Summary.
We propose and prove a convergence of the semi-implicit finite volume approximation scheme for the numerical solution of the modified (in the sense of Catté, Lions, Morel and Coll) Perona–Malik nonlinear image selective smoothing equation (called anisotropic diffusion in the image processing). The proof is based on \(L_2\) a-priori estimates and Kolmogorov's compactness theorem. The implementation aspects and computational results are discussed.
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Received January 7, 1999 / Revised version received May 31, 2000 / Published online March 20, 2001
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Mikula, K., Ramarosy, N. Semi-implicit finite volume scheme for solving nonlinear diffusion equations in image processing. Numer. Math. 89, 561–590 (2001). https://doi.org/10.1007/PL00005479
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DOI: https://doi.org/10.1007/PL00005479