion. The objec of ineres is rendered wih he firs V paricle saes and he likelihoods of he V paricles are evaluaed from he rendering resuls. For he res paricles, each paricle finds he closes rendering and use he rendering resul o evaluae is likelihood. Lef and righ images represen he color and normal renderings in he GPU. (Bes viewed in color) IV. LIKELIHOOD EVALUATION Designing an efficien and robus likelihood funcion is crucial, since i direcly deermines he overall performance of he paricle filering in erms of boh ime and accuracy. When an RGB-D camera is considered, here are various measuremens we can employ: 3D poin coordinaes, colors of poins, surface normals, curvaure, edges from deph disconinuiies or surface exures, ec. In his work, we choose he poin coordinaes x R 3 and heir associaed colors c R 3 and normals n R 3. Thus, a measuremen poin p is defined as p = (x T, n T, c T ) T R 9. (4) For clear noaion, le us define accessing operaors for p such ha x(p) = (x T 1) T R 4 (5) n(p) = (n T 1) T R 4 (6) c(p) = c R 3. (7) The reason we choose he hree measuremens is ha his combinaion allows us o perform direc comparisons beween he given RGB-D scene and he rendering resuls from he compuer graphics pipeline. Hence, we can efficienly calculae he likelihood for a large number of paricles. Given he curren pose hypohesis X (n) and he rendered objec model M, he likelihood of he scene Z is defined as p(z X (n), M ) = (i,j) A p(z (i) X (n), m (j) ) (8) where A = {(i, j) proj(x(z (i) )) = proj(x (n) he se of poin associaions beween he scene Z and he x(m (j) ))} is objec model M, and z (i), m (j) R 9 are corresponding poins in he scene and model, respecively. The operaor proj( ) calculaes 2D image coordinaes of given 3D homogeneous poin coordinaes by projecing he poin wih he known camera inrinsic parameers K R 3 3. Wih he proj operaor, he poin associaions A can be efficienly deermined. The likelihood of each associaion (i, j) is hen defined as p(z (i) X (n), m (j) ) = exp λe de(x(z(i) exp λn dn(n(z(i) ), X (n) x(m (j) )) ), X (n) n(m (j) )) exp λc dc(c(z(i) ), c(m (j) )) where d e (x 1, x 2 ), d n (n 1, n 2 ), and d c (c 1, c 2 ) are Euclidean, normal, and color disances as shown below { x1 x d e (x 1, x 2 ) = 2 if x 1 x 2 τ (1) 1 oherwise d n (n 1, n 2 ) = cos 1 (n T 1 n 2 1) π (11) d c (c 1, c 2 ) = c 1 c 2 (12) and λ e, λ n, λ c are he parameers ha deermines he sensiiviy of he disances o he likelihood. The τ in (1) is a hreshold value for he Euclidean disance beween he wo poins. Noe ha n 1, n 2 R 4 in (11) are homogeneous poin coordinaes, so 1 need o be subraced from he inner produc. For he color disance in (12), any kind of color space can be considered as long as d c (c 1, c 2 ) 1, bu we adoped he HSV color space due mainly o is invariance o illuminaion changes. Please noe ha he poin and normal coordinaes of objec model poin m (j) are in he objec coordinae frame, so he ransformed poin by he curren pose X (n) should be considered o calculae he disances. V. IMPLEMENTATION DETAILS As we already menioned in Secion II, we render our objec of ineres ono V viewpors in he render buffers wih he firs V paricle poses. For he res of he paricles, each paricle finds a closes rendering wih respec o he pose hypohesis and ransforms he close rendering resul wih he curren pose. For his calculaion, we need o access he color, (9)

