The determination of convex bodies from the mean of random sections

Mathematical Proceedings of the Cambridge Philosophical Society

Volumn 112, Issue 2, 1992, Pages 419-430

  Goodey, Paul ^a   Weil, Wolfgang ^b  

^a UNIVERSITY OF OKLAHOMA   (United States)

^b UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84974069771     PISSN: 03050041     EISSN: 14698064     Source Type: Journal    
DOI: 10.1017/S0305004100071085     Document Type: Article

References (24)

1. R. J. Adler and R. Pyke. Problem 91-3. IMS Bulletin 20 (1991), 406-407.
2. Z. Artstein and R. A. Vitale. A strong law of large numbers for random compact sets. Ann. Probab. 5 (1975), 879-882.
3. T. Bonnesen and W. Fenchel. Theorie der Konvexen Korper (Springer-Verlag, 1934).
4. A. Erdéllyi, W. Magnus F. Oberhettinger and E. G. Tricomi. Higher Transcendental Functions, vol. 2 (McGraw-Hill, 1953).
5. P. Goodey and W. Weil. Translative integral formulae for convex bodies. Aequationes Math, 34 (1987), 64-77.
6. P. Goodey and W. Weil. Integral geometric formulae for projection functions. Geom. Dedicata 41 (1992), 117-126.
7. J. F. C. kingman. Random secants of a convex body. J. Appl. Probab. 6 (1969), 660-672.
8. K. Leichtweiβ. Konvexe Mengen (Springer-Verlag, 1980).
9. J. J. Little. An iterative method for reconstructing convex polyhedra from extended Gaussian images. In Proceedings American Association for Artificial Intelligence (AAAI, 1983), pp. 247-250.
10. C. Mallows and J. Clark. Linear-intercept distributions do not characterize plane sets. J. Appl. Probab. 7 (1970), 240-244.
11. G. Matheron. Random Sets and Integral Geometry (Wiley, 1975).
12. C. MÜller. Spherical Harmonics (Springer-Verlag, 1966).
13. W. Nagel. Orientation dependent chord length distributions characterize convex polygons, submitted.
14. R. Schneider. Zu einem Problem von Shephard über die Projektionen konvexer Körper. Math. Z. 101 (1967), 71-82.
15. R. Schneider. Uber eine Integralgleichung in üder Theorie der konvexen Körper. Math. Nachr. 44 (1970), 55-75.
16. R. Schneider. Rekonstruktion eines konvexen Körpers aus seinen Projektionen. Math. Nachr. 79 (1977), 325-329.
17. R. Schneider. Boundary structure and curvature of convex bodies. In Contributions to Geometry, Proc. Geometry Sympos. Siegen 1978 (editors J. Tölke and J. M. Wills) (Birkhauser, 1979), pp. 13-59.
18. R. Schneider and W. Weil. Zonoids and related topics. In Convexity and its Applications (editors P. Gruber and J. M. Wills) (Birkhäuser, 1983), pp. 296-317.
19. R. Schneider and W. Weil. Translative and kinematic integral formulae for curvature measures. Math. Nachr. 129 (1986), 67-80.
20. D. Stoyan W. S. Kendall and J. Mecke. Stochastic Geometry and its Applications (Akademie-Verlag, 1987).
21. P. Waksman. Plane polygons and a conjecture of Blaschke's. Adv. in Appl. Probab. 17 (1985), 774-793.
22. W. Weil. Centrally symmetric convex bodies and distributions, II. Israel J. Math. 32 (1979), 173-182.
23. W. Weil. Stereology - a survey for geometers. In Convexity and its Applications (editors P. Gruber and J. M. Wills) (Birkhäuser, 1983), pp. 360-412.
24. W. Weil. Iterations of translative integral formulae and non-isotropic Poisson processes of particles. Math. Z. 205 (1990), 531-551.