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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 on Photometric and Geometric Deformable Templates

Metrics on Photometric and Geometric Deformable Templates

(p.346) 12 Metrics on Photometric and Geometric Deformable Templates
Pattern Theory

Ulf Grenander

Michael I. Miller

Oxford University Press

In this chapter the metric structure developed for geometric transformations is extended to define a metric structure on the images which they act. Defined as an orbit under the finite and infinite dimensional groups we establish the necessary properties for measuring distance in the image orbit. We extend the results from not only geometric transformation of the images but also to photometric variation in the images.

Keywords:   asymptotic consistency, consistency, detectability, equivalence, fusion of information, hypothesis testing, identifiability, medical imaging registration

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