4 Fig. 3. Mesh models for objecs and kichen. Objec models were generaed by fusing muliple RGB-D views, followed by running he Poisson reconsrucion algorihm [29]. To generae a se of synheic sequences, a kichen model was download from he Google 3D warehouse. From lef o righ, Tide, Milk, Orange Juice, Kinec Box, and Kichen. Fig. 4. Camera rajecories in synheic sequences. Synheic RGB-D sequences were generaed wih heir corresponding ground ruh rajecories of he objecs. Please noe he significan variaions in ranslaion, roaion, and velociy. From lef o righ, rajecories of Tide, Milk, Orange Juice, and Kinec Box. verex (i.e. 3D poin), and normal informaion for all visible poins in he rendered resul. I is relaively sraighforward o ge color informaion via accessing he render buffer, bu i is ricky o access 3D poin and 3D normal daa from he buffer. To ackle his problem, we employ he OpenGL Shading Language (GLSL) o direcly access he poin and normal daa in he middle of he graphics pipeline. For poin informaion, we designed a se of simple verex and fragmen shaders so ha he 3D coordinaes of visible poins gl Verex are saved o color exure poins gl FragColor. Similarly, for normal daa anoher se of verex and fragmen shaders is used so ha he surface normals of he objec gl Normal are saved in color exure poins. Noe ha hese poins and normals are in he objec coordinae frame, so we do no need o perform an inverse ransform on he rendering resul before ransforming hem wih respec o he curren paricle pose. The main purpose of he muliple viewpors rendering is no for visualizaion bu for he likelihood evaluaion of each paricle. Thus using he Frame Buer Objec (FBO, GL ARB framebuffer objec) is a good choice for our rendering purpose. The FBO is an OpenGL exension for off-screen framebuffers. Unlike he defaul framebuffer of OpenGL provided by window sysems, he FBO is more flexible and efficien since all resources bound in he FBO are shared wihin he same conex. The FBO allows users o aach muliple exure images o color aachmens. For our purpose, we aach hree exure images o he hree color aachmens: GL COLOR ATTACHMENT for color daa, GL COLOR ATTACHMENT1 for poin daa, and GL COLOR ATTACHMENT2 for normal daa. In he rendering phase, our objec of ineres is drawn ono each color aachmen. While he color exure is drawn using he usual OpenGL rendering, he poin and normal exures are rendered via he aforemenioned shader programs. For each rendering, he objec is rendered o V viewpors by calling glviewpor(). Afer rendering he objec wih shader programs, we evaluae he likelihood funcion on he GPU. To uilize he exure images aached o he FBO in our likelihood evaluaion kernel, we use he CUDA OpenGL ineroperabiliy ha allows o map/unmap OpenGL buffers o CUDA s memory space. So our CUDA kernel can access he rendered buffers very efficienly. VI. E XPERIMENTS In his secion, we presen a se of comparaive experimens beween he PCL racking and our proposed approach. The performance of he wo approaches is quaniaively evaluaed using a se of synheic RGB-D sequences wih he ground ruh objec rajecories in Secion VI-B, followed by he qualiaive evaluaion using real RGB-D sequences in Secion VI-C. For he evaluaions, boh rackers are iniialized wih he known ground ruh in synheic sequences and wih he converged pose esimaes afer running our racker from a sufficienly close iniial pose. The PCL racking provides an opion for adapive paricle size based on [3], bu here he fixed paricle size is considered for fair comparisons wih our approach and for he performance evaluaion wih respec o differen paricle sizes. All experimens were performed using a sandard deskop compuer (Inel Core2 Quad CPU Q93, 8G RAM) wih an off-he-shelf GPU

5 Fig. 5. Tracking resuls on he Orange Juice and he Kinec Box synheic sequences. For boh sequences, he upper rows show he racking resuls of our approach, while he lower rows presen he resuls of he PCL racking (N = 64 for he Orange Juice sequence and N = 128 for he Kinec Box sequence). In boh sequences, our approach racks he rue objec rajecories well, bu he PCL racking is ofen los due o he limiaion of he objec model. (Bes viewed in color) 4 x Translaion 4 y Translaion 14 z Translaion (mm) 2 2 (mm) 2 (mm) Roll (α) Angle Pich (β) Angle Yaw (γ) Angle (degree) (degree) (degree) 1 5 Ground Truh PCL racking Ours (τ =.1) Fig. 6. The 6-DOF pose plos of he Kinec Box resuls in Fig. 5. While our approach well follows he ground ruh, he PCL racking suffers from wrong racking due o he limiaion of he objec model. (NVIDIA GeForce GTX 59, CUDA 4.1) and an RGB-D camera (ASUS Xion Pro Live). A. Objec Models For he experimens, four objecs were chosen, and he 3D mesh models of he objecs (Fig. 3) were generaed by using an RGB-D sensor. To generae he mesh model, we firs obained muliple RGB-D views and regisered hem. We could use one of he RGB-D SLAM approaches [23], [24], [31] o regiser he muliple views, bu we employed several ARTags for simpliciy. Once he muliple views were fused, he objec cloud was segmened from he background clouds and was reconsruced o resul in a mesh model via he Poisson reconsrucion algorihm [29]. As he PCL racking can no use he 3D mesh models, he objec poin clouds which were obained by rendering wih he iniial poses were fed o be used as reference models. B. Synheic Sequences For a quaniaive analyses, we generaed a se of synheic RGB-D sequences. To simulae a realisic environmen, a virual kichen model (see Fig. 3) was downloaded from he

