Étude d’EDPs liées à l’amélioration de contour d’image par auto similarité intermediaire.

Abstract

The nonlinear diffusion equation is used to analyze the process of edge enhancement in image processing, based on a new evolution model considered as a generalization of mean curvature motion. A free boundary problem is formulated describing the image intensity evolution in the boundary layers around the edges of the image. An asymptotic self-similar solutions to this nonlinear diffusion equation is obtained in explicit forms. The solutions demonstrated that the edge enhancement and its rates depends on the parameters of equation. The experimental results demonstrate the effectiveness of themodel in edge preservation.