Skewed symmetry groups

Author

Liu, Yanxi ; Collins, Robert T.

Author_Institution

Robotics Inst., Carnegie Mellon Univ., Pittsburgh, PA, USA

Volume

1

fYear

2001

fDate

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.

Keywords

computational geometry; computer vision; information retrieval; 2D wallpaper groups; Euclidean symmetry group; affine transformations; indexing; maximal symmetry-based method; periodic pattern; regular patterns; retrieval scheme; shape estimation; skewed symmetry groups; wallpaper group migration map; Chemistry; Crystallography; Crystals; Indexing; Mathematics; Orbits; Pattern classification; Physics; Robots; Shape;

fLanguage

English

Publisher

ieee

Conference_Titel

Computer Vision and Pattern Recognition, 2001. CVPR 2001. Proceedings of the 2001 IEEE Computer Society Conference on

ISSN

1063-6919

Print_ISBN

0-7695-1272-0

Type

conf

DOI

10.1109/CVPR.2001.990576

Filename

990576