A Variational Model for Multiphase Image Segmentation on an Implicit Open Surface and Its Fast Algorithms

摘要

Based on the expression of a open surface on which images are defined as intersection of zero level set of a signed distance function and a binary label function and by making use of concepts of intrinsic gradient and divergence, the partitioning strategy of regions on a surface via m binary label functions for 2~m regions, a general varaitional model for multiphase image segmentation on an implicit open surface is proposed. Based on techniques of convex relaxation and thresholding, the gradient descent method, dual method, Split Bregman method, augmented Lagrange method are designed, where, the last three methods are fast ones. In order to improve its efficiency and make it implement easily, we propose another new method based on dual method without convex relaxation and thresholding of binary label functions, which is referred as direct dual method. Finally, numerical examples validate the model and its fast algorithms proposed in this paper.