Diffeomorphic density registration
Book chapter, 2019

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 their applicability for registering thoracic respiratory correlated CT imaging.

Diffeomorphism groups

Image registration

Random sampling

Information geometry

Optimal transport

Density registration

Fisher-Rao metric


M. Bauer

Florida State University

S. Joshi

University of Utah

Klas Modin

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Riemannian Geometric Statistics in Medical Image Analysis


Subject Categories

Computational Mathematics


Medical Image Processing



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