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78
Nonparametric Belief Propagation
 IN CVPR
, 2002
"... In applications of graphical models arising in fields such as computer vision, the hidden variables of interest are most naturally specified by continuous, nonGaussian distributions. However, due to the limitations of existing inf#6F6F3 algorithms, it is of#]k necessary tof#3# coarse, ..."
Abstract

Cited by 213 (24 self)
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In applications of graphical models arising in fields such as computer vision, the hidden variables of interest are most naturally specified by continuous, nonGaussian distributions. However, due to the limitations of existing inf#6F6F3 algorithms, it is of#]k necessary tof#3# coarse, discrete approximations to such models. In this paper, we develop a nonparametric belief propagation (NBP) algorithm, which uses stochastic methods to propagate kernelbased approximations to the true continuous messages. Each NBP message update is based on an efficient sampling procedure which can accomodate an extremely broad class of potentialf#l3]k[[z3 allowing easy adaptation to new application areas. We validate our method using comparisons to continuous BP for Gaussian networks, and an application to the stereo vision problem.
Tracking Looselimbed People
, 2004
"... We pose the problem of 3D human tracking as one of inference in a graphical model. Unlike traditional kinematic tree representations, our model of the body is a collection of looselyconnected limbs. Conditional probabilities relating the 3D pose of connected limbs are learned from motioncaptured tr ..."
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Cited by 145 (7 self)
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We pose the problem of 3D human tracking as one of inference in a graphical model. Unlike traditional kinematic tree representations, our model of the body is a collection of looselyconnected limbs. Conditional probabilities relating the 3D pose of connected limbs are learned from motioncaptured training data. Similarly, we learn probabilistic models for the temporal evolution of each limb (forward and backward in time). Human pose and motion estimation is then solved with nonparametric belief propagation using a variation of particle filtering that can be applied over a general loopy graph. The looselimbed model and decentralized graph structure facilitate the use of lowlevel visual cues. We adopt simple limb and head detectors to provide "bottomup" information that is incorporated into the inference process at every timestep; these detectors permit automatic initialization and aid recovery from transient tracking failures. We illustrate the method by automatically tracking a walking person in video imagery using four calibrated cameras. Our experimental apparatus includes a markerbased motion capture system aligned with the coordinate frame of the calibrated cameras with which we quantitatively evaluate the accuracy of our 3D person tracker.
Finding and Tracking People from the Bottom Up
, 2003
"... We describe a tracker that can track moving people in long sequences without manual initialization. Moving people are modeled with the assumption that, while configuration can vary quite substantially from frame to frame, appearance does not. This leads to an algorithm that firstly builds a model of ..."
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Cited by 119 (6 self)
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We describe a tracker that can track moving people in long sequences without manual initialization. Moving people are modeled with the assumption that, while configuration can vary quite substantially from frame to frame, appearance does not. This leads to an algorithm that firstly builds a model of the appearance of the body of each individual by clustering candidate body segments, and then uses this model to find all individuals in each frame. Unusually, the tracker does not rely on a model of human dynamics to identify possible instances of people; such models are unreliable, because human motion is fast and large accelerations are common. We show our tracking algorithm can be interpreted as a loopy inference procedure on an underlying Bayes net. Experiments on video of real scenes demonstrate that this tracker can (a) count distinct individuals; (b)identify and track them; (c) recover when it loses track, for example, if individuals are occluded or briefly leave the view; (d) identify the configuration of the body largely correctly; and (e) is not dependent on particular models of human motion.
PAMPAS: RealValued Graphical Models for Computer Vision
, 2003
"... Probabilistic models have been adopted for many computer vision applications, however inference in highdimensional spaces remains problematic. As the statespace of a model grows, the dependencies between the dimensions lead to an exponential growth in computation when performing inference. Many comm ..."
