# Nonlocal Inpainting of Manifold-valued Data on Finite Weighted Graphs

## TL;DR

This paper introduces a novel nonlocal inpainting method for manifold-valued data on graphs, utilizing a new graph infinity-Laplace operator and PDE formulation, with demonstrated effectiveness on synthetic data.

## Contribution

It proposes a new graph infinity-Laplace operator and PDE-based inpainting framework specifically designed for manifold-valued data on finite weighted graphs.

## Key findings

- Effective inpainting on synthetic manifold-valued images
- New graph infinity-Laplace operator introduced
- Numerical scheme successfully evaluated

## Abstract

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.