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Further random tessellations with the classic Poisson polygon distributions

Published online by Cambridge University Press:  01 July 2016

Roger E. Miles  and
Margaret S. Mackisack
Roger E. Miles
Affiliation:
Australian National University
Margaret S. Mackisack
Affiliation:
University of Queensland
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Extract

It is well-known that Poisson lines in the plane, with orientation distribution Θ on [0, π), generate a (random) tessellation M0 of (random) convex polygons whose characteristics (area, perimeter, etc.) conform, in an ergodic sense, to a certain class {DΘ} of distributions.

Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 28 , Issue 2 , June 1996 , pp. 338 - 339
Copyright
Copyright © Applied Probability Trust 1996 

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References

[1] Arak, T., Clifford, P. and Surgailis, D. (1993) Point-based polygonal models for random graphs. Adv. Appl. Prob. 25, 348–372.CrossRefGoogle Scholar
[2] Serra, J. (1982) Image Analysis and Mathematical Morphology. Academic Press, London.Google Scholar