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.

Original languageEnglish (US)
JournalProceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
Volume1
StatePublished - Dec 1 2001
Event2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Kauai, HI, United States
Duration: Dec 8 2001Dec 14 2001

All Science Journal Classification (ASJC) codes

  • Software
  • Computer Vision and Pattern Recognition

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