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

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

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Professional

161 Downloads (Pure)

Abstract

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 language	English
Title of host publication	Mathematical Morphology and its Applications to Image and Signal Processing
Editors	J B T M Roerdink, H J A M Heijmans
Place of Publication	Dordrecht/Boston/London
Publisher	University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science
Pages	59 - 65
Number of pages	7
Publication status	Published - 1998

Keywords

convex polyhedra
reflection symmetry measure
Minkowski addition

Access to Document

1998MathMorphApplImSignProcTuzikov.pdfFinal publisher's version, 158 KB

Handle.net

Persistent link

Cite this

Tuzikov, A. V., Roerdink, J. B. T. M., Heijmans, H. J. A. M., & Sheynin, S. V. (1998). Measures and indices of reflection symmetry for convex polyhedra. In J. B. T. M. Roerdink, & H. J. A. M. Heijmans (Eds.), Mathematical Morphology and its Applications to Image and Signal Processing (pp. 59 - 65). University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science.

Tuzikov, Alexander V. ; Roerdink, Jos B.T.M. ; Heijmans, Henk J.A.M. et al. / Measures and indices of reflection symmetry for convex polyhedra. Mathematical Morphology and its Applications to Image and Signal Processing. editor / J B T M Roerdink ; H J A M Heijmans. Dordrecht/Boston/London : University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science, 1998. pp. 59 - 65

@inbook{20277a9425f94dc79f10666d24a6239b,

title = "Measures and indices of reflection symmetry for convex polyhedra",

abstract = "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.",

keywords = "convex polyhedra, reflection symmetry measure, Minkowski addition",

author = "Tuzikov, {Alexander V.} and Roerdink, {Jos B.T.M.} and Heijmans, {Henk J.A.M.} and Sheynin, {Stanislav V.}",

note = "Relation: http://www.rug.nl/informatica/organisatie/overorganisatie/iwi Rights: University of Groningen. Research Institute for Mathematics and Computing Science (IWI)",

year = "1998",

language = "English",

pages = "59 -- 65",

editor = "Roerdink, {J B T M} and Heijmans, {H J A M}",

booktitle = "Mathematical Morphology and its Applications to Image and Signal Processing",

publisher = "University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science",

}

Tuzikov, AV, Roerdink, JBTM, Heijmans, HJAM & Sheynin, SV 1998, Measures and indices of reflection symmetry for convex polyhedra. in JBTM Roerdink & HJAM Heijmans (eds), Mathematical Morphology and its Applications to Image and Signal Processing. University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science, Dordrecht/Boston/London, pp. 59 - 65.

Measures and indices of reflection symmetry for convex polyhedra. / Tuzikov, Alexander V.; Roerdink, Jos B.T.M.; Heijmans, Henk J.A.M. et al.
Mathematical Morphology and its Applications to Image and Signal Processing. ed. / J B T M Roerdink; H J A M Heijmans. Dordrecht/Boston/London: University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science, 1998. p. 59 - 65.

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Professional

TY - CHAP

T1 - Measures and indices of reflection symmetry for convex polyhedra

AU - Tuzikov, Alexander V.

AU - Roerdink, Jos B.T.M.

AU - Heijmans, Henk J.A.M.

AU - Sheynin, Stanislav V.

N1 - Relation: http://www.rug.nl/informatica/organisatie/overorganisatie/iwi Rights: University of Groningen. Research Institute for Mathematics and Computing Science (IWI)

PY - 1998

Y1 - 1998

N2 - 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.

AB - 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.

KW - convex polyhedra

KW - reflection symmetry measure

KW - Minkowski addition

M3 - Chapter

SP - 59

EP - 65

BT - Mathematical Morphology and its Applications to Image and Signal Processing

A2 - Roerdink, J B T M

A2 - Heijmans, H J A M

PB - University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science

CY - Dordrecht/Boston/London

ER -

Tuzikov AV, Roerdink JBTM, Heijmans HJAM, Sheynin SV. Measures and indices of reflection symmetry for convex polyhedra. In Roerdink JBTM, Heijmans HJAM, editors, Mathematical Morphology and its Applications to Image and Signal Processing. Dordrecht/Boston/London: University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science. 1998. p. 59 - 65

Measures and indices of reflection symmetry for convex polyhedra

Abstract

Keywords

Access to Document

Handle.net

Fingerprint

Cite this