Measures and indices of reflection symmetry for convex polyhedra

Alexander V. Tuzikov, Jos B.T.M. Roerdink, Henk J.A.M. Heijmans, Stanislav V. Sheynin

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This paper discusses measures of reflection symmetry for 3D convex sets which are based on Minkowski addition and Brunn-Minkowski inequalities for volume and mixed volume. These measures are invariant to similitude transformations. It is also shown how these measures can be computed efficiently for convex polyhedra.
Original languageEnglish
Title of host publicationMathematical Morphology and its Applications to Image and Signal Processing
EditorsJ B T M Roerdink, H J A M Heijmans
Place of PublicationDordrecht/Boston/London
PublisherUniversity of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science
Pages59 - 65
Number of pages7
Publication statusPublished - 1998


  • convex polyhedra
  • reflection symmetry measure
  • Minkowski addition

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