Abstract

Cited by 93 (3 self)
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Probabilistic models have been adopted for many computer vision applications, however inference in highdimensional spaces remains problematic. As the statespace of a model grows, the dependencies between the dimensions lead to an exponential growth in computation when performing inference. Many common computer vision problems naturally map onto the graphical model framework; the representation is a graph where each node contains a portion of the statespace and there is an edge between two nodes only if they are not independent conditional on the other nodes in the graph. When this graph is sparsely connected, belief propagation algorithms can turn an exponential inference computation into one which is linear in the size of the graph. However belief propagation is only applicable when the variables in the nodes are discretevalued or jointly represented by a single multivariate Gaussian distribution, and this rules out many computer vision applications.
The correlated correspondence algorithm for unsupervised registration of nonrigid surfaces
 In TRSAIL2004100, at http://robotics.stanford.edu/∼drago/cc/tr100.pdf
, 2004
"... We present an unsupervised algorithm for registering 3D surface scans of an object undergoing significant deformations. Our algorithm does not need markers, nor does it assume prior knowledge about object shape, the dynamics of its deformation, or scan alignment. The algorithm registers two meshes b ..."
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Cited by 76 (4 self)
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We present an unsupervised algorithm for registering 3D surface scans of an object undergoing significant deformations. Our algorithm does not need markers, nor does it assume prior knowledge about object shape, the dynamics of its deformation, or scan alignment. The algorithm registers two meshes by optimizing a joint probabilistic model over all pointtopoint correspondences between them. This model enforces preservation of local mesh geometry, as well as more global constraints that capture the preservation of geodesic distance between corresponding point pairs. The algorithm applies even when one of the meshes is an incomplete range scan; thus, it can be used to automatically fill in the remaining surfaces for this partial scan, even if those surfaces were previously only seen in a different configuration. We evaluate the algorithm on several realworld datasets, where we demonstrate good results in the presence of significant movement of articulated parts and nonrigid surface deformation. Finally, we show that the output of the algorithm can be used for compelling computer graphics tasks such as interpolation between two scans of a nonrigid object and automatic recovery of articulated object models. 1
Loopy belief propagation: Convergence and effects of message errors
 Journal of Machine Learning Research
, 2005
"... Belief propagation (BP) is an increasingly popular method of performing approximate inference on arbitrary graphical models. At times, even further approximations are required, whether due to quantization of the messages or model parameters, from other simplified message or model representations, or ..."
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Cited by 62 (7 self)
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Belief propagation (BP) is an increasingly popular method of performing approximate inference on arbitrary graphical models. At times, even further approximations are required, whether due to quantization of the messages or model parameters, from other simplified message or model representations, or from stochastic approximation methods. The introduction of such errors into the BP message computations has the potential to affect the solution obtained adversely. We analyze the effect resulting from message approximation under two particular measures of error, and show bounds on the accumulation of errors in the system. This analysis leads to convergence conditions for traditional BP message passing, and both strict bounds and estimates of the resulting error in systems of approximate BP message passing. 1
Distributed occlusion reasoning for tracking with nonparametric belief propagation
 In NIPS
, 2004
"... We describe a three–dimensional geometric hand model suitable for visual tracking applications. The kinematic constraints implied by the model’s joints have a probabilistic structure which is well described by a graphical model. Inference in this model is complicated by the hand’s many degrees of fr ..."
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Cited by 54 (0 self)
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We describe a three–dimensional geometric hand model suitable for visual tracking applications. The kinematic constraints implied by the model’s joints have a probabilistic structure which is well described by a graphical model. Inference in this model is complicated by the hand’s many degrees of freedom, as well as multimodal likelihoods caused by ambiguous image measurements. We use nonparametric belief propagation (NBP) to develop a tracking algorithm which exploits the graph’s structure to control complexity, while avoiding costly discretization. While kinematic constraints naturally have a local structure, self– occlusions created by the imaging process lead to complex interpendencies in color and edge–based likelihood functions. However, we show that local structure may be recovered by introducing binary hidden variables describing the occlusion state of each pixel. We augment the NBP algorithm to infer these occlusion variables in a distributed fashion, and then analytically marginalize over them to produce hand position estimates which properly account for occlusion events. We provide simulations showing that NBP may be used to refine inaccurate model initializations, as well as track hand motion through extended image sequences. 1
Attractive people: Assembling looselimbed models using nonparametric belief propagation
 In NIPS. 2004
"... The detection and pose estimation of people in images and video is made challenging by the variability of human appearance and the high dimensionality of articulated body models. To cope with these problems we exploit rich image likelihood models and represent the 3D human body using a graphical mod ..."
