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

作者：Gu Ying^*; Wang Li Lian; Tai Xue Cheng

来源：IEEE Transactions on Image Processing, 2012, 21(5): 2399-2411.

DOI：10.1109/TIP.2011.2182522

• Augmented Lagrangian method (ALM)
• Chambolle%26apos
• s algorithm
• continuous Potts model
• global optimum
• multiclass labeling
• multiphase segmentation
• Mumford-Shah model
• primal-dual formulation

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.

• 出版日期2012-5
• 单位南阳理工学院