@Article{NMTMA-15-2,
author = {Xiakai, Wang and Zhongyi, Huang and Zhu, Wei},
title = {Multi-Phase Segmentation Using Modified Complex Cahn-Hilliard Equations},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2022},
volume = {15},
number = {2},
pages = {442--463},
abstract = {<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>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2021-0099},
url = {https://global-sci.com/article/90258/multi-phase-segmentation-using-modified-complex-cahn-hilliard-equations}
}