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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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Markov Random Fields On Undirected Graphs

Markov Random Fields On Undirected Graphs

(p.95) 4 Markov Random Fields On Undirected Graphs
Pattern Theory

Ulf Grenander

Michael I. Miller

Oxford University Press

This chapter focuses on random fields on lattices and undirected graphs. Discrete finite state spaces are examined in the context of Markov and Gibbs fields. The subsequent chapter studies state spaces on the continuum through Gaussian fields. This chapter examines texture representation and segmentation, exploring the Gibbs random fields. For dealing with the partition function asymptotics are derived allowing for the explicit calculation of the asymptotic approximation to the log-normalizer required for the Bayes solution. Zhu’s maximum-entropy model is explored for representing random field textures.

Keywords:   Butterworth filters, Toeplitz covariance, actin-myosin shapes, cyclo-stationary Gaussian processes, mitochondria, oriented textures, torus graphs

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