Diffeomorphic registration of densities by optimal information transport

Klas Modin
Department of Mathematical Sciences
Chalmers University of Technology
Göteborg

Abstract:

I will address the following problem: given two smooth probability densities on a manifold, find an optimal diffeomorphism that transforms one density into the other. A common approach is to use optimal mass transport. I will discuss a different setup, called "optimal information transport", where instead of the Wasserstein distance we use the Fisher--Rao metric and the corresponding spherical Hellinger distance. This modification allows us to construct numerical algorithms that are significantly more efficient than those based on optimal mass transport (Poisson instead of Monge-Ampere equation). Our methods have applications in medical image registration, texture mapping, image morphing, non-uniform random sampling, and mesh adaptivity. Some of these applications are illustrated in examples.