Min Norm Point Algorithm for Higher Order MRF-MAP Inference

Many tasks in computer vision and machine learning can be modelled as the inference problems in an MRF-MAP formulation and can be reduced to minimizing a submodular function. Using higher order clique potentials to model complex dependencies between pixels improves the performance but the current state of the art inference algorithms fail to scale for larger clique sizes. We adapt a well known Min Norm Point algorithm from mathematical optimization literature to exploit the sum of submodular structure found in the MRF-MAP formulation. Unlike some contemporary methods, we do not make any assumptions (other than submodularity) on the type of the clique potentials. Current state of the art inference algorithms for general submodular function takes many hours for problems with clique size 16, and fail to scale beyond. On the other hand, our algorithm is highly efficient and can perform optimal inference in few seconds even on clique size an order of magnitude larger. The proposed algorithm can even scale to clique sizes of many hundreds, unlocking the usage of really large size cliques for MRF-MAP inference problems in computer vision. We demonstrate the efficacy of our approach by experimenting on synthetic as well as real datasets.