Explicit constructions of operator scaling Gaussian fields

TL;DR

This paper introduces explicit methods to generate a broad class of operator scaling Gaussian fields, enabling better modeling of anisotropic textures and structures in images with controlled geometric properties.

Contribution

It provides a novel explicit construction technique for operator scaling Gaussian fields with specified Hurst index and exponent, enhancing simulation and analysis capabilities.

Findings

Allows explicit generation of operator scaling Gaussian fields

Enables controlled anisotropic geometries in models

Facilitates texture simulation and anisotropy detection

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.