On the mean normal measures of a particle process

Advances in Applied Probability

Volumn 33, Issue 1, 2001, Pages 25-38

  Schneider, Rolf ^a  

^a UNIVERSITY OF FREIBURG   (Germany)

Author keywords

Anisotropy; Blaschke body; Determination from intersections; Mean normal measure; Particle process; Stereology

Indexed keywords

ANISOTROPY; DESCRIBING FUNCTIONS; PARAMETER ESTIMATION; PARTICLE SIZE ANALYSIS; RANDOM PROCESSES;

BLASCHKE BODY; MEAN NORMAL MEASURE; PARTICLE PROCESS; STEREOLOGY;

NORMAL DISTRIBUTION;

EID: 0035272525     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1239/aap/999187895     Document Type: Article

References (27)

1. BENEŠ, V. AND GOKHALE, A. (2000). Planar anisotropy revisited. Kybernetika 36, 149-164.
2. CAMPI, S., HAAS, D. AND WEIL, W. (1994). Approximation of zonoids by zonotopes in fixed directions. Discrete Comput. Geom. 11, 419-431.
3. GARDNER, R. J. (1995). Geometric Tomography. Cambridge University Press.
4. GROEMER, H. (1996). Geometric Applications of Fourier Series and Spherical Harmonics. Cambridge University Press.
5. GOODEY, P., KIDERLEN, M. AND WEIL, W. (1998). Section and projection means of convex bodies. Monatsh. Math. 126, 37-54.
6. GOODEY, P. AND WEIL, W. (1992). The determination of convex bodies from the mean of random sections. Math. Proc. Camb. Phil. Soc. 112, 419-430.
7. KIDERLEN, M. (1999). Schnittmittelungen und äquivariante Endomorphismen konvexer Körper. Doctoral Thesis, Universität Karlsruhe.
8. MATHERON, G. (1975). Random Sets and Integral Geometry. John Wiley, New York.
9. MOLCHANOV, I. S. (1995). Statistics of the Boolean model: from the estimation of means to the estimation of distributions. Adv. Appl. Prob. 27, 63-86.
10. RATAJ, J. (1996). Estimation of oriented direction distribution of a planar body. Adv. Appl. Prob. 28, 294-404.
11. RATAJ, J. (1996). Estimation of oriented normal direction distribution via mixed areas. Acta Stereologica 15, 77-82.
12. SCHNEIDER, R. (1970). Über eine Integralgleichung in der Theorie der konvexen Körper. Math. Nachr. 44, 55-75.
13. SCHNEIDER, R. (1982). Random hyperplanes meeting a convex body. Z. Wahrscheinlichkeitsth. 61, 379-387.
14. SCHNEIDER, R. (1993). Convex Bodies: the Brunn-Minkowski Theory. Cambridge University Press.
15. SCHNEIDER, R. AND WEIL, W. (1983). Zonoids and related topics. In Convexity and its Applications, eds P. M. Gruber, J. M. Wills, Birkhäuser, Basel, pp. 296-317.
16. SCHNEIDER, R. AND WEIL, W. (1992). Integralgeometrie. Teubner, Stuttgart.
17. SCHNEIDER, R. AND WEIL, W. (2000). Stochastische Geometrie. Teubner. Stuttgart.
18. STOYAN, D., KENDALL, W. S. AND MECKE, J. (1995). Stochastic Geometry and its Applications, 2nd edn. John Wiley, Chichester.
19. WEIL, W. (1987). Point processe of cylinders, particles and flats. Acta Appl. Math. 9, 103-136.
20. WEIL, W. (1995). The estimation of mean shape and mean particle number in overlapping particle systems in the plane. Adv. Appl. Prob. 27, 102-119.
21. WEIL, W. (1997). On the mean shape of particle processes. Adv. Appl. Prob. 29, 890-908.
22. WEIL, W. (1997). Mean bodies associated with random closed sets. Rend. Circ. Mat. Palermo, II, Suppl. 50, 387-412.
23. WEIL, W. (1997). The mean normal distribution of stationary random sets and particle processes. In Advances in Theory and Applications of Random Sets (Proc. Int. Symp., Fontainebleau, France), ed. D. Jeulin. World Scientific, Singapore, pp. 21-33.
24. WIEACKER, J. A. (1984). Translative Poincaré formulae for Hausdorff rectifiable sets. Geom. Dedicata 16, 231-248.
25. WIEACKER, J. A. (1986). Intersections of random hypersurfaces and visibility. Prob. Theory Rel. Fields 71, 405-433.
26. WIEACKER, J. A. (1989). Geometric inequalities for random surfaces. Math. Nachr. 142, 73-106.
27. ZäHLE, M. (1982). Random processes of Hausdorff rectifiable closed sets. Math. Nachr. 108, 49-72.