Nonparametric belief propagation

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.