Yanxi Liu and Robert Collins,
"Frieze and Wallpaper Symmetry Group Classification under Affine
and Perspective Distortion", Technical Report CMU RI-98-37,
Robotics Institute, Carnegie Mellon University, December 1998.
In this paper we study classification of 2D repeated patterns in
terms of their respective symmetry groups -- the well-known seven
Frieze groups and 17 wallpaper groups. Computer algorithms for
Frieze and wallpaper symmetry group classification are developed in
Euclidean as well as affine spaces. Several symmetry invariants of these
groups under affine transformations are analyzed in detail and used to
extend the Euclidean group classification algorithm for patterns
that are distorted under affine transformations. Experimental results
on computer generated images and photos of natural scenes are presented.
Precise classification of 2D repeated patterns in terms of their
symmetry groups provides a computational means for image indexing,
image matching, object recognition, and motion recovery. This is a report
of an on-going research effort. Existing problems and future work
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