Submodular relaxation for MRFs with high-order potentials

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. © 2012 Springer-Verlag.