Abstract. Solving a multi-labeling problem with a convex penalty can
be achieved in polynomial time if the label set is totally ordered. In
this paper we propose a generalization to partially ordered sets. To this
end, we assume that the label set is the Cartesian product of totally
ordered sets and the convex prior is separable. For this setting we introduce a general combinatorial optimization framework that provides an
approximate solution. More specifically, we first construct a graph whose
minimal cut provides a lower bound to our energy. The result of this relaxation is then used to get a feasible solution via classical move-making
cuts. To speed up the optimization, we propose an efficient coarse-to-fine
approach over the label space. We demonstrate the proposed framework
through extensive experiments for optical flow estimation