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

TL;DR

This paper presents a novel graphical model inference method using Wasserstein distances and geometric assignment, enabling smooth approximation and efficient convergence for image labeling tasks.

Contribution

It introduces a Wasserstein-based smoothing approach combined with a geometric update scheme for MAP inference in discrete graphical models.

Findings

Rapid convergence of the proposed method

Parallelizable updates across graph edges

Effective approximation of labelings in image analysis

Abstract

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.