An Adaptive Finite Volume Scheme for Solving Nonlinear Diffusion Equations in Image Processing

We propose the coarsening strategy for the finite volume computational method given by K. Mikula and N. Ramarosy (Numer. Math. 89, 2001, 561–590) for the numerical solution of the (modified in the sense of F. Catté et al. (SIAM J. Numer. Anal. 29, 1992, 182–193)) Perona–Malik nonlinear image selective smoothing equation (called anisotropic diffusion in image processing). The adaptive aproach is directly at hand because a solution tends to be flat in large subregions of the image, and thus it is not necessary to consider the same fine resolution of computations in the whole spatial domain. This access reduces computational effort, because the coarsening of the computational grid rapidly reduces the number of unknowns in the linear systems to be solved at discrete scale steps of the method. C © 2002 Elsevier Science (USA)