A direct approach toward global minimization for multiphase labeling and segmentation problems

• Main Authors: Tai, Xue Cheng, Gu, Ying, Wang, Li-Lian
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2013
• Online Access: https://hdl.handle.net/10356/98959; http://hdl.handle.net/10220/13483
• Institution: Nanyang Technological University

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.