Characterization of Partial Intrinsic Symmetries

  • Aurela ShehuEmail author
  • Alan Brunton
  • Stefanie Wuhrer
  • Michael Wand
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8928)


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.


Symmetry Shape analysis Shape matching Intrinsic geometry Slippability analysis 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Aurela Shehu
    • 1
    • 2
    Email author
  • Alan Brunton
    • 3
  • Stefanie Wuhrer
    • 1
  • Michael Wand
    • 4
  1. 1.Cluster of Excellence MMCISaarland UniversitySaarbrückenGermany
  2. 2.Saarbrücken Graduate School of Computer ScienceSaarbrückenGermany
  3. 3.Fraunhofer Institute for Computer Graphics Research IGDDarmstadtGermany
  4. 4.Utrecht UniversityUtrechtNetherlands

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