Extending a scaling based flow algorithm for higher order MRF-MAP inference in vision

Abstract

Several tasks in computer vision and Machine Learning are modeled as MRF-MAP inference problems. The problem can often be modeled as minimizing sum of submodular functions. Since, sum of submodular functions (SoS) is also submodular, therefore, existing Submodular Function Minimization (SFM) techniques can be employed for MRF-MAP inference. SFM algorithms do not exploit the sum property and because of their high complexity, cannot be directly employed for the inference task. There have been attempts to exploit sum property in Schrijver's and Minnorm algorithms [8], with reasonable success. In this work we explore exploiting SoS property in an augmenting path SFM algorithm embedded in a scaling framework. The flow based SFM algorithm developed by Iwata, Fleischer, Fujishige [3] is weakly polynomial with O(n5logM) complexity. The proposed adapted algorithm has a complexity of O(k:n2:m3 logM) where k is the number of cliques, m is the size of largest clique. We have created an implementation of both non SoS and the proposed algorithm. The proposed algorithm shows significant improvement over the original (non SoS) one, though not as efficient as the other adaptations of Schrijver's and Min Norm Point.