Riemannian Geometric Statistics in Medical Image Analysis

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Diffeomorphic density registration

Martin Bauer^a; Sarang Joshi^b; Klas Modin^c    aFlorida State University, Department of Mathematics, Tallahassee, FL, United States^bUniversity of Utah, Department of Bioengineering, Scientific Computing and Imaging Institute, Salt Lake City, UT, United States^cChalmers University of Technology and the University of Gothenburg, Department of Mathematical Sciences, Göteborg, Sweden

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 ...