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.

本文通过解决多网格方法框架下的最小割最小化问题，提出了一种多相图像分割方法。在最小割问题的多重网格方法的每个级别，我们首先将其转换为等效形式，例如最大流量问题，然后实际解决最大流量问题的对偶问题。特别地，经典的多重网格方法用于解决子最小化问题。多个外部迭代用于多重网格方法。提出的想法可用于一般的最小切割/最大流量最小化问题。我们以多相图像分割为例。在模拟和真实图像上的大量实验证明了该方法的有效性和有效性。