Riemannian Geometric Statistics in Medical Image Analysis

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Riemannian geometry on shapes and diffeomorphisms

Statistics via actions of the diffeomorphism group

Stephen Marsland^a; Stefan Sommer^b    aVictoria University of Wellington, School of Mathematics and Statistics, Wellington, New Zealand^bUniversity of Copenhagen, Department of Computer Science, Copenhagen, Denmark

Abstract

Shapes, which can informally be thought of as curves or surfaces marking the outlines of physical items, are examples of objects that are amenable to statistical analysis using Riemannian geometry. The shapes, either described as continuous curves or surfaces or parameterized as a set of landmark points or an image, can be deformed one to another using smooth invertible functions with smooth inverse (diffeomorphisms). The set of ...