Robotics Institute: A Computational Model for Repeated Pattern Perception using Frieze and Wallpaper Groups

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

Yanxi Liu and Robert Collins
2000 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR 2000), June, 2000, pp. 537 - 544.

Download

Adobe portable document format (pdf) (979KB)

Copyright notice: This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. These works may not be reposted without the explicit permission of the copyright holder.

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(s) / Consortia: Vision and Autonomous Systems Center

Associated Lab(s) / Group(s): Computational Symmetry

Associated Project(s): A Computational Model for Repeated Pattern Perception using Crystallographic Groups

Text Reference

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

BibTeX Reference

@inproceedings{Liu_2000_3302,
   author = "Yanxi Liu and Robert Collins",
   title = "A Computational Model for Repeated Pattern Perception using Frieze and Wallpaper Groups",
   booktitle = "2000 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR 2000)",
   pages = "537 - 544",
   month = "June",
   year = "2000",
   volume = "1",
}

The Robotics Institute

Menu