Résumé (EN)

Applications of anisotropic diffusion equation to texture enhancement have shown that an image can be smoothed while preserving high frequency features like edges. However, preserving textures still remains challenging. One way to preserve textures is by adding an extra term to the diffusion equation. This additional term can be interpreted as a potential, similar to the role of Schrödinger's potential in the complex diffusion equation, or as a reaction term in a reaction-diffusion process. We show the effect of such potentials on texture denoising, highlighting that anisotropic diffusion with potential combines properties of diffusion (piecewise-smoothing) and potential (enhancing fine structures) filters. Simulations performed on pure texture samples indicate that the reconstruction depends on the type of texture and the transform operator used in the potential. The diffusion-with-potential approach is extended. Local and nonlocal results show that nonlocal diffusion improves the quality of denoising.