Explicit constructions of operator scaling Gaussian fields

Abstract

We propose an explicit way to generate a large class of Operator scaling Gaussian random fields (OSGRF). Such fields are anisotropic generalizations of selfsimilar fields. More specifically, we are able to construct any Gaussian field belonging to this class with given Hurst index and exponent. Our construction provides - for simulations of texture as well as for detection of anisotropies in an image - a large class of models with controlled anisotropic geometries and structures.