Abstract
In the paper we propose a novel dual decomposition scheme for approximate MAP-inference in Markov Random Fields with sparse high-order potentials, i.e. potentials encouraging relatively a small number of variable configurations. We construct a Lagrangian dual of the problem in such a way that it can be efficiently evaluated by minimizing a submodular function with a min-cut/max-flow algorithm. We show the equivalence of this relaxation to a specific type of linear program and derive the conditions under which it is equivalent to generally tighter LP-relaxation solved in [1]. Unlike the latter our relaxation has significantly less dual variables and hence is much easier to solve. We demonstrate its faster convergence on several synthetic and real problems.
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Osokin, A., Vetrov, D. (2012). Submodular Relaxation for MRFs with High-Order Potentials. In: Fusiello, A., Murino, V., Cucchiara, R. (eds) Computer Vision – ECCV 2012. Workshops and Demonstrations. ECCV 2012. Lecture Notes in Computer Science, vol 7585. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33885-4_31
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DOI: https://doi.org/10.1007/978-3-642-33885-4_31
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