### 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 language | English (US) |
---|---|

Title of host publication | Algebraic Frames for the Perception-Action Cycle - 2nd International Workshop, AFPAC 2000, Proceedings |

Editors | Yehoshua Y. Zeevi, Gerald Sommer |

Publisher | Springer Verlag |

Pages | 241-250 |

Number of pages | 10 |

ISBN (Electronic) | 3540410139, 9783540410133 |

State | Published - Jan 1 2000 |

Event | 2nd International Workshop on Algebraic Frames for the Perception-Action Cycle, AFPAC 2000 - Kiel, Germany Duration: Sep 10 2000 → Sep 11 2000 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Volume | 1888 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 2nd International Workshop on Algebraic Frames for the Perception-Action Cycle, AFPAC 2000 |
---|---|

Country | Germany |

City | Kiel |

Period | 9/10/00 → 9/11/00 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*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.

}

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Periodic pattern analysis under affine distortions using wallpaper groups

AU - Liu, Yanxi

AU - Collins, Robert

PY - 2000/1/1

Y1 - 2000/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84937424473&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84937424473&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84937424473

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 241

EP - 250

BT - Algebraic Frames for the Perception-Action Cycle - 2nd International Workshop, AFPAC 2000, Proceedings

A2 - Zeevi, Yehoshua Y.

A2 - Sommer, Gerald

PB - Springer Verlag

ER -