Exemplar-Based Image Inpainting and Applications

Non-local methods for image denoising and inpainting have gained considerable attention in recent years. This is due to their superior performance in textured images, a known weakness of purely local methods. Local methods on the other hand have shown to be very appropriate for the recovering of geometric structure such as image edges. The synthesis of both types of methods is a trend in current research. Variational analysis in particular is an appropriate tool for a unified treatment of local and non-local methods. We discuss a general variational framework for the problem of non-local image inpainting, from which some previous inpainting schemes can be derived, in addition to leading to novel ones. We give an statistical mechanics interpretation of the proposed framework and discuss some open mathematical questions.