Global Minimization for Continuous Multiphase Partitioning Problems Using a Dual Approach

This paper is devoted to the optimization problem of continuous multipartitioning, or multi-labeling, which is based on a convex relaxation of the continuous Potts model. In contrast to previous efforts, which are trying to tackle the optimal labeling problem in a direct manner, we first propose a novel dual model and then build up a corresponding dualitybased approach. By analyzing the dual formulation, sufficient conditions are derived which shows that the relaxation is often exact, i.e. there exists optimal solutions that are also globally optimal to the original nonconvex Potts model. In order to deal with the nonsmooth dual problem, we suggest a smoothing method based on the log-sum exponential function and also indicate that such smoothing approach gives rise to the novel smoothed primal-dual model and suggests labelings with maximum entropy. Such smoothing method for the dual model produces a highly efficient expectation maximization algorithm for the multi-labeling problem, ...

• Type: Journal
• Year: 2011
• Where: IJCV
• Authors: Egil Bae, Jing Yuan, Xue-Cheng Tai
• Keywords: Dual Model, IJCV 2011, Potts Model, Smoothing Method