Skewed Symmetry Groups

Liu, Yanxi; Collins, Robert T.

doi:10.1109/CVPR.2001.990576

Skewed Symmetry Groups

Yanxi Liu, Robert T. Collins

CVPR 2001 pp. I:872-879

doi:10.1109/CVPR.2001.990576 /cvpr/2001/liu2001cvpr-skewed/

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.

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Cite

Text

Liu and Collins. "Skewed Symmetry Groups." IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2001. doi:10.1109/CVPR.2001.990576

Markdown

[Liu and Collins. "Skewed Symmetry Groups." IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2001.](https://mlanthology.org/cvpr/2001/liu2001cvpr-skewed/) doi:10.1109/CVPR.2001.990576

BibTeX

@inproceedings{liu2001cvpr-skewed,
  title     = {{Skewed Symmetry Groups}},
  author    = {Liu, Yanxi and Collins, Robert T.},
  booktitle = {IEEE/CVF Conference on Computer Vision and Pattern Recognition},
  year      = {2001},
  pages     = {I:872-879},
  doi       = {10.1109/CVPR.2001.990576},
  url       = {https://mlanthology.org/cvpr/2001/liu2001cvpr-skewed/}
}