We present a "pull" approach to approximate products of Gaussian mixtures within message updates for Nonparametric Belief Propagation (NBP) inference. Existing NBP methods often represent messages between continuous-valued latent variables as Gaussian mixture models. To avoid computational intractability in loopy graphs, NBP necessitates an approximation of the product of such mixtures. Sampling-based product approximations have shown effectiveness for NBP inference. However, such approximations used within the traditional "push" message update procedures quickly become computationally prohibitive for multi-modal distributions over high-dimensional variables. In contrast, we propose a "pull" method, as the Pull Message Passing for Nonparametric Belief propagation (PMPNBP) algorithm, and demonstrate its viability for efficient inference. We report results using an experiment from an existing NBP method, PAMPAS, for inferring the pose of an articulated structure in clutter. Results from this illustrative problem found PMPNBP has a greater ability to efficiently scale the number of components in its mixtures and, consequently, improve inference accuracy.
Probabilistic graphical models, such as the Markov Random Field (MRF), are widely used in computational perception to model problems involving inference of random variables under considerable uncertainty. Many algorithms have been proposed to compute the joint probability of graphical models in these cases. Belief propagation algorithms are a category of algorithms that are guaranteed to converge on tree-structured graphs. For graph structures with loops, Loopy Belief Propagation (LBP) @cite_10 is empirically proven to perform for discrete variables. Recently, @cite_2 proposed a belief propagation over factor graphs to generate scenes satisfying the scene grammars. The problem becomes much more challenging when the latent variables take continuous values. @cite_12 and @cite_5 introduced methods for nonparametric belief propagation to address such continuous-valued cases. Both of these approaches approximate a continuous-valued function as a mixture of weighted Gaussians and use local Gibbs sampling to approximate the product of mixtures. This approach to message passing has been effectively used in applications such as human pose estimation @cite_1 and hand tracking @cite_9 by modeling the graph as a tree structured particle network. In order to viably pursue NBP for robotic problems, such as scene perception, the computational efficiency of NBP methods needs to be revisited.
@cite_9 @cite_1 @cite_2 @cite_5 @cite_10 @cite_12
2122768476 2415775569 2951088220 2167947196
This paper develops probabilistic methods for visual tracking of a three-dimensional 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 edge-based 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 KD-tree 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. We describe a general framework for probabilistic modeling of complex scenes and inference from ambiguous observations. The approach is motivated by applications in image analysis and is based on the use of priors defined by stochastic grammars. We define a class of grammars that capture relationships between the objects in a scene and provide important contextual cues for statistical inference. The distribution over scenes defined by a probabilistic scene grammar can be represented by a graphical model and this construction can be used for efficient inference with loopy belief propagation. We show experimental results with two different applications. One application involves the reconstruction of binary contour maps. Another application involves detecting and localizing faces in images. In both applications the same framework leads to robust inference algorithms that can effectively combine local information to reason about a scene. Recently, researchers have demonstrated that loopy belief propagation - the use of Pearls polytree algorithm IN a Bayesian network WITH loops OF error- correcting codes.The most dramatic instance OF this IS the near Shannon - limit performance OF Turbo Codes codes whose decoding algorithm IS equivalent TO loopy belief propagation IN a chain - structured Bayesian network. IN this paper we ask : IS there something special about the error - correcting code context, OR does loopy propagation WORK AS an approximate inference schemeIN a more general setting? We compare the marginals computed using loopy propagation TO the exact ones IN four Bayesian network architectures, including two real - world networks : ALARM AND QMR.We find that the loopy beliefs often converge AND WHEN they do, they give a good approximation TO the correct marginals.However,ON the QMR network, the loopy beliefs oscillated AND had no obvious relationship TO the correct posteriors. We present SOME initial investigations INTO the cause OF these oscillations, AND show that SOME simple methods OF preventing them lead TO the wrong results. In many applications of graphical models arising in computer vision, the hidden variables of interest are most naturally specified by continuous, non-Gaussian distributions. There exist inference algorithms for discrete approximations to these continuous distributions, but for the high-dimensional variables typically of interest, discrete inference becomes infeasible. Stochastic methods such as particle filters provide an appealing alternative. However, existing techniques fail to exploit the rich structure of the graphical models describing many vision problems. Drawing on ideas from regularized particle filters and belief propagation (BP), this paper develops a nonparametric belief propagation (NBP) algorithm applicable to general graphs. Each NBP iteration uses an efficient sampling procedure to update kernel-based approximations to the true, continuous likelihoods. The algorithm can accommodate an extremely broad class of potential functions, including nonparametric representations. Thus, NBP extends particle filtering methods to the more general vision problems that graphical models can describe. We apply the NBP algorithm to infer component interrelationships in a parts-based face model, allowing location and reconstruction of occluded features.