6 TABLE I RMS ERRORS AND COMPUTATION TIME IN SYNTHETIC RGB-D SEQUENCES (PCL VS. OUR TRACKING) Objecs Tracker N Tide Milk Orange Juice Kinec Box PCL Ours (τ =.1) PCL Ours (τ =.1) PCL Ours (τ =.1) PCL Ours (τ =.1) For he sake of comparison, beer resuls are indicaed in bold ype. RMS Errors Time (ms) X (mm) Y (mm) Z (mm) Roll (deg) Pich (deg) Yaw (deg)

7 Fig. 7. Tracking resuls on he Tide and Milk real sequences. For boh sequences, he upper rows show he racking resuls of our approach, while he lower rows presen he resuls of he PCL racking (N = 16). As he objecs undergo significan variaions in roaions, he PCL racking suffered from false pose esimaes. Thanks o muliple model renderings every ime, our racking reliably racks he rue poses of he objecs. (Bes viewed in color) Compuaion Time Time (ms) Time (ms) Compuaion Time Number of papricles Number of papricles Fig. 8. Boxplos showing compuaion ime of our racking (lef) and he PCL racking (righ) on he Tide synheic sequence. For boh approaches, ime linearly increases as he number of he paricles N increases, bu our increasing rae is much smaller. Noe ha he compuaion ime of our approach is less han 5 ms unil N 32. Google 3D warehouse. Afer placing each objec model in he kichen model, a se of synheic sequences was generaed by moving he virual camera around he objec. Fig. 4 shows he camera rajecories of he synheic daa which exhibi high variaions in ranslaion, roaion, and velociy of he camera. The objec rajecories were saved o be used as ground ruh poses of he objecs wih respec o he camera coordinae frame. To compare our approach wih he PCL racking, we calculaed he roo mean square (RMS) errors and average compuaion ime per frame over he four synheic RGB-D sequences as shown in Table I. For he sake of comparison, beer resuls are indicaed in bold ype. The RMS errors vary depending on boh he objec ype and he difficuly of he sequences. Bu he overall rend here is ha as he number of he paricles N increases he ranslaional and roaional errors are decreased. In he Tide sequence which is raher simple compared o he oher sequences, for example, he PCL racking repors slighly beer resuls when N 8. Bu as N increases, our racker shows more accurae resuls. An ineresing fac in he Tide sequence is ha he PCL racking shows slighly beer resul in z ranslaion. This may be due o he fac ha he PCL racking has only one reference objec poin cloud as an objec model so ha i does resul in smaller error in ha direcion. However, he limied number of he reference cloud is geing problemaic when i runs on more challenging sequences. Please noe ha big errors in boh ranslaion and roaions in he Milk, Orange Juice, and Kinec Box sequences. Since he objecs are self-symmeric hemselves, he one reference view of each objec is no enough o rack he objecs over he enire sequences. As shown in Fig. 5 and Fig. 6, he PCL racking is ofen suck in local minima during he racking, while our approach robusly racks he objecs in he sequences. For roboic applicaions, he compuaion ime is really imporan since i direcly deermines he performance and he reliabiliy of he roboic sysems. As we can see in boh Table I and Fig. 8, he compuaion ime of boh approaches

8 increases linearly as N increases. However, our racking only akes abou 5 ms per frame (i.e. 2 frames per second) wih several housands paricles, whereas he PCL racking suffers from low frame raes. Alhough he PCL racking shows comparable performance in he Tide sequence, if we consider he real frame raes he PCL racking would have much higher errors due o he los frames. C. Real Sequences We ran boh racking approaches in a se of real image sequences which exhibis significan noise and more variable objec moions compared o he synheic sequences. Fig. 7 shows he pose racking resuls on he Tide and Milk sequences. For clear visualizaion, he RGB channels from he RGB-D sequences were convered o gray scale, and each rendered objec model was drawn on op of hem. Invalid deph poins (also known as Nan poins) were shown as black poins. For boh sequences, N = 16 paricles were employed. As he objecs experience significan variaions in roaions, he PCL racking (lower rows in each sequence) ofen loses is racking. Thanks o employing he 3D objec model and rendering i in muliple views, our racking dependably racks he objec in spie of he challenging roaional moions. VII. CONCLUSIONS We presened an approach for RGB-D objec racking which is based on a paricle filer on a GPU. Rich visual feaures were employed o evaluae he likelihood of each paricle, and his process, which is a ypical boleneck in mos paricle filers, was parallelized on he GPU so ha our proposed soluion achieves real-ime performance. Through a se of exensive experimens wih boh synheic and real RGB-D sequences, we verified ha our approach is no only faser bu also more accurae han he PCL racking. VIII. ACKNOWLEDGMENTS This work has in par been sponsored by he Boeing Corporaion. The suppor is graefully acknowledged. REFERENCES [1] L. G. 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