Stability of Semi-Implicit Finite Volume Scheme for Level Set Like Equation

Abstract

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.