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The Transparent Dead Leaves Model

Part of: Geometric probability and stochastic geometry Stochastic processes

Published online by Cambridge University Press:  04 January 2016

B. Galerne  and
Y. Gousseau
B. Galerne*
Affiliation:
ENS Cachan
Y. Gousseau*
Affiliation:
Télécom ParisTech
*
∗ Postal address: CMLA, ENS Cachan, CNRS, UniverSud, 61 Avenue du Président Wilson, F-94230 Cachan, France. Email address: [email protected]
∗∗ Postal address: LTCI CNRS, Télécom ParisTech, 46 rue Barrault, F-75013 Paris, France.
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Abstract

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In this paper we introduce the transparent dead leaves (TDL) random field, a new germ-grain model in which the grains are combined according to a transparency principle. Informally, this model may be seen as the superposition of infinitely many semitransparent objects. It is therefore of interest in view of the modeling of natural images. Properties of this new model are established and a simulation algorithm is proposed. The main contribution of the paper is to establish a central limit theorem, showing that, when varying the transparency of the grain from opacity to total transparency, the TDL model ranges from the dead leaves model to a Gaussian random field.

Keywords

Germ-grain modeldead leaves modeltransparencyocclusionimage modelingtexture modeling

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 60G60: Random fields
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 44 , Issue 1 , March 2012 , pp. 1 - 20
Copyright
© Applied Probability Trust 

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