Learning Higher Order Potentials for MRFs

Higher order MRF-MAP formulation has been shown to improve solutions in many popular computer vision problems. Most of these approaches have considered hand tuned clique potentials only. Over the last few years, while there has been steady improvement in inference techniques making it possible to perform tractable inference for clique sizes even up to few hundreds, the learning techniques for such clique potentials have been limited to clique size of merely 3 or 4. In this paper, we investigate learning of higher order clique potentials up to clique size of 16. We use structural support vector machine (SSVM), a large-margin learning framework, to learn higher order potential functions from data. It formulates the training problem as a quadratic programming problem (QP) that requires solving MAP inference problems in the inner iteration. We introduce multiple innovations in the formulation by introducing soft submodularity constraints which keep QP constraints manageable and at the same time makes MAP inference tractable. Unlike contemporary approaches to solving the original problem using the cutting plane technique, we propose to solve the problem using subgradient descent. This allows us to scale for problems with clique size even up to 16. We give indicative experiments to show the improvement gained in real applications using learned potentials instead of hand tuned ones.