Optimal Mass Transport for Shape Matching and Comparison

Geodesic Shape Retrieval via Optimal Mass Transport

This paper presents a new method for 2-D and 3-D shape retrieval based on geodesic signatures. These signatures are high dimensional statistical distributions computed by extracting several features from the set of geodesic distance maps to each point. The resulting high dimensional distributions are matched to perform retrieval using a fast approximate Wasserstein metric. This allows to propos...

A Perfect Match Condition for Point-Set Matching Problems Using the Optimal Mass Transport Approach

We study the performance of optimal mass transport-based methods applied to point-set matching problems. The present study, which is based on the L2 mass transport cost, states that perfect matches always occur when the product of the point-set cardinality and the norm of the curl of the non-rigid deformation field does not exceed some constant. This analytic result is justified by a numerical ...

Optimal Mass Transport over Bridges

We present an overview of our recent work on implementable solutions to the Schrödinger bridge problem and their potential application to optimal transport and various generalizations.

Vector-Valued Optimal Mass Transport

In this note, we propose a straightforward notion of transport distance on a graph that is readily computable via a convex optimization reformulation. Similar ideas lead to a Wasserstein distance on vector-valued densities, that allow us to apply optimal mass transport to graphs whose nodes represent vectorial and not just scalar data. We are interested in the application to various communicati...

Diffeomorphic Density Matching by Optimal Information Transport