Diffeomorphic density matching by optimal information transport

TL;DR

This paper introduces a novel diffeomorphic density matching method based on optimal information transport, leveraging Fisher-Rao geometry to develop efficient algorithms for applications like medical imaging and texture mapping.

Contribution

It presents a new framework connecting Fisher-Rao metric with diffeomorphisms for density matching, offering more efficient algorithms than existing optimal mass transport methods.

Findings

Algorithms outperform traditional methods in efficiency.

Applicable to medical image registration and texture mapping.

Demonstrated successful examples in various applications.

Abstract

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, allows 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, non-uniform random sampling, and mesh adaptivity. Some of these applications are illustrated in examples.