Frieze and Wallpaper Symmetry Groups Classification under Affine and Perspective Distortion

Yanxi Liu and Robert Collins
tech. report CMU-RI-TR-98-37, Robotics Institute, Carnegie Mellon University, July, 1998


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Abstract
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 prbolems and future work are dis-cussed.


Notes
Associated Center(s) / Consortia: Vision and Autonomous Systems Center
Associated Lab(s) / Group(s): Computational Symmetry
Associated Project(s): A Computational Model for Repeated Pattern Perception using Crystallographic Groups

Text Reference
Yanxi Liu and Robert Collins, "Frieze and Wallpaper Symmetry Groups Classification under Affine and Perspective Distortion," tech. report CMU-RI-TR-98-37, Robotics Institute, Carnegie Mellon University, July, 1998

BibTeX Reference
@techreport{Liu_1998_2605,
   author = "Yanxi Liu and Robert Collins",
   title = "Frieze and Wallpaper Symmetry Groups Classification under Affine and Perspective Distortion",
   booktitle = "",
   institution = "Robotics Institute",
   month = "July",
   year = "1998",
   number= "CMU-RI-TR-98-37",
   address= "Pittsburgh, PA",
}