Multi-Phase Segmentation Using Modified Complex Cahn-Hilliard Equations  

作　　者：Xiakai Wang Zhongyi Huang Wei Zhu 

机构地区：[1]Department of Mathematical Sciences,Tsinghua University,Beijing 100084,China [2]Department ofMathematics,University of Alabama,Box 870350,Tuscaloosa,AL 35487,USA

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2022年第2期442-463,共22页高等学校计算数学学报（英文版）

基　　金：supported by the NSFC(Projects No.12025104,11871298,81930119).

摘　　要：In this paper,we propose a novel PDE-based model for the multi-phase segmentation problem by using a complex version of Cahn-Hilliard equations.Specifically,we modify the original complex system of Cahn-Hilliard equations by adding the mean curvature term and the fitting term to the evolution of its real part,which helps to render a piecewisely constant function at the steady state.By applying the K-means method to this function,one could achieve the desired multiphase segmentation.To solve the proposed system of equations,a semi-implicit finite difference scheme is employed.Numerical experiments are presented to demonstrate the feasibility of the proposed model and compare our model with other related ones.

关 键 词：Image segmentation Cahn-Hilliard equation semi-implicit finite difference scheme 

分 类 号：O17[理学—数学]