This paper copes with the optimization of Markov Random Fields with pairwise interactions defined on arbitrary graphs. The set of labels is assumed to be linearly ordered and the priors are supposed to be submodular. Under these assumptions we propose an algorithm which computes an exact minimizer of the Markovian energy. Our approach relies on mapping the original into a combinatorial one which involves only binary variables. The latter is shown to be exactly solvable via computing a maximum flow. The restatement into a binary combinatorial problem is done by considering the level-sets of the labels instead of the label values themselves. The submodularity of the priors is shown to be a necessary and sufficient condition for the applicability of the proposed approach.
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