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Characterization of partial intrinsic symmetries

: Shehu, Aurela; Brunton, Alan; Wuhrer, Stefanie; Wand, Michael


Agapito, L.:
Computer vision - ECCV 2014 Workshops. Pt.4 : 13th European Conference on Computer Vision, ECCV 2014; Zurich, Switzerland, September 6 - 7 and 12, 2014; Proceedings
Cham: Springer International Publishing, 2015 (Lecture Notes in Computer Science 8928)
ISBN: 978-3-319-16219-5 (Print)
ISBN: 978-3-319-16220-1 (Online)
European Conference on Computer Vision (ECCV) <13, 2014, Zurich>
Conference Paper
Fraunhofer IGD ()
shape analysis; shape matching; 3D computer vision; 3D Data; 3D data processing; 3D data representation; 3D graphics; deformable models; geometric modeling; geometry processing

We present a mathematical framework and algorithm for characterizing and extracting partial intrinsic symmetries of surfaces, which is a fundamental building block for many modern geometry processing algorithms. Our goal is to compute all significant symmetry information of the shape, which we define as r-symmetries, i.e., we report all isometric self-maps within subsets of the shape that contain at least an intrinsic circle or radius r. By specifying r, the user has direct control over the scale at which symmetry should be detected. Unlike previous techniques, we do not rely on feature points, voting or probabilistic schemes. Rather than that, we bound computational efforts by splitting our algorithm into two phases. The first detects infinitesimal r-symmetries directly using a local differential analysis, and the second performs direct matching for the remaining discrete symmetries. We show that our algorithm can successfully characterize and extract intrinsic symmetries from a number of example shapes.