NONLOCAL VARIATIONAL MODELS FOR INPAINTING AND INTERPOLATION

In this paper we study some nonlocal variational models for different image inpainting tasks. Nonlocal methods for denoising and inpainting have gained considerable attention due to their good performance on textured images, a known weakness of classical local methods which are performant in recovering the geometric structure of the image. We first review a general variational framework for the problem of nonlocal inpainting that exploits the self-similarity of natural images to copy information in a consistent way from the known parts of the image. We single out two particular methods depending on the information we copy: either the gray level (or color) information or its gradient. We review the main properties of the corresponding energies and their minima. Then we discuss three other applications: we consider the problem of stereo inpainting, some simple cases of video inpainting, and the problem of interpolation of incomplete depth maps knowing a reference image. Incomplete depth maps can be obtained as a result of stereo algorithms, or given for instance by Time-of-Flight cameras (in that case the interpolated result can be used to generate the images of the stereo pair). We discuss the basic algorithms to minimize the energies and we display some numerical experiments illustrating the main properties of the proposed models.