Abstract: Two prevailing working directions in connection with image labeling and segmentation are TV-based regularization in connection with continuous variational models, and convex polyhedral relaxations in connection with discrete graphical models. In this talk, I will sketch an alternative novel ansatz where image labeling is modelled as a Riemannian gradient flow on a simple manifold. This approach may be seen as a smooth non-convex inner relaxation of the image labeling problem, as opposed to the convex outer relaxations that dominate the current literature. While convexity is lost, numerical efficiency is gained through geodesic updates that sufficiently converge after few dozens of sparse updates, even for large-scale problems. A clear mathematical separation of the assignment mechanism from what is assigned to a given image enables wide applicability in a uniform manner.