Image Labeling Based on Graphical Models Using Wasserstein Messages and Geometric Assignment
This is an incremental improvement for image labeling tasks, offering a novel method for a known bottleneck in graphical model inference.
The paper tackles the problem of Maximum A Posteriori inference in discrete graphical models by introducing a method that uses Wasserstein distances and geometric assignment to smoothly approximate the objective, resulting in rapidly converging parallel iterations that satisfy local marginalization constraints.
We introduce a novel approach to Maximum A Posteriori 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.