Properties of length estimation in spatial fibre models

Environmetrics

Volumn 8, Issue 5, 1997, Pages 397-407

  Beneš, Viktor ^a   Chadoeuf, Joel ^b   Kretzschmar, Andre ^b  

^a CZECH TECHNICAL UNIVERSITY IN PRAGUE   (Czech Republic)

^b CEMAGREF   (France)

Author keywords

Earthworm burrow; Estimation variance; Fibre process; Length intensity

Indexed keywords

EID: 0030870491     PISSN: 11804009     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-095X(199709/10)8:5<397::AID-ENV260>3.0.CO;2-3     Document Type: Article

References (25)

1. Beneš, V., Chadœuf, J. and Ohser, J. (1994). 'On some characteristics of anisotropic fibre processes', Mathematische Nachrichten, 169, 5-17.
2. Beneš, V. (1995). 'On second-order formulas in anisotropic stereology', Advances in Applied Probability, 27, 326-343.
3. Beneš, V., Chadœuf, J. and Ohser, J. (1996). 'AnisotropiC stereology of fibres and surfaces', Acta Stereologica, 15/1, 3-8.
4. 3', Technical report, INRA Biometrie.
5. Chadœuf, J. and Beneš, V. (1994). 'On some estimation variances in spatial statistics', Kybernetika, 30, 245-262.
6. Chadœuf, J., Beneš, V., Monestiez, P. and Kretzschmar, A. (1993). 'Second order stereology for anisotropic Boolean segment processes', Acta Stereologica, 12/2, 175-180.
7. Cressie, N. (1991). Spatial Statistics, Wiley, New York.
8. Cruz-Orive, L. M., Hoppeler, H., Mathieu, O. and Weibel, E. R. (1985). 'Stereological analysis of anisotropic structures using directional statistics', Journal of the Royal Statistical Society, Series C, 34, 14-32.
9. Cruz-Orive, L. M. and Gual-Arnau, X. (1996). 'Consistency of stereological estimators based on serial sections', Report 3/96, Departemento Estadistica, Universidad Santander.
10. Cruz-Orive, L. M. and Howard, C. V. (1991). 'Estimating the length of a bounded curve in three dimensions using total vertical projections', Journal of Microscopy, 163, 101-113.
11. Daley, D. J. and Vere-Jones, D. (1988). An Introduction to the Theory of Point Processes, Springer-Verlag, Berlin.
12. Favard, J. (1932). 'Definition de la longueur et de l'aire', Comptes Rendus de l'Academie des Sciences, Paris, 194, 344-346.
13. Gokhale, A. M. (1993). 'Utility of the horizontal slice for stereological characterisation of lineal features', Journal of Microscopy, 170, 3-8.
14. Hilliard, J. E. (1967). 'Determination of structural anisotropy', in Elias, H. (ed.), Stereology, Springer, New York, pp. 219-227.
15. Kanatani, K. (1988). 'Stereological determination of structural anisotropy', International Journal of Engineering Sciences, 22, 531-546.
16. Karlsson, L. M. and Cruz-Orive, L. M. (1992). 'The new stereological tools in metallography: estimation of pore size and number in aluminium', Journal of Microscopy, 165/3, 391-415.
17. Matheron, G. (1971). The Theory of Regionalized Variables and its Applications, Cahiers Centre de Morphology, No. 5, Ecole National Superiore des Mines, Paris.
18. Monestiez, P., Kretzschmar, A. and Chadœuf, J. (1993). 'Modelling natural burrow systems in soil by fibre processes: Monte Carlo tests on independence of fibre characteristics', Acta Stereologica, 12, 237-242.
19. Moran, P. (1944). 'Measuring the surface area of a convex body', Annals of Mathematics, 45, 783-789.
20. Ohser, J. (1991). 'Variances of different estimators for the specific line length', Stochastic Geometry, Geometrical Statistics, Stereology, Oberwolfach, unpublished.
21. Ripley, B. D. (1981). Spatial Statistics, Wiley, New York.
22. Ripley, B. D. (1988). Statistical Inference for Spatial Processes, Cambridge University Press, Cambridge.
23. Schladitz, K. (1995). 'Unbiased estimators for the length intensity of stationary planar line processes', 9th European Congress for Stereology, Copenhagen, unpublished.
24. Stoyan, D., Kendall, W. S. and Mecke, J. (1995). Stochastic Geometry and its Applications, 2nd edn, Wiley, New York.
25. Weibel, E. R. (1980). Stereological Methods, vol. 2, Academic Press, London.