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.
|Original language||English (US)|
|Journal||Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition|
|State||Published - Dec 1 2001|
|Event||2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Kauai, HI, United States|
Duration: Dec 8 2001 → Dec 14 2001
All Science Journal Classification (ASJC) codes
- Computer Vision and Pattern Recognition