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...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.展开更多
基金supported by the CAS AMSS-PolyU Joint Laboratory of Applied Mathematics.Z.Qiao’s work is partially supported by the Hong Kong Research Grant Council RFS grant RFS2021-5S03GRF grants 15300417,15302919Q.Zhang’s research is supported by the 2019 Hong Kong Scholar Program G-YZ2Y.
文摘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.
