Image completion by diffusion maps and spectral relaxation

We present a framework for image inpainting that utilizes the diffusion framework approach to spectral dimensionality reduction. We show that on formulating the inpainting problem in the embedding domain, the domain to be inpainted is smoother in general, particularly for the textured images. Thus, the textured images can be inpainted through simple exemplar-based and variational methods. We discuss the properties of the induced smoothness and relate it to the underlying assumptions used in contemporary inpainting schemes. As the diffusion embedding is nonlinear and noninvertible, we propose a novel computational approach to approximate the inverse mapping from the inpainted embedding space to the image domain. We formulate the mapping as a discrete optimization problem, solved through spectral relaxation. The effectiveness of the presented method is exemplified by inpainting real images, where it is shown to compare favorably with contemporary state-of-the-art schemes.