This project aims to investigate methods to perform image processing and data analysis on manifold-valued data defined on a graph. This reaches from defining meaningful models and differential operators for data on Riemannian manifolds, to deriving numerical optimization schemes to solve the related problems, to the investigation of theoretical properties as convergence rates and upper bounds, to finally applying derived algorithms to real world applications, e.g., in medical imaging.
- Bergmann, R and Tenbrinck, D (2017). Nonlocal inpainting of manifold-valued data on finite weighted graphs. Geometric Science of Information – 3rd Conference on Geometric Science of Information. Springer International Publishing, Cham. 604–12