A Multigrid Algorithm for Maxflow and Min-Cut Problems with Applications to Multiphase Image Segmentation

In this paper, we propose a multiphase image segmentation method via solving the min-cut minimization problem under the multigrid method framework. At each level of the multigrid method for the min-cut problem, we first transfer it to the equivalent form, e.g., max-flow problem, then actually solve the dual of the max-flow problem. Particularly, a classical multigrid method is used to solve the sub-minimization problems. Several outer iterations are used for the multigrid method. The proposed idea can be used for general min-cut/max-flow minimization problems. We use multiphase image segmentation as an example in this work. Extensive experiments on simulated and real images demonstrate the efficiency and effectiveness of the proposed method.