Solving MRF minimization by mirror descent

Abstract

Markov Random Fields (MRF) minimization is a well-known problem in computer vision. We consider the augmented dual of the MRF minimization problem and develop a Mirror Descent algorithm based on weighted Entropy and Euclidean Projection. The augmented dual problem consists of maximizing a non-differentiable objective function subject to simplex and linear constraints. We analyze the convergence properties of the algorithm and sharpen its convergence rate. In addition, we also use the convergence analysis to identify an optimal stepsize strategy for weighted entropy projection and an adaptive stepsize strategy for weighted Euclidean projection. Experimental results on synthetic and vision problems demonstrate the effectiveness of our approach. © 2012 Springer-Verlag.