Résumé : This report addresses the problem of vector-valued image regularization with variational methods and PDE's. From the study of existing global and local formalisms, we propose a new framework that unifies a large number of previous methods within a generic local formulation. On one hand, resulting equations are more adapted to analyze the local geometric behaviors of the diffusion processes. On the other hand, it can be used to design a new regularization PDE that takes important local smoothing properties into account. Specific numerical schemes are also naturally emerging from this formulation. Finally, we illustrate the capability of our approach to deal with classical image processing applications, such as color image restoration, inpainting, magnification and flow visualization.