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We introduce a novel approach to Maximum A Posteriori inference based ondiscrete graphical models. By utilizing local Wasserstein distances forcoupling assignment measures across edges of the underlying graph, a givendiscrete objective function is smoothly approximated and restricted to theassignment manifold. A corresponding multiplicative update scheme combines in asingle process (i) geometric integration of the resulting Riemannian gradientflow and (ii) rounding to integral solutions that represent valid labelings.Throughout this process, local marginalization constraints known from theestablished LP relaxation are satisfied, whereas the smooth geometric settingresults in rapidly converging iterations that can be carried out in parallelfor every edge.

Image Labeling Based on Graphical Models Using Wasserstein Messages and Geometric Assignment