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...

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Vydáno v:IEEE transactions on pattern analysis and machine intelligence Ročník 26; číslo 3; s. 354 - 371
Hlavní autoři: Yanxi Liu, Collins, R.T., Tsin, Y.
Médium: Journal Article
Jazyk:angličtina
Vydáno: United States IEEE 01.03.2004
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Algorithms
Animals
Application software
Artificial Intelligence
Biological Clocks - physiology
Computational modeling
Computer Graphics
Crystallography
Dogs
Form Perception
Gait - physiology
Humans
Image coding
Image Enhancement - methods
Image Interpretation, Computer-Assisted - methods
Information Storage and Retrieval - methods
Mathematical model
Models, Statistical
Numerical Analysis, Computer-Assisted
Pattern Recognition, Automated
Periodic structures
Periodicity
Reproducibility of Results
Sensitivity and Specificity
Signal Processing, Computer-Assisted
Solid modeling
Subtraction Technique
User-Computer Interface
ISSN:0162-8828, 2160-9292, 1939-3539
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Popis
Shrnutí: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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ISSN:0162-8828
2160-9292
1939-3539
DOI:10.1109/TPAMI.2004.1262332