On the empty space function of some germ-grain models

Pattern Recognition

Volumn 32, Issue 9, 1999, Pages 1587-1600

  Last, G ^a   Holtmann, M ^a  

^a NONE

Author keywords

Empty space function; Germ grain model; Hazard rate; Point process; Poisson cluster process; Simulation; Spherical distance; Stochastic geometry

Indexed keywords

COMPUTATIONAL GEOMETRY; COMPUTER SIMULATION; NUMERICAL METHODS; RANDOM PROCESSES;

EMPTY SPACE FUNCTION; GERM GRAIN MODEL; HAZARD RATE; POINT PROCESS; POISSON CLUSTER PROCESS; SPHERICAL DISTANCE; STOCHASTIC GEOMETRY;

PATTERN RECOGNITION;

EID: 0032686073     PISSN: 00313203     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0031-3203(99)00022-9     Document Type: Article

References (15)

1. [1] G. Matheron, Random Sets and Integral Geometry, Wiley, New York, 1975.
2. [2] D. Stoyan, W.S. Kendall, J. Mecke, Stochastic Geometry and its Applications, second ed., Wiley, Chichester, 1995.
3. [3] A. Baddeley, R.D. Gill, The empty space hazard of spatial pattern, preprint 845, Department of Mathematics, University Utrecht, 1994.
4. [4] G. Last, R. Schassberger, On the distribution of the spherical contact vector of stationary grain models, Adv. Appl. Proba. 30 (1998) 36-52.
5. [5] M.N.M. van Lieshout, A. Baddeley, A nonparametric measure of spatial interaction in point patterns, Statist. Neerland. 50 (1996) 344-361.
6. [6] R. Schneider, Parallelmengen mit Vielfachheit und Steiner-Formeln, Geom. Dedicata 9 (1980) 111-127.
7. [7] W. Weil, J.A. Wieacker, Stochastic geometry, in: Handbook of Convex Geometry, North-Holland, Amsterdam, 1993, pp. 1391-1438.
8. [8] L. Heinrich, On existence and mixing properties of germ-grain models, Statistics 23 (1992) 271-286.
9. [9] J. Rataj, I. Saxl, Boolean cluster models: mean cluster dilations and spherical distances, Math. Bohemica 122 (1995) 21-36.
10. [10] L. Heinrich, L. Muche, On the pair correlation function of the point process of nodes in a Voronoi tesselation, preprint 94-07, TU Bergakademie Freiberg, 1994.
11. [11] R. Schneider, Convex Bodies : the Brunn-Minkowski Theory, in: Encyclopedia of Mathematics and its Applications, Vol. 44, Cambridge University Press, Cambridge, 1993.
12. [12] L. Heinrich, I.S. Molchanov, Central limit theorem for a class of random measures associated with germ-grain models, CWI Report BS-R9518; Adv. Appl. Probab., 1999, in press.
13. [13] X.X. Nguyen, H. Zessin, Integral and differential characterizations of the Gibbs process, Mathematische Nachrichten 88 (1979) 105-115.
14. [14] O. Kallenberg, Random Measures, Akademie-Verlag, Berlin and Academic Press, London, 1983.
15. [15] D. Hug, G. Last, On support measures in Minkowski spaces and contact distributions in stochastic geometry, preprint, Universität Freiburg, 1999, submitted for publication.