A computational model for periodic pattern perception based on frieze and wallpaper groups
We present a computational model for periodic pattern perception based on the mathematical theory of crystallographic groups. In each N-dimensional Euclidean space, a finite number of symmetry groups can characterize the structures of an infinite variety of periodic patterns. In 2D space, there are...
| Veröffentlicht in: | IEEE transactions on pattern analysis and machine intelligence. - 1979. - 26(2004), 3 vom: 24. März, Seite 354-71 |
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| Weitere Verfasser: | , |
| Format: | Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2004
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| Zugriff auf das übergeordnete Werk: | IEEE transactions on pattern analysis and machine intelligence |
| Schlagworte: | Comparative Study Evaluation Study Journal Article Research Support, U.S. Gov't, Non-P.H.S. Validation Study |
| Zusammenfassung: | We present a computational model for periodic pattern perception based on the mathematical theory of crystallographic groups. In each N-dimensional Euclidean space, a finite number of symmetry groups can characterize the structures of an infinite variety of periodic patterns. In 2D space, there are seven frieze groups describing monochrome patterns that repeat along one direction and 17 wallpaper groups for patterns that repeat along two linearly independent directions to tile the plane. We develop a set of computer algorithms that "understand" a given periodic pattern by automatically finding its underlying lattice, identifying its symmetry group, and extracting its representative motifs. We also extend this computational model for near-periodic patterns using geometric AIC. Applications of such a computational model include pattern indexing, texture synthesis, image compression, and gait analysis |
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| Beschreibung: | Date Completed 12.10.2004 Date Revised 10.12.2019 published: Print Citation Status MEDLINE |
| ISSN: | 1939-3539 |