Chouder, Rafaa2018-03-212018-03-212018-02-11http://dspace.univ-msila.dz:8080//xmlui/handle/123456789/3786The theory of nonlinear diffusion equations is used to analyze the process of contour enhancement in image processing. The aim of this research is to seek new exact solutions to nonlinear diffusion equation that occurs in image processing called degenerate parabolic equation. For that, we have used the general self-similar solutions and the `travelling profiles method' in order to find, explicitly, new exact solutions to this equation under some conditions. Some these explicit solutions are related with the phenomenon of contour enhancement. An interesting particular case has been discussed; this case coincides with particular solutions called `intermediate asymptotic solutions' used to study the contour enhancement.nonlinear diffusion equations; self similar solution; travelling profiles method; fractional derivatives; image processing; contour enhancement.Thesis