A Direct Approach Toward Global Minimization for Multiphase Labeling and Segmentation Problems.

This paper intends to extend the minimization algorithm developed by Bae, Yuan and Tai [IJCV, 2011] in several directions. First, we propose a new primal-dual approach for global minimization of the continuous Potts model with applications to the piecewise constant Mumford–Shah model for multiphase image segmentation. Different from the existing methods, we work directly with the binary setting without using convex relaxation, which is thereby termed as a direct approach. Second, we provide the sufficient and necessary conditions to guarantee a global optimum. Moreover, we provide efficient algorithms based on a reduction in the intermediate unknowns from the augmented Lagrangian formulation. As a result, the underlying algorithms involve significantly fewer parameters and unknowns than the naive use of augmented Lagrangian-based methods; hence, they are fast and easy to implement. Furthermore, they can produce global optimums under mild conditions. [ABSTRACT FROM PUBLISHER]