基于修正复Cahn-Hilliard方程的多相分割

IF 1.9 4区数学 Q1 MATHEMATICS

Numerical Mathematics-Theory Methods and Applications Pub Date : 2022-06-01 DOI:10.4208/nmtma.oa-2021-0099

Xiakai Wang, Zhongyi Huang null, Wei Zhu

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引用次数: 0

摘要

在本文中，我们使用复杂版本的Cahn-Hilliard方程，为多阶段分割问题提出了一种新的基于PDE的模型。具体来说，我们通过将平均曲率项和拟合项添加到其实部的演化中来修改Cahn-Hilliard方程组的原始复系统，这有助于在稳态下呈现分段常数函数。通过将K-means方法应用于该函数，可以实现期望的多相分割。为了求解所提出的方程组，采用了半隐式有限差分格式。数值实验证明了该模型的可行性，并与其他相关模型进行了比较。AMS受试者分类：68U10、65K10、65N06

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Multi-Phase Segmentation Using Modified Complex Cahn-Hilliard Equations

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. AMS subject classifications: 68U10, 65K10, 65N06

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来源期刊

Numerical Mathematics-Theory Methods and Applications 数学-数学

CiteScore

2.80

自引率

7.70%

发文量

审稿时长

>12 weeks

期刊介绍： Numerical Mathematics: Theory, Methods and Applications (NM-TMA) publishes high-quality original research papers on the construction, analysis and application of numerical methods for solving scientific and engineering problems. Important research and expository papers devoted to the numerical solution of mathematical equations arising in all areas of science and technology are expected. The journal originates from the journal Numerical Mathematics: A Journal of Chinese Universities (English Edition). NM-TMA is a refereed international journal sponsored by Nanjing University and the Ministry of Education of China. As an international journal, NM-TMA is published in a timely fashion in printed and electronic forms.