Multi-label Generic Cuts: Optimal Inference in Multi-label Multi-clique MRF-MAP Problems

We propose an algorithm called Multi Label Generic Cuts (MLGC) for computing optimal solutions to MRF-MAP problems with submodular multi label multi-clique potentials. A transformation is introduced to convert a m-label k-clique problem to an equivalent 2-label (mk)-clique problem. We show that if the original multi-label problem is submodular then the transformed 2-label multi-clique problem is also submodular. We exploit sparseness in the feasible configurations of the transformed 2-label problem to suggest an improvement to Generic Cuts [3] to solve the 2-label problems efficiently. The algorithm runs in time O(mk n3) in the worst case (n is the number of pixels) generalizing O(2k n3) running time of Generic Cuts. We show experimentally that MLGC is an order of magnitude faster than the current state of the art [17, 20]. While the result of MLGC is optimal for submodular clique potential it is significantly better than the compared methods even for problems with non-submodular clique potential.