VASC Seminar Announcement ========================= 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)