VASC Seminar Announcement
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Date: Monday, 4/24/00
Time: 3:45-4:45
Place: NSH 3002
Speaker: Yanxi Liu
CMU Robotics Institute
Title: A Computational Model for Repeated Pattern Analysis using
Frieze and Wallpaper Groups
Abstract:
Humans have an innate ability to perceive symmetry yet it is not
obvious how to automate this powerful insight. Our work aims at
making computers understand repeated patterns in terms of their
symmetry groups, based on a mature mathematical theory of frieze and
wallpaper groups. The symmetry group of a repeated pattern is an
attractive descriptor for computer vision research due to its
independence of scale, absolute color, lighting, orientation and
position of the pattern. Despite the infinite variety of monochrome
planar repeated patterns, there are seven frieze groups for 2D
patterns repeated along one dimension, and seventeen wallpaper groups
describing patterns extended by two linearly independent translational
generators. This finite set of symmetry groups completely
characterizes the possible structural symmetry of any repeated
pattern.
Our work is the first to use group theory for analyzing repeated
patterns in an image, and to recognize the symmetry group of a
repeated pattern under Euclidean, affine or perspective distortions.
The algorithm can also extract a small finite set of candidate motifs
(visually meaningful building blocks) using knowledge of the interplay
between rotation, reflection, glide-reflection and translation
symmetries in the repeated pattern. Experiments on both synthetic and
real images show that the resulting pattern motifs conform well with
human perception. Applications of this work include gait analysis and
texture replacement, among others.
Joint work with Robert Collins, Steve Seitz and Jon Rowlett
References
Yanxi Liu and Robert Collins.
``A Computational Model for Repeated Pattern Perception using Frieze and
Wallpaper Groups'', CMU RI-00-08 (a shorter version of this report will
appear in CVPR2000)
Yanxi Liu and Robert T. Collins.
``Frieze and Wallpaper Symmetry Groups Classification under Affine and
Perspective Distortion''. CMU RI-98-37 (a shorter version of this report
will appear in ICIG2000)