Riemannian geometry on shapes and diffeomorphisms
Statistics via actions of the diffeomorphism group
Stephen Marslanda; Stefan Sommerb aVictoria University of Wellington, School of Mathematics and Statistics, Wellington, New ZealandbUniversity of Copenhagen, Department of Computer Science, Copenhagen, Denmark
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 ...
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