Submodular Relaxation for MRFs with High-Order Potentials

  • Anton Osokin
  • Dmitry Vetrov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7585)


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.


Markov random fields energy minimization MAP-inference dual decomposition high-order potentials 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Anton Osokin
    • 1
  • Dmitry Vetrov
    • 1
  1. 1.Moscow State UniversityRussia

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