Distance measurements on processes of flats

Advances in Applied Probability

Volumn 35, Issue 1, 2003, Pages 70-95

  Hug, Daniel ^a   Last, Günter ^b   Weil, Wolfgang ^b  

^a UNIVERSITY OF FREIBURG   (Germany)

^b UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

Contact distribution function; k flat; Poisson point process; Radon transform; Stochastic geometry; Support (curvature) measure

Indexed keywords

BOOLEAN FUNCTIONS; COMPUTATIONAL GEOMETRY; POISSON EQUATION; RANDOM PROCESSES;

RADON TRANSFORM; STOCHASTIC GEOMETRY;

DISTANCE MEASUREMENT;

EID: 0037360622     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1239/aap/1046366100     Document Type: Article

References (28)

1. Arbeiter, E. and Zähle, M. (1991). Kinematic relations for Hausdorff moment measures in spherical spaces. Math. Nachr. 153, 333-348.
2. Fallert, H. (1992). Intensitätsmaße und Quermaßdichten für (nichstationäre) zufällige Mengen und geometrische Punktprozesse. Dissertation, Universität Karlsruhe.
3. Fallert, H. (1996). Quermaßdichten für Punktprozesse konvexer Körper und Boolesche Modelle. Math. Nachr. 181, 165-184.
4. Goodey, P. and Howard, R. (1990). Processes of flats induced by higher-dimensional processes. Adv. Math. 80, 92-109.
5. Goodey, P. and Howard, R. (1990). Processes of flats induced by higher-dimensional processes II. Contemp. Math. 113, 111-119.
6. Goodey, P. and Weil, W. (1991). Centrally symmetric convex bodies and Radon transforms on higher order Grassmannians. Mathematika 38, 117-133.
7. Goodey, P. and Weil, W. (1993). Zonoids and generalisations. In Handbook of Convex Geometry, eds P. M. Gruber and J. M. Wills, Elsevier, Amsterdam, pp. 1297-1326.
8. Goodey, P., Howard, R. and Reeder, M. (1996). Processes of flats induced by higher-dimensional processes III. Geom. Dedicata 61, 257-269.
9. Groemer, H. (1996). Geometric Applications of Fourier Series and Spherical Harmonics. Cambridge University Press.
10. Hug, D. and Last, G. (2000). On support measures in Minkowski spaces and contact distributions in stochastic geometry. Ann. Prob. 28, 796-850.
11. Hug, D., Last, G. and Weil, W. (2002). Generalized contact distributions of inhomogeneous Boolean models. Adv. Appl. Prob. 34, 21-47.
12. Hug, D., Last, G. and Weil, W. (2002). A survey on contact distributions. In Morphology of Condensed Matter: Physics and Geometry of Spatially Complex Systems (Lecture Notes Phys. 600), eds K. Mecke and D. Stoyan, Springer, Berlin, pp. 317-357.
13. Kalf, H. (1995). On the expansion of a function in terms of spherical harmonics in arbitrary dimensions. Bull. Belgian Math. Soc. 2, 361-380.
14. Kiderlen, M. and Weil, W. (1999). Measure-valued valuations and mixed curvature measures of convex bodies. Geom. Dedicata 76, 291-329.
15. Matheron, G. (1975). Random Sets and Integral Geometry. John Wiley, New York.
16. Mecke, J., Schneider, R., Stoyan, D. and Weil, W. (1990). Stochastische Geometrie. Birkhäuser, Basel.
17. Miles, R. (1961). Random polytopes: the generalisation to n dimensions of the intervals of a Poisson process. Thesis, Cambridge University.
18. Schneider, R. (1993). Convex Bodies: the Brunn-Minkowski Theory. Cambridge University Press.
19. Schneider, R. (1999). A duality for Poisson flats. Adv. Appl. Prob. 31, 63-68.
20. Schneider, R. (2003). Nonstationary Poisson hyperplanes and their induced tessellations. Adv. Appl. Prob. 35, 139-158.
21. Schneider, R. and Weil, W. (2000). Stochastische Geometrie. Teubner, Stuttgart.
22. Schneider, R. and Wieacker, J. A. (1993). Integral geometry. In Handbook of Convex Geometry, eds P. M. Gruber and J. M. Wills, Elsevierm, Amsterdam, pp. 1349-1390.
23. Spodarev, E. (2001). Selected topics in the theory of spatial stationary flat processes. Dissertation, Universität Jena.
24. Spodarev, E. (2001). On the rose of intersections of stationary flat processes. Adv. Appl. Prob. 33, 584-599.
25. Spodarev, E. (2003). Isoperimetric problems and roses of neighborhood for stationary flat processes. To appear in Math. Nachr.
26. Stoyan, D., Kendall, W. S. and Mecke, J. (1995). Stochastic Geometry and Its Applications, 2nd edn. John Wiley, New York.
27. Weil, W. (1979). Kinematic integral formulas for convex bodies. In Contributions to Geometry, Proc. Geometry Symp. (Siegen 1978), eds J. Tölke and J. M. Wills, Birkhäuser, Basel, pp. 60-76.
28. Weil, W. (1981). Zufällige Berührung konvexer Körper durch q-dimensionale Ebenen. Resultate Math. 4, 84-101.