Efficient algorithms for MRF-MAP inference problem: using polytope based methods in conjunction with flow based methods

Abstract

Use of higher order clique potentials in MRF-MAP problems has been limited primarily because of the inefficiencies of the existing algorithmic schemes. A combinatorial algorithm called Generic Cuts Algorithm was proposed in [1] for computing optimal solutions to 2 label MRF- MAP problems with higher order clique potentials. The algorithm runs in time O(2kn3) in the worst case (k is size of clique and n is the number of pixels). This is a significant improvement over other techniques, but suffers from exponential worst-case time with respect to clique size. We try to create efficient algorithms to overcome this by exploiting the properties of the clique potential functions.As we can see, this is a submodular function minimization problem. But we may stumble across a scenario (not uncommon) where the potential function ceases to be submodular. We devise an approach to find an answer for this case, either by compromising on the time complexity of the program, or the accuracy of the result.