The Transparent Dead Leaves Model

Bruno Galerne (1) , Yann Gousseau (2)

1 CMLA - Centre de Mathématiques et de Leurs Applications
2 LTCI - Laboratoire Traitement et Communication de l'Information

This paper introduces 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 semi-transparent 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.

Mots clés: Germ-grain model; dead leaves model; transparency; occlusion; image modeling; texture modeling

Domaines: Probabilités [math.PR]

Bruno Galerne, Yann Gousseau. The Transparent Dead Leaves Model. Advances in Applied Probability, 2012, 44 (1), pp.1--20. ⟨10.1239/aap/1331216642⟩. ⟨hal-00505281v3⟩