Nonlocal Inpainting of Manifold-valued Data on Finite Weighted Graphs
This work extends inpainting techniques to manifold-valued data on graphs, addressing a gap in non-Euclidean image processing, but the evaluation is limited to synthetic data.
The paper introduces a nonlocal inpainting method for manifold-valued data on finite weighted graphs, using a new graph infinity-Laplace operator. The method is evaluated on synthetic manifold-valued images, showing effective inpainting results.
Recently, there has been a strong ambition to translate models and algorithms from traditional image processing to non-Euclidean domains, e.g., to manifold-valued data. While the task of denoising has been extensively studied in the last years, there was rarely an attempt to perform image inpainting on manifold-valued data. In this paper we present a nonlocal inpainting method for manifold-valued data given on a finite weighted graph. We introduce a new graph infinity-Laplace operator based on the idea of discrete minimizing Lipschitz extensions, which we use to formulate the inpainting problem as PDE on the graph. Furthermore, we derive an explicit numerical solving scheme, which we evaluate on two classes of synthetic manifold-valued images.