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http://hdl.handle.net/10397/96613
Title: | Two-phase image segmentation by the Allen-Cahn equation and a nonlocal edge detection operator | Authors: | Qiao, Z Zhang, Q |
Issue Date: | 2022 | Source: | Numerical mathematics : theory, methods and applications, 2022, v. 15, no. 4, p. 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. | Keywords: | Image segmentation Allen-Cahn equation Nonlocal edge detection operator Maximum principle Energy stability |
Publisher: | Global Science Press | Journal: | Numerical mathematics : theory, methods and applications | ISSN: | 1004-8979 | EISSN: | 2079-7338 | DOI: | 10.4208/nmtma.OA-2022-0008s | Rights: | ©2022 Global-Science Press This is the accepted version of the following article: Qiao, Z., & Zhang, Q. (2022). Two-phase image segmentation by the Allen-Cahn equation and a nonlocal edge detection operator. Numerical Mathematics: Theory, Methods and Applications, 15(4), 1147-1172, which has been published in https://doi.org/10.4208/nmtma.OA-2022-0008s. |
Appears in Collections: | Journal/Magazine Article |
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Qiao_Image_Segmentation_Allen-Cahn.pdf | Pre-Published version | 8.86 MB | Adobe PDF | View/Open |
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