TY - JOUR
T1 - Multi-Phase Segmentation Using Modified Complex Cahn-Hilliard Equations
AU - Wang , Xiakai
AU - Huang , Zhongyi
AU - Zhu , Wei
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 2
SP - 442
EP - 463
PY - 2022
DA - 2022/03
SN - 15
DO - http://doi.org/10.4208/nmtma.OA-2021-0099
UR - https://global-sci.org/intro/article_detail/nmtma/20359.html
KW - Image segmentation, Cahn–Hilliard equation, semi-implicit finite difference scheme.
AB - <p style="text-align: justify;">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.</p>