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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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Matrix Group Actions Transforming Patterns

Matrix Group Actions Transforming Patterns

Chapter:
(p.174) 7 Matrix Group Actions Transforming Patterns
Source:
Pattern Theory
Author(s):

Ulf Grenander

Michael I. Miller

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198505709.003.0008

Thus far Pattern theory has been combinatore constructing complex patterns by connecting simpler ones via graphs. Patterns typically occurring in nature may be extremely complex and exhibit invariances. For example, spatial patterns may live in a space where the choice of coordinate system is irrelevant; temporal patterns may exist independently of where time is counted from, and so on. For this matrix groups as transformations are introduced, these transformations often forming groups which act on the generators.

Keywords:   Chan-Vese model, Green’s formula, Inverse Function Theorem, Jacobian matrices, Lie group action, active closed contours, boundary integral

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