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Pattern TheoryFrom representation to inference$
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Ulf Grenander and Michael I. Miller

Print publication date: 2006

Print ISBN-13: 9780198505709

Published to Oxford Scholarship Online: November 2020

DOI: 10.1093/oso/9780198505709.001.0001

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Metrics Spaces for the Matrix Groups

Metrics Spaces for the Matrix Groups

(p.316) 10 Metrics Spaces for the Matrix Groups
Pattern Theory

Ulf Grenander

Michael I. Miller

Oxford University Press

In this chapter the metric space structure of shape is developed. We do this by first studying the action of the matrix groups on the coordinate systems of shape. We begin by reviewing the well-known properties of the finite-dimensional matrix groups, including their properties as smooth Riemannian manifolds, allowing us to develop metric distances between the groupelements. We explore the construction of the metric structure of these diffeomorphisms and develop many of the properties which hold for the finite dimensional matrix groups and subsequently in the infinite dimensional setting as well.

Keywords:   Burger’s equation, N-shapes, differential operators, landmark mapping

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