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Diffeomorphic density registration

Chapter in book
Authors M. Bauer
S. Joshi
Klas Modin
Published in Riemannian Geometric Statistics in Medical Image Analysis. Xavier Pennec, Stefan Sommer and Tom Fletcher (red.)
Pages 577-603
ISBN 9780128147269
Publisher Elsevier
Publication year 2020
Published at Department of Mathematical Sciences
Pages 577-603
Language en
Links dx.doi.org/10.1016/B978-0-12-814725...
Keywords Density registration, Diffeomorphism groups, Fisher-Rao metric, Image registration, Information geometry, Optimal transport, Random sampling
Subject categories Medical Image Processing, Geometry

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 their applicability for registering thoracic respiratory correlated CT imaging. © 2020 Elsevier Ltd All rights reserved.

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