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The dead leaves model: a general tessellation modeling occlusion

Part of: Stochastic processes Geometric probability and stochastic geometry General convexity

Published online by Cambridge University Press:  01 July 2016

Charles Bordenave ,
Yann Gousseau  and
François Roueff
Charles Bordenave*
Affiliation:
Ecole Normale Supérieure and INRIA
Yann Gousseau*
Affiliation:
Télécom Paris
François Roueff*
Affiliation:
Télécom Paris
*
∗ Postal address: Département d'Informatique, Ecole Normale Supérieure, 45 rue d'Ulm, F-75230 Paris Cedex 05, France. Email address: charles.bordenave@ens.fr
∗∗ Postal address: Département Traitement du Signal et des Images, CNRS UMR 5141, ENST, 46 rue Barrault, 75634 Paris Cedex 13, France.
∗∗ Postal address: Département Traitement du Signal et des Images, CNRS UMR 5141, ENST, 46 rue Barrault, 75634 Paris Cedex 13, France.
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Abstract

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In this article, we study a particular example of general random tessellation, the dead leaves model. This model, first studied by the mathematical morphology school, is defined as a sequential superimposition of random closed sets, and provides the natural tool to study the occlusion phenomenon, an essential ingredient in the formation of visual images. We generalize certain results of G. Matheron and, in particular, compute the probability of n compact sets being included in visible parts. This result characterizes the distribution of the boundary of the dead leaves tessellation.

Keywords

General tessellationdead leaves modeltypical cellimage modeling

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 60G55: Point processes 52A22: Random convex sets and integral geometry 68U10: Image processing

Information

Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 38 , Issue 1 , March 2006 , pp. 31 - 46
Copyright
Copyright © Applied Probability Trust 2006 

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