{"title": "Attractive People: Assembling Loose-Limbed Models using Non-parametric Belief Propagation", "book": "Advances in Neural Information Processing Systems", "page_first": 1539, "page_last": 1546, "abstract": "", "full_text": "Attractive People: Assembling Loose-Limbed\n\nModels using Non-parametric Belief Propagation\n\nLeonid Sigal\n\nDepartment of Computer Science\n\nBrown University\n\nProvidence, RI 02912\nls@cs.brown.edu\n\nMichael Isard\n\nMicrosoft Research Silicon Valley\n\nMountain View, CA 94043\n\nmisard@microsoft.com\n\nBenjamin H. Sigelman\n\nMichael J. Black\n\nDepartment of Computer Science\n\nDepartment of Computer Science\n\nBrown University\n\nProvidence, RI 02912\n\nBrown University\n\nProvidence, RI 02912\n\nbhsigelm@cs.brown.edu\n\nblack@cs.brown.edu\n\nAbstract\n\nThe detection and pose estimation of people in images and video is made\nchallenging by the variability of human appearance, the complexity of\nnatural scenes, and the high dimensionality of articulated body mod-\nels. To cope with these problems we represent the 3D human body as a\ngraphical model in which the relationships between the body parts are\nrepresented by conditional probability distributions. We formulate the\npose estimation problem as one of probabilistic inference over a graphi-\ncal model where the random variables correspond to the individual limb\nparameters (position and orientation). Because the limbs are described\nby 6-dimensional vectors encoding pose in 3-space, discretization is im-\npractical and the random variables in our model must be continuous-\nvalued. To approximate belief propagation in such a graph we exploit a\nrecently introduced generalization of the particle \ufb01lter. This framework\nfacilitates the automatic initialization of the body-model from low level\ncues and is robust to occlusion of body parts and scene clutter.\n\n1\n\nIntroduction\n\nRecent approaches to person detection and tracking exploit articulated body models\nin which the body is viewed as a kinematic tree in 2D [14], 2.5D [16, 23], or 3D\n[2, 5, 6, 19, 21] leading to a parametric state-space representation of roughly 25\u201335 di-\nmensions. The high dimensionality of the resulting state-space has motivated the devel-\nopment of specialized stochastic search algorithms that either exploit the highly redundant\ndynamics of typical human motions [19], or use hierarchical sampling schemes to exploit\nthe tree-structured nature of the model [5, 15]. These schemes have been effective for\ntracking people wearing increasingly complex clothing in increasingly complex cluttered\nbackgrounds [21]. There are however a number of important shortcomings of these ap-\n\n\fproaches. Hierarchical body models lead to \u201ctop-down\u201d search algorithms that make it\ndif\ufb01cult to incorporate \u201cbottom-up\u201d information about salient body parts available from\nspecial-purpose detectors (e.g. face or limb detectors). As a result, few, if any, of the above\nmethods deal with the problem of automatic initialization of the body model. Furthermore,\nthe dif\ufb01culty of incorporating bottom-up information means that the algorithms are brittle;\nthat is, when they lose track of the body, they have no way to recover. Finally, the fully\ncoupled kinematic model results in a computationally challenging search problem because\nthe search space cannot be naturally decomposed.\n\nTo address these problems, we propose a \u201cloose-limbed\u201d body model in which the limbs\nare not rigidly connected but are rather \u201cattracted\u201d to each other (hence the title \u201cAttrac-\ntive People\u201d). Instead of representing the body as a single 33-dimensional kinematic tree,\neach limb is treated quasi-independently with soft constraints between the position and\norientation of adjacent parts. The model resembles a Push Puppet toy which has elastic\nconnections between the limbs (Figure 1a).\n\nThis type of model is not new for \ufb01nding or tracking articulated objects and dates back at\nleast to Fischler and Elschlager\u2019s pictorial structures [9]. Variations on this type of model\nhave been recently applied by Burl et al. [1], Felzenszwalb and Huttenlocher [8], Coughlan\nand Ferreira [3] and Ioffe and Forsyth [11, 17]. The main bene\ufb01ts are that it supports\ninference algorithms where the computational cost is linear rather than exponential in the\nnumber of body parts, it allows elegant treatment of occlusion, and it permits automatic\ninitialization based on individually unreliable low-level body-part detectors [25].