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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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Gaussian Random Fields on Undirected Graphs

Gaussian Random Fields on Undirected Graphs

Chapter:
(p.123) 5 Gaussian Random Fields on Undirected Graphs
Source:
Pattern Theory
Author(s):

Ulf Grenander

Michael I. Miller

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198505709.003.0006

This chapter focuses on state spaces of the continuum studying Gaussian random fields on discrete lattices. Covariances are induced via difference operators and the associated neighborhood structure of the resulting random field is explored. Texture representation and segmentation are studied via the general Gaussian random field structures. For dealing with the partition function determined by the log-determinant of the covariance asymptotics are derived connecting the eigenvalues of the finite covariance fields to the spectrum of the infinite stationary extension.

Keywords:   Hammersley Clifford result, Platonic solids, aircraft tracking, bond function, canonical representation, grammatical transformations, local regularity, moving body systems, sentence-language set

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