A new PDE based approach for image restoration and enhancement using robust diffusion directions and directional derivatives based diffusivities

This article proposes a novel, partial derivatives based filter, for oriented patterns filtering and enhancement. We propose a filtering and restoration process with a strong anisotropic behaviour. Locally, our filter uses a superposition of one-dimensional diffusion processes; in each pixel the diffusion directions are given by a principal component analysis, on these directions the processes behaviour is modulated by non-linear functions depending on the absolute values of the directional derivatives. Selectively, depending on these measures, the filter can act like a classical diffusion filter, simplifying the image, or it can produce edge and corner enhancement. The equation we propose is very general and it can be modified for specific image restoration tasks. Through applications samples we would show the efficiency of our method both on synthetic images and on real ones.