EXACT SIMULATION OF A BOOLEAN MODEL

Authors

  • Christian Lantuéjoul Ecole des Mines-Paristech

DOI:

https://doi.org/10.5566/ias.v32.p101-105

Keywords:

Boolean model, importance sampling, Minkowsky functionals, Steiner formula

Abstract

A Boolean model is a union of independent objects (compact random subsets) located at Poisson points. Two algorithms are proposed for simulating a Boolean model in a bounded domain. The first one applies only to stationary models. It generates the objects prior to their Poisson locations. Two examples illustrate its applicability. The second algorithm applies to stationary and non-stationary models. It generates the Poisson points prior to the objects. Its practical difficulties of implementation are discussed. Both algorithms are based on importance sampling techniques, and the generated objects are weighted.

References

Lantu´ejoul C (2002). Geostatistical simulation. Models

and algorithms. Berlin: Springer.

Matheron G (1975). Random sets and integral geometry.

New York:Wiley.

Miles R E (1969). Poisson flats in euclidean spaces. Adv.

Appl. Prob., Vol. 1, pp 211-237.

Miles R E (1974). A synopsis of Poisson flats in

euclidean spaces. In Stochastic geometry (Harding E F

and Kendall D G, eds.). New York:Wiley, pp. 202-227.

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Published

2013-06-27

How to Cite

Lantuéjoul, C. (2013). EXACT SIMULATION OF A BOOLEAN MODEL. Image Analysis and Stereology, 32(2), 101–105. https://doi.org/10.5566/ias.v32.p101-105

Issue

Section

Original Research Paper

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