Weighted tensorized fractional Brownian textures

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.