Rotation invariance in exemplar-based image inpainting

Because of their good performance on textured images, exemplar-based methods for image recovery have been the subject of research in recent years. In this work, the variational framework of exemplar-based inpainting is reviewed and enriched by rotation invariance as an additional degree of freedom in patch searching. For an efficient rotation invariant comparison of image patches we present methods based on sampled Circular Harmonics (CH) expansions, in particular, we also elaborate a method for gradient-based comparisons thanks to the property of CH of being eigenfunctions of the Laplacian. These new pattern matching methods allow for an extremely efficient implementation of the alternating optimization scheme of exemplar-based inpainting, also when rotation invariant patch matching is considered. The patch non-local means algorithm and its performance in the recovery of image structures and textures are described in detail and we demonstrate by numerical examples the significant improvement in recovering smooth edges, which is due to the additional rotation invariance.