\n\nThe work described here, like the previous work above, exploits this notion of \ufb02exible\n\u201cspring\u201d-like constraints [8] de\ufb01ned over individually modeled body parts [11, 17, 23],\nthough we extend the approach to locate the parts in 3-space rather than the 2-dimensional\nimage plane. The body is treated as a graphical model [13], where each node in the graph\ncorresponds to an independently parameterized body part. The spatial constraints between\nbody parts are de\ufb01ned as directed edges in the graph. Each edge has an associated condi-\ntional distribution that models the probabilistic relationship between the parts. Each node\nin the graph also has a corresponding image likelihood function that models the probability\nof observing various image measurements conditioned on the position and orientation of\nthe part. Person detection (or tracking) then exploits belief propagation [24] to estimate\nthe belief distribution over the parameters which takes into account the constraints and the\nobservations.\n\nThis graphical inference problem is carried out using a recently proposed method that al-\nlows the parameters of the individual parts to be modeled using continuous-valued random\nvariables rather than the discrete variables used in previous approaches. This is vital in\nour problem setting, since the discretization used in [8] is impractical once the body is\nmodeled in 3-space. Similar versions of the algorithm were independently introduced by\nSudderth et al. [22] under the name of Non-parametric Belief Propagation (NBP) and by\nIsard [12] as the PAMPAS algorithm. We adopt the framework of Isard while making use\nof the Gibbs sampler introduced by Sudderth et al. The algorithm extends the \ufb02exibility of\nparticle \ufb01lters to the problem of belief propagation and, in our context, allows the model\nto cope with general constraints between limbs, permits realistic appearance models, and\nprovides resilience to clutter.\n\nWe develop the loose-limbed model in detail, formulate the constraints between limbs using\nmixture models, and outline the inference method. Using images from calibrated cameras\nwe illustrate the inference of 3D human pose with belief propagation. We simulate noisy,\nbottom-up, feature detectors for the limbs and show how the inference method can resolve\nambiguities and cope with clutter. While our focus here is on static detection and pose\nestimation, the body model can be extended in time to include temporal constraints on the\nlimb motion; we save tracking for future work.\n\n\f9\n\n0\n\n7\n\n8\n\n5\n\n6\n\n1\n\n3\n\ny1,2\n\ny3,4\n\n2\n\ny2,1\n\ny4,3\n\n4\n\n(a)\n\n(b)\n\n(c)\n\nFigure 1: (a) Toy Push Puppet with elastic joints. (b) Graphical model for a person. Nodes represent\nlimbs and arrows represent conditional dependencies between limbs. (c) Parameterization of part i.\n\n2 A self-assembling body model\n\nThe body is represented by a graphical model in which each graph node corresponds to a\nbody part (upper leg, torso, etc.). Each part has an associated con\ufb01guration vector de\ufb01ning\nthe part\u2019s position and orientation in 3-space. Placing each part in a global coordinate frame\nenables the part detectors to operate independently while the full body is assembled by in-\nference over the graphical model. Edges in the graphical model correspond to spatial and\nangular relationships between adjacent body parts, as illustrated in Figure 1b. As is stan-\ndard for graphical models we assume the variables in a node are conditionally independent\nof those in non-neighboring nodes given the values of the node\u2019s neighbors1.\nEach part/limb is modeled by a tapered cylinder having 5 \ufb01xed (person speci\ufb01c) and 6 esti-\nmated parameters. The \ufb01xed parameters (cid:8)i = (li; wp\ni ) correspond respectively\nto the part length, width at the proximal and distal ends and the offset of the proximal and\ndistal joints along the axis of the limb as shown in Figure 1c. The estimated parameters\ni ) represent the con\ufb01guration of the part i in a global coordinate frame\nXT\nwhere xi 2 R3 and (cid:2)i 2 SO(3) are the 3D position of the proximal joint and the angular\norientation of the part respectively. The rotations are represented by unit quaternions.