Semi-implicit complementary volume scheme for solving level set like equations in image processing and curve evolution |
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Authors: | Handlovi?ová Angela Mikula Karol Sgallari Fiorella |
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Institution: | (1) Department of Mathematics, Slovak University of Technology, Radlinského 11, 813 68 Bratislava, Slovakia; e-mail: {angela,mikula}@vox.svf.stuba.sk , SK;(2) Department of Mathematics, University of Bologna, Piazza di Porta S. Donato 5, 40127 Bologna, Italy; e-mail: sgallari@dm.unibo.it , IT |
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Abstract: | 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 and 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.
Received April 25, 2000 / Revised version received June 11, 2001 / Published online November 15, 2001 |
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Keywords: | Mathematics Subject Classification (1991): 65U10 |
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