Diffeomorphic density matching by optimal information transport
Artikel i vetenskaplig tidskrift, 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

Författare

M. Bauer

Universität Wien

S. Joshi

University of Utah

Klas Modin

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

SIAM Journal on Imaging Sciences

1936-4954 (ISSN)

Vol. 8 1718-1751

Ämneskategorier

Beräkningsmatematik

Geometri

Fundament

Grundläggande vetenskaper

Styrkeområden

Livsvetenskaper och teknik

DOI

10.1137/151006238