Yanxi Liu and Robert T. Collins,
"Skewed Symmetry Groups,"
IEEE Computer Vision and Pattern Recognition,
Kauai, Hawaii, December 2001, pp.872-879.
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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