Jump to ContentJump to Main Navigation
Pattern TheoryFrom representation to inference$
Users without a subscription are not able to see the full content.

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

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2022. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use.date: 01 July 2022

The Canonical Representations Of General Pattern Theory

The Canonical Representations Of General Pattern Theory

(p.154) 6 The Canonical Representations Of General Pattern Theory
Pattern Theory

Ulf Grenander

Michael I. Miller

Oxford University Press

Pattern theory is combinatory in spirit or, to use a fashionable term, connectionist: complex structures are built from simpler ones. To construct more general patterns, we will generalize from combinations of sites to combinations of primitives, termed generators, which are structured sets. The interactions between generators is imposed via the directed and undirected graph structures, defining how the variables at the sites of the graph interact with their neighbors in the graph. Probabilistic structures on the representations allow for expressing the variation of natural patterns. Canonical representations are established demonstrating a unified manner for viewing DAGs, MRFs, Gaussian random fields and probabilistic formal languages.

Keywords:   circle packing, directional derivatives, equivalence classes, forest graphs, geodesic generation, homogeneous coordinates, independent loops, leaf model, maple leaf model

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .