Year: 2022
Author: Xiakai Wang, Zhongyi Huang, Wei Zhu
Numerical Mathematics: Theory, Methods and Applications, Vol. 15 (2022), Iss. 2 : pp. 442–463
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2021-0099
Numerical Mathematics: Theory, Methods and Applications, Vol. 15 (2022), Iss. 2 : pp. 442–463
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Image segmentation Cahn–Hilliard equation semi-implicit finite difference scheme.