Diffeomorphic density registration

TL;DR

This chapter explores the Riemannian geometric framework for density registration on manifolds, with applications in medical imaging, and introduces efficient algorithms for diffeomorphic transformations.

Contribution

It develops a geometric approach to density registration using Riemannian metrics and proposes novel algorithms for practical implementation in medical imaging.

Findings

Established the link between Riemannian metrics on diffeomorphisms and densities.

Developed computationally efficient algorithms for density registration.

Demonstrated applicability in thoracic CT imaging for organ motion tracking.

Abstract

In this book chapter we study the Riemannian Geometry of the density registration problem: Given two densities (not necessarily probability densities) defined on a smooth finite dimensional manifold find a diffeomorphism which transforms one to the other. This problem is motivated by the medical imaging application of tracking organ motion due to respiration in Thoracic CT imaging where the fundamental physical property of conservation of mass naturally leads to modeling CT attenuation as a density. We will study the intimate link between the Riemannian metrics on the space of diffeomorphisms and those on the space of densities. We finally develop novel computationally efficient algorithms and demonstrate there applicability for registering RCCT thoracic imaging.