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A Computational Model for Repeated Pattern Perception using Frieze and Wallpaper Groups
Y. Liu and R. Collins
tech. report CMU-RI-TR-00-08, Robotics Institute, Carnegie Mellon University, April, 2000.

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Abstract

Humans have an innate ability to perceive symmetry, but it is not obvious how to automate this powerful insight. In this paper the mathematical theory of Frieze and wallpaper groups is used to extract visually meaningful building blocks (motifs) from a repeated pattern. A novel peak detection algorithm based on ?regions of dominance? is used to automatically detect the underlying translational lattice of a repeated pattern. Following automatic classification of the pattern?s symmetry group, knowledge of the interplay between rotation, reflection, glide-reflection and translation in that group leads to a small set of candidate motifs that exhibit local symmetry consistent with the global symmetry of the entire pattern. Although other work has addressed detection of the translational lattice of a repeated pattern, ours is the first to seek a principled method for determining a representative motif. Experiments show that the resulting pattern motifs conform well with human perception.

Notes

Associated center: VASC
Associated lab/group: Computational Symmetry
Associated project: A Computational Model for Repeated Pattern Perception using Crystallographic Groups

Text Reference

Y. Liu and R. Collins, A Computational Model for Repeated Pattern Perception using Frieze and Wallpaper Groups, tech. report CMU-RI-TR-00-08, Robotics Institute, Carnegie Mellon University, April, 2000.

BibTeX Reference

@techreport{Liu_2000_3306,
   author = "Yanxi Liu and Robert Collins",
   title = "A Computational Model for Repeated Pattern Perception using Frieze and Wallpaper Groups",
   institution = "Robotics Institute, Carnegie Mellon University",
   month = "April",
   year = "2000",
   number = "CMU-RI-TR-00-08",
   address = "Pittsburgh, PA"
}