Skewed Symmetry Groups

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


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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.

Keywords
skewed symmetry, group theory, wallpaper groups,

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",
}