Diffeomorphic density matching by optimal information transport
Journal article, 2015

We address the following problem: given two smooth densities on a manifold, find an optimal diffeomorphism that transforms one density into the other. Our framework builds on connections between the Fisher–Rao information metric on the space of probability densities and right-invariant metrics on the infinite-dimensional manifold of diffeomorphisms. This optimal information transport, and modifications thereof, allow us to construct numerical algorithms for density matching. The algorithms are inherently more efficient than those based on optimal mass transport or diffeomorphic registration. Our methods have applications in medical image registration, texture mapping, image morphing, nonuniform random sampling, and mesh adaptivity. Some of these applications are illustrated in examples.

Density matching

Fisher–rao metric

Diffeomorphism groups

Image registration

Information geometry

Optimal transport

Random sampling

Author

M. Bauer

University of Vienna

S. Joshi

University of Utah

Klas Modin

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

SIAM Journal on Imaging Sciences

1936-4954 (ISSN)

Vol. 8 3 1718-1751

Subject Categories

Computational Mathematics

Geometry

Roots

Basic sciences

Areas of Advance

Life Science Engineering (2010-2018)

DOI

10.1137/151006238

More information

Latest update

3/29/2018