A novel approach is introduced to Maximum A Posteriori inference based on discrete graphical models. The given discrete objective function is smoothly approximated using regularized local Wasserstein distances in order to couple assignment measures across edges of the underlying graph. This approximation is restricted to the assignment manifold and optimized by a multiplicative update combining (i) geometric integration of the resulting Riemannian gradient flow and (ii) rounding to integral solutions that represent valid labelings.

This presentation is part of Minisymposium “MS31 - Variational Approaches for Regularizing Nonlinear Geometric Data (3 parts)”
organized by: Martin Storath (Universität Heidelberg) , Martin Holler (École Polytechnique, Université Paris Saclay) , Andreas Weinmann (Hochschule Darmstadt) .

Authors:

Ruben Hühnerbein (Universität Heidelberg)

Keywords:

assignment manifold, fisher-rao metric, graphical models, image segmentation, riemannian gradient flow, wasserstein distance