\n\ni = (xT\n\ni ; (cid:2)T\n\ni ; wd\n\ni ; op\n\ni ; od\n\nEach directed edge between parts i and j has an associated conditional distribution\n ij(Xi; Xj) that encodes the compatibility between pairs of part con\ufb01gurations; that is,\nit models the probability of con\ufb01guration Xj of part j conditioned on the Xi of part i.\nFor notational convenience we de\ufb01ne an ordering on body parts going from the torso out\ntowards the extremities and refer to conditionals that go along this ordering as \u201cforward\u201d\nconditionals. Conversely, the conditionals that go from the extremities towards the torso\nare referred to as \u201cbackward\u201d conditionals. These intuitively correspond to kinematic and\ninverse-kinematic constraints respectively.\n\nConditional distributions were constructed by hand to capture the physical constraints of\nthe joints and limbs of the human body. A typical range of motion information for the\nvarious joints is approximated by the model. In general, these conditionals can, and should,\nbe learned from motion capture data.\n\nBecause we have chosen the local coordinate frame to be centered at the proximal joint of\n\n1Self-occlusion and self-intersection violate this assumption. These can be modeled by adding\nadditional edges in the graph between the possibly occluding or inter-penetrating parts. In the limit\nthis would lead to quadratic as opposed to linear computation time in the number of parts.\n\n\f(a)\n\n(b)\n\nFigure 2: (a) For the forwards conditional the location of part i tightly constrains the proximal joint\nof part j (light dots) while the position of the distal joint (dark dots) lies along an arc around the\nprincipal axis of rotation, approximated by a Gaussian mixture. (b) For the backwards conditional\npart i constrains the distal joint of part j (dark dots), so the proximal joint position (light dots) lies in\na non-Gaussian volume again approximated using a mixture distribution.\n\na part, the forward and backward conditionals are not symmetric. In both directions the\nprobability of Xj, conditioned on Xi, is non-Gaussian and it is approximated by a mixture\nof Mij Gaussians (typically 5-7 in the experiments here): ij(Xi; Xj) =\n\n(cid:21)0N (Xj; (cid:22)ij; (cid:3)ij) + (1 (cid:0) (cid:21)0)PMij\n\nm=1 (cid:14)ijmN (Xj; Fijm(Xi); Gijm(Xi))\n\n(1)\n\nwhere (cid:21)0 is a \ufb01xed outlier probability, (cid:22)ij and (cid:3)ij are the mean and covariance of the\nGaussian outlier process, and Fijm(:) and Gijm(:) are functions computing the mean and\ncovariance matrix respectively of the m-th Gaussian mixture component. These functions\nallow the mean and variance of the mixture components to be function of the limb pose Xi.\n\nm=1 (cid:14)ijm = 1.\n\n(cid:14)ijm is the relative weight of an individual component and PMij\n\nFigure 2a and b illustrate the forward and backward conditionals respectively. For the\nforward case, we examine the distribution of calf con\ufb01gurations conditioned on the thigh.\nTo illustrate the conditional distribution we sample from it and plot the endpoints of the\nsampled limb con\ufb01gurations. In the forward direction the conditional distribution over xj\n(the position of the proximal joint of part j) is well approximated by a Gaussian so each\nmixture component has the same mean and covariance for xj. This can be seen in the tight\nclustering of the light dots which lie almost on top of each other. The probability of the\nlower leg angle is restricted to a range of legal motions conditioned on the upper leg. This\ndistribution over rotations is modeled by giving each mixture component a different mean\nrotation, (cid:2)j, spaced evenly around the principal axis of the joint. This angular uncertainty\nis illustrated by the dark dots.\n\nFor the backward conditional we show the distribution over torso con\ufb01gurations condi-\ntioned on the thigh. In this direction the conditional predicting xj (e.g. torso position) is\nmore complicated. The location of xi restricts xj to lie near a hemisphere, and the ori-\nentation (cid:2)i and principal axis of rotation further restrict xj to a strip on that hemisphere\nwhich can be seen in Figure 2b (light dots). Thus each mixture component in (1) is spaced\nevenly in (cid:2)j and xj to represent this range of uncertainty. The combined uncertainty in\ntorso location and orientation can be seen in the distribution of the dark dots representing\nthe distal torso joint.