Planar anisotropy revisited

Viktor Beneš; Arun M. Gokhale

Kybernetika (2000)

  • Volume: 36, Issue: 2, page [149]-164
  • ISSN: 0023-5954

Abstract

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The paper concerns estimation of anisotropy of planar fibre systems using the relation between the rose of directions and the rose of intersections. The discussion about the properties of the Steiner compact estimator is based on both theoretical and simulation results. The approach based on the distribution of the Prokhorov distance between the estimated and true rose of directions is developed. Finally the curved test systems are investigated in both Fourier and Steiner compact analysis of anisotropy.

How to cite

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Beneš, Viktor, and Gokhale, Arun M.. "Planar anisotropy revisited." Kybernetika 36.2 (2000): [149]-164. <http://eudml.org/doc/33475>.

@article{Beneš2000,
abstract = {The paper concerns estimation of anisotropy of planar fibre systems using the relation between the rose of directions and the rose of intersections. The discussion about the properties of the Steiner compact estimator is based on both theoretical and simulation results. The approach based on the distribution of the Prokhorov distance between the estimated and true rose of directions is developed. Finally the curved test systems are investigated in both Fourier and Steiner compact analysis of anisotropy.},
author = {Beneš, Viktor, Gokhale, Arun M.},
journal = {Kybernetika},
keywords = {planar anisotropy; planar fibre system; Steiner compact analysis; planar anisotropy; planar fibre system; Steiner compact analysis},
language = {eng},
number = {2},
pages = {[149]-164},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Planar anisotropy revisited},
url = {http://eudml.org/doc/33475},
volume = {36},
year = {2000},
}

TY - JOUR
AU - Beneš, Viktor
AU - Gokhale, Arun M.
TI - Planar anisotropy revisited
JO - Kybernetika
PY - 2000
PB - Institute of Information Theory and Automation AS CR
VL - 36
IS - 2
SP - [149]
EP - 164
AB - The paper concerns estimation of anisotropy of planar fibre systems using the relation between the rose of directions and the rose of intersections. The discussion about the properties of the Steiner compact estimator is based on both theoretical and simulation results. The approach based on the distribution of the Prokhorov distance between the estimated and true rose of directions is developed. Finally the curved test systems are investigated in both Fourier and Steiner compact analysis of anisotropy.
LA - eng
KW - planar anisotropy; planar fibre system; Steiner compact analysis; planar anisotropy; planar fibre system; Steiner compact analysis
UR - http://eudml.org/doc/33475
ER -

References

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  6. Kufner A., Kadlec J., Fourier Series, Academia, Praha 1971 Zbl0215.17901MR0393989
  7. Matheron G., Random Sets and Integral Geometry, Wiley, New York 1975 Zbl0321.60009MR0385969
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  9. Philofski E. M., Hilliard J. E., On the measurement of the orientation distribution of lineal and areal arrays, Trans. ASM 27 (1967), 1, 79–86 (1967) 
  10. Rachev S. T., Probability Metrics, Wiley, New York 1991 Zbl1178.91046MR1105086
  11. Rataj J., Saxl I., 10.2307/3214407, J. Appl. Probab. 26 (1989), 490–502 (1989) Zbl0694.60010MR1010938DOI10.2307/3214407
  12. Rychlik T., Order statistics of variables with given marginal distributions, In: Distributions with Fixed Marginals and Related Topics (L. Rüschendorf, B. Schweizer and M. D. Taylor, eds.), IMS Lecture Notes – Monograph Series 28 (1996), pp. 297–306 (1996) MR1485539
  13. Schneider R., Convex Bodies: The Brunn–Minkowski Theory, Encyclopedia Math. Appl. 44 (1993) (1993) Zbl0798.52001MR1216521
  14. Stoyan S., Kendall W. S., Mecke J., Stochastic Geometry and Its Applications, Second edition. Wiley, New York, Chichester 1995 Zbl1155.60001

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