Summary.
We introduce linear semi-implicit complementary volume numerical scheme for solving level set like nonlinear degenerate diffusion equations arising in image processing and curve evolution problems. We study discretization of image selective smoothing equation of mean curvature flow type given by Alvarez, Lions and Morel ([3]). Solution of the level set equation of Osher and Sethian ([26], \[30]) is also included in the study. We prove \(L_\infty\) and \(W^{1,1}\) estimates for the proposed scheme and give existence of its (generalized) solution in every discrete time-scale step. Efficiency of the scheme is given by its linearity and stability. Preconditioned iterative solvers are used for computing arising linear systems. We present computational results related to image processing and plane curve evolution.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Additional information
Received April 25, 2000 / Revised version received June 11, 2001 / Published online November 15, 2001
Rights and permissions
About this article
Cite this article
Handlovičová, A., Mikula, K. & Sgallari, F. Semi-implicit complementary volume scheme for solving level set like equations in image processing and curve evolution. Numer. Math. 93, 675–695 (2003). https://doi.org/10.1007/s002110100374
Issue Date:
DOI: https://doi.org/10.1007/s002110100374