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RI | Publications | Skewed Symmetry Groups
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Skewed Symmetry Groups
Y. Liu and R. Collins
IEEE Conference on Computer Vision and Pattern Recognition, Vol. 1, 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.
| Notes |
Associated center: VASC
Associated lab/group: Computational Symmetry
Associated project: A Computational Model for Repeated Pattern Perception using Crystallographic Groups
Number of pages: 8
| Text Reference |
Y. Liu and R. Collins, "Skewed Symmetry Groups," IEEE Conference on Computer Vision and Pattern Recognition, Vol. 1, 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",
month = "December",
year = "2001",
volume = "1",
pages = "872 - 879"
}