| Title:
|
Planar anisotropy revisited (English) |
| Author:
|
Beneš, Viktor |
| Author:
|
Gokhale, Arun M. |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
36 |
| Issue:
|
2 |
| Year:
|
2000 |
| Pages:
|
[149]-164 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
planar anisotropy |
| Keyword:
|
planar fibre system |
| Keyword:
|
Steiner compact analysis |
| MSC:
|
52A22 |
| MSC:
|
60D05 |
| MSC:
|
60K10 |
| MSC:
|
62M40 |
| idZBL:
|
Zbl 1249.60185 |
| idMR:
|
MR1760022 |
| . |
| Date available:
|
2009-09-24T19:31:48Z |
| Last updated:
|
2015-03-26 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135341 |
| . |
| Reference:
|
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| Reference:
|
[2] Digabel H.: Determination practique de la rose des directions.In: 15 fascicules de morphologie mathematique appliquee (6), Fontainebleau 1975 |
| Reference:
|
[3] Heyer H.: Probability Measures on Locally Compact Groups.Springer, Berlin 1977 Zbl 0528.60010, MR 0501241 |
| Reference:
|
[4] Hilliard J. E.: Specification and measurement of microstructural anisotropy.Trans. Metall. Soc. AIME 224 (1962), 1201–1211 |
| Reference:
|
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| Reference:
|
[6] Kufner A., Kadlec J.: Fourier Series.Academia, Praha 1971 Zbl 0215.17901, MR 0393989 |
| Reference:
|
[7] Matheron G.: Random Sets and Integral Geometry.Wiley, New York 1975 Zbl 0321.60009, MR 0385969 |
| Reference:
|
[8] Mecke J.: Formulas for stationary planar fibre processes III-intersections with fibre systems.Math. Oper. Statist., Ser. Statist. 12 (1981), 201–210 Zbl 0472.60016, MR 0618605 |
| Reference:
|
[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 |
| Reference:
|
[10] Rachev S. T.: Probability Metrics.Wiley, New York 1991 Zbl 1178.91046, MR 1105086 |
| Reference:
|
[11] Rataj J., Saxl I.: Analysis of planar anisotropy by means of the Steiner compact.J. Appl. Probab. 26 (1989), 490–502 Zbl 0694.60010, MR 1010938, 10.2307/3214407 |
| Reference:
|
[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 MR 1485539 |
| Reference:
|
[13] Schneider R.: Convex Bodies: The Brunn–Minkowski Theory.Encyclopedia Math. Appl. 44 (1993) Zbl 0798.52001, MR 1216521 |
| Reference:
|
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| . |