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Cited by 50 (2 self)
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The detection and pose estimation of people in images and video is made challenging by the variability of human appearance and the high dimensionality of articulated body models. To cope with these problems we exploit rich image likelihood models and represent the 3D human body using a graphical model in which the relationships between the body parts are represented by conditional probability distributions. We formulate the pose estimation problem as one of probabilistic inference over a graphical model where the random variables correspond to the individual limb parameters (position and orientation). Because the limbs are described by 6dimensional vectors encoding pose in 3space, discretization is impractical and the random variables in our model must be continuousvalued. To approximate belief propagation in such a graph we exploit a recently introduced generalization of the particle filter. This framework facilitates the automatic initialization of the bodymodel from low level cues and is robust to occlusion of body parts and scene clutter. 1
Visual hand tracking using nonparametric belief propagation
 Propagation,” IEEE Workshop on Generative Model Based Vision
, 2004
"... Abstract — This paper develops probabilistic methods for visual tracking of a threedimensional geometric hand model from monocular image sequences. We consider a redundant representation in which each model component is described by its position and orientation in the world coordinate frame. A prio ..."
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Cited by 50 (1 self)
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Abstract — This paper develops probabilistic methods for visual tracking of a threedimensional geometric hand model from monocular image sequences. We consider a redundant representation in which each model component is described by its position and orientation in the world coordinate frame. A prior model is then defined which enforces the kinematic constraints implied by the model’s joints. We show that this prior has a local structure, and is in fact a pairwise Markov random field. Furthermore, our redundant representation allows color and edgebased likelihood measures, such as the Chamfer distance, to be similarly decomposed in cases where there is no self–occlusion. Given this graphical model of hand kinematics, we may track the hand’s motion using the recently proposed nonparametric belief propagation (NBP) algorithm. Like particle filters, NBP approximates the posterior distribution over hand configurations as a collection of samples. However, NBP uses the graphical structure to greatly reduce the dimensionality of these distributions, providing improved robustness. Several methods are used to improve NBP’s computational efficiency, including a novel KDtree based method for fast Chamfer distance evaluation. We provide simulations showing that NBP may be used to refine inaccurate model initializations, as well as track hand motion through extended image sequences. I.
Beyond trees: Common factor models for 2D human pose recovery
 In ICCV
, 2005
"... Tree structured models have been widely used for determining the pose of a human body, from either 2D or 3D data. While such models can effectively represent the kinematic constraints of the skeletal structure, they do not capture additional constraints such as coordination of the limbs. Tree struct ..."
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Cited by 50 (1 self)
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Tree structured models have been widely used for determining the pose of a human body, from either 2D or 3D data. While such models can effectively represent the kinematic constraints of the skeletal structure, they do not capture additional constraints such as coordination of the limbs. Tree structured models thus miss an important source of information about human body pose, as limb coordination is necessary for balance while standing, walking, or running, as well as being evident in other activities such as dancing and throwing. In this paper we consider the use of undirected graphical models that augment a tree structure with latent variables in order to account for coordination between limbs. We refer to these as commonfactor models, since they are constructed by using factor analysis to identify additional correlations in limb position that are not accounted for by the kinematic tree structure. These commonfactor models have an underlying tree structure and thus a variant of the standard Viterbi algorithm for a tree can be applied for efficient estimation. We present some experimental results contrasting commonfactor models with tree models, and quantify the improvement in pose estimation for 2D image data. 1.