The Robotics Institute

Carnegie Mellon Robotics Institute

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

We introduce the term skewed symmetry groups and provide a complete theoretical treatment for 2D wallpaper groups under affine transformations. For the first time, a given periodic pattern can be classified not simply by its Euclidean symmetry group but by its highest ``potential'' symmetry group under affine deformation. A concise wallpaper group migration map is constructed that separates the 17 affinely deformed wallpaper groups into small, distinct orbits. The practical value of this result includes a novel indexing and retrieval scheme for regular patterns, and a maximal-symmetry-based method for estimating shape and orientation from texture under unknown views.

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

Number of pages: 8

Text Reference

Yanxi Liu and Robert Collins, "Skewed Symmetry Groups," IEEE Conference on Computer Vision and Pattern Recognition, December, 2001, pp. 872 - 879.

BibTeX Reference

@inproceedings{Liu_2001_3815,
   author = "Yanxi Liu and Robert Collins",
   title = "Skewed Symmetry Groups",
   booktitle = "IEEE Conference on Computer Vision and Pattern Recognition",
   pages = "872 - 879",
   month = "December",
   year = "2001",
   volume = "1",
}

The Robotics Institute

Menu