We introduce a novel approach to Maximum A Posteriori (MAP) inference based on discrete graphical models. By utilizing local Wasserstein distances for coupling assignment measures across edges of the underlying graph, a given discrete objective function is smoothly approximated and restricted to the assignment manifold. A corresponding multiplicative update scheme combines in a single process (i) geometric integration of the resulting Riemannian gradient flow, and (ii) rounding to integral solutions that represent valid labelings. Throughout this process, local marginalization constraints known from the established LP relaxation are satisfied, whereas the smooth geometric setting results in rapidly converging iterations that can be carried out in parallel for every edge.

In this work we introduce a variational nonconvex model for color image regularization. We express the variational problem as an instance of the half quadratic algorithm (HQA). Moreover, the generalized HQA allows us to prove convergence of the variational problem. As a demonstrator of our framework, we consider a vectorial total variation (VTV) formulation with an additional nonconvex pair-wise color-channel coupling matrix. Numerical evidence show the applicability of the proposed framework compared to VTV methods and state-of-the-art image denoising methods.