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A Global Perspective on MAP Inference for Low-Level Vision

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Executive Summary

In recent years the Markov Random Field (MRF) has become the de facto probabilistic model for low-level vision applications. However, in a Maximum A Posteriori (MAP) framework, MRFs inherently encourage delta function marginal statistics. By contrast, many low-level vision problems have heavy tailed marginal statistics, making the MRF model unsuitable. This paper introduces a more general Marginal Probability Field (MPF), of which the MRF is a special, linear case, and shows that convex energy MPFs can be used to encourage arbitrary marginal statistics. The paper introduces a flexible, extensible framework for effectively optimizing the resulting NP-hard MAP problem, based around dual-decomposition and a modified min-cost flow algorithm, and which achieves global optimality in some instances.

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