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.
Click here for
full paper (1433727 bytes, compressed using gzip).