\n\n\fImage Likelihoods\n\nThe inference algorithm outlined in the next section combines the body model described\nabove with a probabilistic image likelihood model. In particular, we de\ufb01ne (cid:30)i(Xi) to be the\nlikelihood of observing the image measurements conditioned on the pose of limb i. Ideally\nthis model would be robust to partial occlusions, the variability of image statistics across\ndifferent input sequences, and variability among subjects. To that end, we combine a vari-\nety of cues including multi-scale edge and ridge \ufb01lters as well as background subtraction\ninformation. Following related work [18], the likelihoods are estimated independently for\neach image view by projecting the 3D model of a limb into the corresponding image pro-\njection plane. These likelihoods are then combined across views, assuming independence,\nand are weighted by the observability of the limb in a given view (more weight is given to\nviews in which the limb lies parallel to the image projection plane). For more information\non the formulation of the image likelihoods see [20].\n\n3 Non-parametric Belief Propagation\n\nHaving de\ufb01ned the model it remains to specify an algorithm which will perform inference\nand estimate a belief distribution for each of the body parts. If it were feasible to discretize\nthe Xi we could apply traditional belief propagation or a specialized inference algorithm\nas set out in [8]. However, the 6-dimensional con\ufb01guration vector compels the use of\ncontinuous-valued random variables, and so we adopt the algorithm introduced in [12, 22]\nfor just such types of model. It is a generalization of particle \ufb01ltering [7] which allows\ninference over arbitrary graphs rather than just a chain. This generalization is achieved by\ntreating the particle set which is propagated in a standard particle \ufb01lter as an approximation\nto the \u201cmessage\u201d used in the belief propagation algorithm, and replacing the conditional\ndistribution from the previous time step by a product of incoming message sets.\nA message mij from node i ! j is written\n\nmij(Xj) = Z ij(Xi; Xj)(cid:30)i(Xi) Yk2Ainj\n\nmkj(Xi)dXi;\n\n(2)\n\nwhere Ai is the set of neighbors of node i and (cid:30)i(Xi) is the local likelihood associated\nwith node i. The message mij(Xj) can be approximated by importance sampling N 0 =\n(N (cid:0) 1)=Mij times from a proposal function f (Xi), and then doing importance correction.\n(See [22] for an alternative algorithm that uses more general potential functions than the\nconditional distributions used here.) As discussed in [12] the samples may be strati\ufb01ed into\ngroups with different proposal functions f ((cid:1)), so some samples come from the product of all\nincoming messages Ai into the node, some from Ainj (i.e. Ai excluding j) and some from\na static importance function Q(Xi) \u2014 we use a limb proposal distribution based on local\nimage measurements. For reasons of space we present only a simpli\ufb01ed algorithm to update\nmessage mij in Figure 3 which does not include the strati\ufb01cation but the full algorithm can\nbe found in [12]. We use the Gibbs sampler described in [22] to form message products of\nD > 2 messages.\nThe algorithm must sample, evaluate, and take products over Gaussian distributions de\ufb01ned\n2 SO(3) and represented in terms of unit quaternions. We adopt the approximation given\nin [4] for dealing with rotational distributions by treating the quaternions locally linearly in\nR4 \u2014 this approximation is only valid for kernels with small rotational covariance and can\nin principle suffer from singularities if product distributions are widely distributed about\nthe sphere, but we have not encountered problems in practice.\n\n\f1. Draw N 0 = (N (cid:0) 1)=Mij samples from the proposal function:\n\n~sn0\nij (cid:24) f (Xi); n0 2 [1; N 0]:\n\n2. Compute importance corrections for n0 2 [1; N 0]:\n\n(cid:17)n0\nij =\n\n(cid:30)i(~sn0\n\nij )Qk2Ainj mki(~sn0\n\nij )\n\n:\n\nf (~sn0\nij )\n\n3. Store normalized weights and mixture components for n0 2 [1; N 0]; m 2 [1; Mij]:\n\n(a) n = (n0 (cid:0) 1)Mij + m\n(b) (cid:22)n\n(c) (cid:3)n\n\nij = Fijm(~sn0\nij )\nij = Gijm(~sn0\nij )\n\n(d) (cid:25)n\n\nij = (1 (cid:0) (cid:21)0)\n\n(cid:17)n0\nij (cid:14)ijm\nPN 0\nk=1 (cid:17)k\n\nij\n\n.