Symmetry Measure Computation for Convex Polyhedra

  title={Symmetry Measure Computation for Convex Polyhedra},
  author={Alexander V. Tuzikov and Stanislav Sheynin},
  journal={Journal of Mathematical Imaging and Vision},
The paper discusses measures and indices of different kind of symmetry (central, reflection, rotation, mirror rotation) for 3D convex shapes. The measures are based on Minkowski addition and inequalities for volume and mixed volume and are valid for convex shapes only. Symmetry index computation in 3D case is a complicated optimization problem. Taking advantage of convex polyhedra we investigate the situations when these indices can be computed efficiently. 
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Publications referenced by this paper.
Showing 1-10 of 18 references

Measures of symmetry for convex sets,

  • B. Grünbaum
  • Proc. Sympos. Pure Math., Providence, USA,
  • 1963
Highly Influential
4 Excerpts

Calculating critical orientations of polyhedra for similarity measure evaluation,

  • H. Bekker, J.B.T.M. Roerdink
  • Proc. 2nd Annual IASTED International Conference…
  • 1999
Highly Influential
3 Excerpts

Efficient algorithms for shape and symmetry analysis of geometric objects and digital images,

  • S. Sheynin
  • Ph.D. Thesis, Institute of Engineering…
  • 2001
1 Excerpt

Symmetry measures for 3D convex shapes,” in Fundamental Structural Properties in Image and Pattern Analysis

  • A. V. Tuzikov, S. A. Sheynin
  • Budapest,
  • 1999
1 Excerpt

Measures and indices of reflection symmetry for convex polyhedra,

  • A. V. Tuzikov, J.B.T.M. Roerdink, H.J.A.M. Heijmans, S. A. Sheynin
  • Mathematical Morphology and its Application to…
  • 1998
1 Excerpt

Symmetry measures for 3 D convex shapes

  • A. V. Tuzikov, S. A. Sheynin
  • Fundamental Structural Properties in Image and…
  • 1998

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