Abstract
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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 354-371 |
| Number of pages | 18 |
| Journal | IEEE Transactions on Pattern Analysis and Machine Intelligence |
| Volume | 26 |
| Issue number | 3 |
| DOIs | |
| State | Published - Mar 1 2004 |
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All Science Journal Classification (ASJC) codes
- Software
- Computer Vision and Pattern Recognition
- Computational Theory and Mathematics
- Artificial Intelligence
- Applied Mathematics
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A Computational Model for Periodic Pattern Perception Based on Frieze and Wallpaper Groups. / Liu, Yanxi; Collins, Robert T.; Tsin, Yanghai.
In: IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 26, No. 3, 01.03.2004, p. 354-371.Research output: Contribution to journal › Article
TY - JOUR
T1 - A Computational Model for Periodic Pattern Perception Based on Frieze and Wallpaper Groups
AU - Liu, Yanxi
AU - Collins, Robert T.
AU - Tsin, Yanghai
PY - 2004/3/1
Y1 - 2004/3/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=1342282159&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=1342282159&partnerID=8YFLogxK
U2 - 10.1109/TPAMI.2004.1262332
DO - 10.1109/TPAMI.2004.1262332
M3 - Article
C2 - 15376882
AN - SCOPUS:1342282159
VL - 26
SP - 354
EP - 371
JO - IEEE Transactions on Pattern Analysis and Machine Intelligence
JF - IEEE Transactions on Pattern Analysis and Machine Intelligence
SN - 0162-8828
IS - 3
ER -