Non-local image smoothing by applying anisotropic diffusion PDE's in the space of patches

We design a family of non-local image smoothing algorithms which approximate the application of diffusion PDE's on a specific Euclidean space of image patches. We first map a noisy image onto this high-dimensional space and estimate its geometric structure thanks to a straightforward extension of the structure tensor field. The tensors spectral elements allows us to design an oriented high-dimensional smoothing process by the means of anisotropic regularization PDE's which have both local and non-local properties and whose solutions are estimated by locally oriented high-dimensional convolutions. We show that the Bilateral Filtering and Non-Local Means methods are the isotropic cases of our denoising framework.