Yanxi Liu and Robert Collins,
"A Computational Model for Repeated Pattern Perception using Frieze 
and Wallpaper Groups,"  IEEE Computer Vision and Pattern 
Recognition (CVPR 2000), Hilton Head, NC, June 2000, pp. 537-544. 


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.

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