Diffusion PDEs on vector-valued images

Abstract

In this article, we propose a local and geometric point of view of vector image filtering using diffusion PDEs. It allows us to analyze proposed methods of vector data regularization, as well as propose a new vector PDE, well adapted for image restoration. This equation, whose key feature is the use of a local vector geometry, combines the advantages of diffusion PDEs for noise removing but also uses vector shock filters to enhance blurred edges. The extension to norm constrained vector fields can be the start for other well-known constrained problems, as optical flow computation, orientation analysis, and tensor image restoration.