Infinitely Divisible Cascades to Model the Statistics of Natural Images

We propose to model the statistics of natural images, thanks to the large class of stochastic processes called Infinitely Divisible Cascades (IDCs). IDCs were first introduced in one dimension to provide multifractal time series to model the so-called
intermittency phenomenon
in hydrodynamical turbulence. We have extended the definition of scalar IDCs from one to
N
dimensions and commented on the relevance of such a model in fully developed turbulence in [1 ]. In this paper, we focus on the particular 2D case. IDCs appear as good candidates to model the statistics of natural images. They share most of their usual properties and appear to be consistent with several independent theoretical and experimental approaches of the literature. We point out the interest of IDCs for applications to procedural texture synthesis.