We discuss the extension of the L2-Wasserstein metric in different contexts of interest. After reviewing the extension of the Wasserstein metric to the space of nonnegative Radon measure, we present an efficient algorithm to solve it based on entropic regularization. We showcase applications to diffeomorphic matching of embedded surfaces and we discuss its application to images. Last, we present an extension of these transport distances to the case of cone valued measures.

This presentation is part of Minisymposium “MS63 - Geometric methods for shape analysis with applications to biomedical imaging and computational anatomy”
organized by: Martin Bauer (Florida State University) , Nicolas Charon (Johns Hopkins University) .

Authors:

François-Xavier Vialard (University Paris-Dauphine)

Keywords:

image registration, partial differential equation models