The transparent dead leaves model. (English) Zbl 1245.60011

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.


60D05 Geometric probability and stochastic geometry
60G60 Random fields
62M40 Random fields; image analysis
Full Text: DOI


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