Slow and fast diffusion effects in image processing |
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Authors: | Jozef Kačur Karol Mikula |
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Affiliation: | (1) Comenius University, Faculty of Mathematics and Physics, Dept. of Numerical Analysis and Optimization, Mlynska Dolina, 842 15 Bratislava, Slovakia (e-mail: kacur@fmph.uniba.sk), SV;(2) Slovak Technical University, Dept. of Mathematics, Radlinskeho 11, 813 68 Bratislava, Slovakia (e-mail: mikula@vox.svf.stuba.sk), SV |
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Abstract: | A mathematical model for a nonlinear image multiscale analysis is studied. Processing of an image is based on a solution of the strongly nonlinear parabolic partial differential equation, which can degenerate depending on values of the greylevel intensity function. The governing PDE is a generalization of the regularized (in the sense of Catté, Lions, Morel and Coll) Perona-Malik anisotropic diffusion equation. We present numerical techniques for solving the suggested initial-boundary value problem and also existence and convergence results. Numerical experiments are discussed. Received: 6 May 1998 / Accepted: 27 July 2000 |
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