\n\n4. Assign outlier component: (cid:25)N\n\nij = (cid:21)0; (cid:22)N\n\nij = (cid:22)0\n\nij; (cid:3)N\n\nij = (cid:3)0\nij\n\nFigure 3: The simpli\ufb01ed PAMPAS non-parametric belief propagation algorithm.\n\n4 Experiments\n\nWe illustrate the approach by recovering 3D body pose given weak bottom-up informa-\ntion and clutter. The development of bottom-up part detectors is beyond the scope of this\npaper. Here we exploit a realistic simulation of such detectors in which: 1) the limbs are\nonly detected 50% of the time \u2014 the remaining samples are clutter; 2) the limb detectors\nare non-speci\ufb01c in that they cannot distinguish the left and right sides of the body or the\nupper from lower limbs (they do, however, distinguish between legs and arms) \u2014 the re-\nsult is that only a small fraction of bottom-up samples fall in the right place with the right\ninterpretation; 3) the detectors are noisy and do not detect the limb position and orienta-\ntion accurately; 4) no correct initialization samples are generated for the torso, simulating\ndetector failure or occlusion.\n\nFigure 4 shows results for two time instants in a video sequence taken from three calibrated\ncameras. After 10 iterations of belief propagation, the algorithm has discarded the samples\nwhich originated in clutter and has correctly assigned the limbs. The \ufb01gure shows the\ninitialization and the \ufb01nal distribution over limb poses which is computed by sampling\nfrom the belief distribution. Note that the torso is well localized even though there was no\nbottom-up detector for it.\n\n5 Conclusion\n\nWe present a new body model and inference method that supports the goals of automati-\ncally locating and tracking an articulated body in three dimensions. We show that a \u201cloose-\nlimbed\u201d model with continuous-valued parameters can effectively represent a person\u2019s lo-\ncation and pose, and that inference over such a model can be tractably performed using\nbelief propagation over particle sets. Moreover, we demonstrate robust location of the per-\nson starting from imperfect initialization using a simulated body-part detector. The detector\nis assumed to generate both false positive initializations and false negatives; i.e. failures to\ndetect some body parts altogether.\n\nIt is straightforward to extend the graphical model across time to implement a person\n\n\f(a)\n\n(b)\n\nFigure 4: Inferring attractive people: Two experiments are shown; (a) and (b) show results\nfor two different time instants in a walking cycle. Each experiment used three calibrated\ncamera views. Left: Initialization samples drawn from noisy simulated part detectors. Part\ndetectors are assumed to have high failure rate, generating 50% of the samples far away\nfrom any true body part. They are also non-speci\ufb01c; e.g. the left thigh samples are equally\ndistributed over left and right thigh and calf. The torso is assumed to be undetectable.\nRight: Belief after 10 iterations of PAMPAS. We use 100 particles to model the messages\nbetween the nodes, and show 20 samples from the belief distribution, as well as the average\nof the top 10 percent of the belief samples as the \u201dbest\u201d pose estimate. For brevity, (b) only\nshows the best pose from a single view.\n\ntracker. There are several advantages of this approach compared with traditional particle\n\ufb01ltering: the complexity of the search task is linear rather than exponential in the number\nof body parts; bottom-up initialization information can be incorporated in every frame; and\nforward-backward smoothing, either over a time-window or an entire sequence, is straight-\nforward.\n\nIn future work we intend to build automatic body-part detectors. Constructing reliable\ndetectors using only low-level information (static appearance) is a challenging problem\nbut we have the advantage of being robust to imperfect detection as noted above. 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Object segmentation by graph partitioning Concurrent object\nrecognition and segmentation by graph partitioning, Advances in Neural Info. Proc. Sys. 15,\npp. 1407\u20131414, 2003.\n\n\f", "award": [], "sourceid": 2499, "authors": [{"given_name": "Leonid", "family_name": "Sigal", "institution": null}, {"given_name": "Michael", "family_name": "Isard", "institution": null}, {"given_name": "Benjamin", "family_name": "Sigelman", "institution": null}, {"given_name": "Michael", "family_name": "Black", "institution": null}]}