A Computational Model for Repeated Pattern Perception Using Frieze and Wallpaper Groups

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. Followingautomatic classi cation of the pattern's symmetrygroup, knowledge of the interplay between rotation, re ection, glide-re ection and translation in that group leads to a small set of candidate motifsthat exhibit local symmetryconsistent with the globalsymmetryof the entire pattern. Although other work has addressed detection of the translational lattice of a repeated pattern, ours is the rst to seek a principled method for determining a representative motif. Experiments show that the resulting pattern motifs conform well with human perception.

• Type: Conference
• Year: 2000
• Where: CVPR
• Authors: Yanxi Liu, Robert T. Collins
• Keywords: Building Blocks Motifs, Computer Vision, CVPR 2000, Entire Pattern, Pattern Motifs, Peak Detection Algorithm, Translational Lattice