Skewed Symmetry Groups
Conference Paper, Proceedings of (CVPR) Computer Vision and Pattern Recognition, pp. 872 - 879, December, 2001
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.
BibTeX
@conference{Liu-2001-8360,author = {Yanxi Liu and Robert Collins},
title = {Skewed Symmetry Groups},
booktitle = {Proceedings of (CVPR) Computer Vision and Pattern Recognition},
year = {2001},
month = {December},
pages = {872 - 879},
keywords = {skewed symmetry, group theory, wallpaper groups,},
}
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