TY - JOUR
T1 - Two-Phase Image Segmentation by the Allen-Cahn Equation and a Nonlocal Edge Detection Operator
AU - Qiao , Zhonghua
AU - Zhang , Qian
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 1147
EP - 1172
PY - 2022
DA - 2022/10
SN - 15
DO - http://doi.org/10.4208/nmtma.OA-2022-0008s
UR - https://global-sci.org/intro/article_detail/nmtma/21097.html
KW - Image segmentation, Allen-Cahn equation, nonlocal edge detection operator, maximum principle, energy stability
AB - <p style="text-align: justify;">Based on a nonlocal Laplacian operator, a novel edge detection method
of the grayscale image is proposed in this paper. This operator utilizes the information of neighbor pixels for a given pixel to obtain effective and delicate edge detection. The nonlocal edge detection method is used as an initialization for solving
the Allen-Cahn equation to achieve two-phase segmentation of the grayscale image.
Efficient exponential time differencing (ETD) solvers are employed in the time integration, and finite difference method is adopted in space discretization. The maximum bound principle and energy stability of the proposed numerical schemes are
proved. The capability of our segmentation method has been verified in numerical
experiments for different types of grayscale images.</p>