Year: 2022
Author: Zhonghua Qiao, Qian Zhang
Numerical Mathematics: Theory, Methods and Applications, Vol. 15 (2022), Iss. 4 : pp. 1147–1172
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2022-0008s
Numerical Mathematics: Theory, Methods and Applications, Vol. 15 (2022), Iss. 4 : pp. 1147–1172
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Image segmentation Allen-Cahn equation nonlocal edge detection operator maximum principle energy stability
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