The transparent dead leaves model. (English) Zbl 1245.60011

Galerne, B.; Gousseau, Y.

Adv. Appl. Probab. 44, No. 1, 1-20 (2012).

The authors generalise the famous dead leaves model by G. Matheron by assuming that each grain (leave) has a random grey level (intensity) and combining them according to a transparency principle. Namely, when adding a new grain, the new grey values are obtained as a linear combination of former grey values and the intensity of the grain. The suggested model can be used to model natural grey-scale images.
The authors explore probabilistic properties of the transparent dead leaves model, like marginal distribution and the covariance, and describe a simulation algorithm. The main result is a limit theorem showing that, when varying the transparency from opacity to the full transparency, the suggested model ranges from the classical dead leaves model to a Gaussian random field.

Reviewer: Ilya S. Molchanov (Bern)

MSC:

60D05	Geometric probability and stochastic geometry
60G60	Random fields
62M40	Random fields; image analysis

Keywords:

germ-grain model; dead leaves model; grey-scale image; occlusion; image modeling; texture modeling

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