Weighted tensorized fractional Brownian textures

TL;DR

This paper introduces weighted tensorized fractional Brownian fields as a new texture model, relaxing tensor-product constraints, with proven statistical properties and spectral simulation methods.

Contribution

It proposes a novel class of fractional Brownian fields with relaxed tensor structure, extending operator scaling and providing spectral simulation techniques.

Findings

Fields exhibit self-similarity and stationary increments.

Statistical properties are rigorously derived.

Simulations demonstrate practical applicability.

Abstract

This paper presents a new model of textures, obtained as realizations of a new class of fractional Brownian fields. These fields, called weighted tensorized fractional Brownian fields, are obtained by a relaxation of the tensor-product structure that appears in the definition of fractional Brownian sheets. Statistical properties such as self-similarity, stationarity of rectangular increments and regularity properties are obtained. An operator scaling extension is defined and we provide simulations of the fields using their spectral representation.