Periodic pattern analysis under affine distortions using wallpaper groups

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

In this paper, the mathematical theory of wallpaper groups is used to construct a computational tool for symmetry analysis of periodic patterns. Starting with a novel peak detection algorithm based on “regions of dominance", an input periodic pattern can be automatically classified into one of the 17 wallpaper groups. The orbits of stabilizer subgroups within the group lead to a small set of candidate motifs that exhibit local symmetry consistent with the global symmetry of the entire pattern. We further consider affine distorted periodic patterns and show that each such pattern can be classified into a small set of symmetry groups that describe the patterns' potential symmetries under affine transformation.

Original languageEnglish (US)
Title of host publicationAlgebraic Frames for the Perception-Action Cycle - 2nd International Workshop, AFPAC 2000, Proceedings
EditorsYehoshua Y. Zeevi, Gerald Sommer
PublisherSpringer Verlag
Pages241-250
Number of pages10
ISBN (Electronic)3540410139, 9783540410133
StatePublished - Jan 1 2000
Event2nd International Workshop on Algebraic Frames for the Perception-Action Cycle, AFPAC 2000 - Kiel, Germany
Duration: Sep 10 2000Sep 11 2000

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1888
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other2nd International Workshop on Algebraic Frames for the Perception-Action Cycle, AFPAC 2000
CountryGermany
CityKiel
Period9/10/009/11/00

Fingerprint

Pattern Analysis
Orbits
Symmetry
Symmetry Group
Affine transformation
Orbit
Entire
Subgroup

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Liu, Y., & Collins, R. (2000). Periodic pattern analysis under affine distortions using wallpaper groups. In Y. Y. Zeevi, & G. Sommer (Eds.), Algebraic Frames for the Perception-Action Cycle - 2nd International Workshop, AFPAC 2000, Proceedings (pp. 241-250). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1888). Springer Verlag.
Liu, Yanxi ; Collins, Robert. / Periodic pattern analysis under affine distortions using wallpaper groups. Algebraic Frames for the Perception-Action Cycle - 2nd International Workshop, AFPAC 2000, Proceedings. editor / Yehoshua Y. Zeevi ; Gerald Sommer. Springer Verlag, 2000. pp. 241-250 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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Liu, Y & Collins, R 2000, Periodic pattern analysis under affine distortions using wallpaper groups. in YY Zeevi & G Sommer (eds), Algebraic Frames for the Perception-Action Cycle - 2nd International Workshop, AFPAC 2000, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1888, Springer Verlag, pp. 241-250, 2nd International Workshop on Algebraic Frames for the Perception-Action Cycle, AFPAC 2000, Kiel, Germany, 9/10/00.

Periodic pattern analysis under affine distortions using wallpaper groups. / Liu, Yanxi; Collins, Robert.

Algebraic Frames for the Perception-Action Cycle - 2nd International Workshop, AFPAC 2000, Proceedings. ed. / Yehoshua Y. Zeevi; Gerald Sommer. Springer Verlag, 2000. p. 241-250 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1888).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Liu Y, Collins R. Periodic pattern analysis under affine distortions using wallpaper groups. In Zeevi YY, Sommer G, editors, Algebraic Frames for the Perception-Action Cycle - 2nd International Workshop, AFPAC 2000, Proceedings. Springer Verlag. 2000. p. 241-250. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).