离散化
数学
能量泛函
分割
缩小
图像分割
能量最小化
艾伦-卡恩方程
应用数学
分拆(数论)
数学分析
算法
数学优化
计算机科学
人工智能
物理
组合数学
量子力学
作者
Liu, Chaoyu,Qiao, Zhonghua,Zhang, Qian
出处
期刊:Cornell University - arXiv
日期:2022-03-27
标识
DOI:10.48550/arxiv.2203.14233
摘要
This paper proposes an Allen-Cahn Chan-Vese model to settle the multi-phase image segmentation. We first integrate the Allen--Cahn term and the Chan--Vese fitting energy term to establish an energy functional, whose minimum locates the segmentation contour. The subsequent minimization process can be attributed to variational calculation on fitting intensities and the solution approximation of several Allen-Cahn equations, wherein $n$ Allen-Cahn equations are enough to partition $m = 2^n$ segments. The derived Allen-Cahn equations are solved by efficient numerical solvers with exponential time integrations and finite difference space discretization. The discrete maximum bound principle and energy stability of the proposed numerical schemes are proved. Finally, the capability of our segmentation method is verified in various experiments for different types of images.
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