Global optimization for first order Markov Random Fields with submodular priors

This paper copes with the global optimization of Markovian energies. Energies are defined on an arbitrary graph and pairwise interactions are considered. The label set is assumed to be linearly ordered and of finite cardinality, while each interaction term (prior) shall be a submodular function. We propose an algorithm that computes a global   optimizer under these assumptions. The approach consists of mapping the original problem into a combinatorial one that is shown to be globally solvable using a maximum-flow/ss-tt minimum-cut algorithm. This restatement relies on considering the level sets of the labels (seen as binary variables) instead of the label values themselves. The submodularity assumption of the priors is shown to be a necessary and sufficient condition for the applicability of the proposed approach. Finally, some numerical results are presented.