In this paper, a theoretical framework for the conditional diffusion ofdigitalimagesispresented. Differentapproacheshavebeenproposed to solve this problem by extrapolating the idea of the anisotropic diffusionforagreylevelimagestovector-valuedimages. Then, thediffusion of each channel is conditioned to a direction which normally takes into account information from all channels. In our approach, the diffusion model assumes the a priori knowledge of the diffusion direction during all the process. The consistency of the model is shown by proving the existence and uniqueness of solution for the proposed equation from the viscosity solutions theory. Also a numerical scheme adapted to this equation based on the neighborhood filter is proposed. Finally, we discuss severalapplicationsand we comparethe correspondingnumerical schemes for the proposed model.
