Explicit Reconstruction for Image Inpainting

Image inpainting refers to techniques which allow to fill in a gap $\Omega$ given the intensities around it. In this paper, we focus on geometric image inpainting for which several PDE based models have been proposed. Most of them rely on a transport or/and a diffusion equation of the intensity inside $\Omega$. The direction of the reconstructed isophotes and the gray levels are generally computed in a coupled way. Instead, we propose in this paper a two step approach. First we estimate the tangents of the missing isophotes using a tensor field diffusion process. Then we simply recover the gray levels by integrating along integral curves of the tensors principal eigenvectors. Such an approach has very few parameters to tune and we illustrate its performance on several synthetic and real examples