Commun. Math. Res., 31 (2015), pp. 351-361.
Published online: 2021-05
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We study numerical methods for level set like equations arising in image processing and curve evolution problems. Semi-implicit finite volume-element type schemes are constructed for the general level set like equation (image selective smoothing model) given by Alvarez et al. (Alvarez L, Lions P L, Morel J M. Image selective smoothing and edge detection by nonlinear diffusion II. SIAM J. Numer. Anal., 1992, 29: 845–866). Through the reasonable semi-implicit discretization in time and co-volume method for space approximation, we give finite volume schemes, unconditionally stable in $L_∞$ and $W^{1,2} (W^{1,1})$ sense in isotropic (anisotropic) diffusion domain.
}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2015.04.07}, url = {http://global-sci.org/intro/article_detail/cmr/18919.html} }We study numerical methods for level set like equations arising in image processing and curve evolution problems. Semi-implicit finite volume-element type schemes are constructed for the general level set like equation (image selective smoothing model) given by Alvarez et al. (Alvarez L, Lions P L, Morel J M. Image selective smoothing and edge detection by nonlinear diffusion II. SIAM J. Numer. Anal., 1992, 29: 845–866). Through the reasonable semi-implicit discretization in time and co-volume method for space approximation, we give finite volume schemes, unconditionally stable in $L_∞$ and $W^{1,2} (W^{1,1})$ sense in isotropic (anisotropic) diffusion domain.