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Efficient Belief Propagation for Higher Order Cliques Using Linear Constraint Nodes (2008)
| Citations: | 8 - 2 self |
BibTeX
@MISC{Potetz08efficientbelief,
author = {Brian Potetz and Tai Sing Lee},
title = { Efficient Belief Propagation for Higher Order Cliques Using Linear Constraint Nodes},
year = {2008}
}
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Abstract
Belief propagation over pairwise connected Markov Random Fields has become a widely used approach, and has been successfully applied to several important computer vision problems. However, pairwise interactions are often insufficient to capture the full statistics of the problem. Higher-order interactions are sometimes required. Unfortunately, the complexity of belief propagation is exponential in the size of the largest clique. In this paper, we introduce a new technique to compute belief propagation messages in time linear with respect to clique size for a large class of potential functions over real-valued variables. We discuss how this technique can be generalized to still wider classes of potential functions at varying levels of efficiency. Also, we develop a form of nonparametric belief representation specifically designed to address issues common to networks with higher-order cliques and also to the use of guaranteed-convergent forms of belief propagation. To illustrate these techniques, we perform efficient inference in graphical models where the spatial prior of natural images is captured by 2×2 cliques. This approach shows significant improvement over the commonly used pairwise-connected models, and may benefit a variety of applications using belief propagation to infer images or range images, including stereo, shape-from-shading, image-based rendering, segmentation, and matting.
Keyphrases
belief propagation efficient belief propagation potential function markov random field image-based rendering full statistic large class range image significant improvement efficient inference belief propagation message spatial prior natural image higher-order interaction guaranteed-convergent form new technique pairwise-connected model several important computer vision problem real-valued variable higher-order clique graphical model pairwise interaction nonparametric belief representation
