title: A computational model for periodic pattern perception based on frieze and wallpaper groups.
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.
authors.affiliation: Robotics Institute, School of Computer Science, Carnegie Mellon University, 5000 Forbes Ave., Pittsburgh, PA 15213, USA. yanxi@cs.cmu.edu
authors.forename: Yanxi
authors.initials: Y
authors.lastname: Liu
authors.forename: Robert T
authors.initials: RT
authors.lastname: Collins
authors.forename: Yanghai
authors.initials: Y
authors.lastname: Tsin
mesh_terms: D000465:Algorithms; D000818:Animals; D001185:Artificial Intelligence; D001683:Biological Clocks / Q000502:physiology; D003196:Computer Graphics; D004285:Dogs; D005556:Form Perception; D005684:Gait / Q000502:physiology*; D006801:Humans; D007089:Image Enhancement / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods; D015233:Models, Statistical; D009716:Numerical Analysis, Computer-Assisted; D010363:Pattern Recognition, Automated; D010507:Periodicity; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted; D013382:Subtraction Technique; D014584:User-Computer Interface