A strong optimality result for anisotropic self--similar textures

TL;DR

This paper provides a mathematical analysis linking anisotropy and self-similarity in Gaussian random fields, showing that the best measure of smoothness is related to their anisotropic geometry.

Contribution

It offers a rigorous proof connecting anisotropic properties with the optimal smoothness measurement in self-similar Gaussian fields.

Findings

Sharpest smoothness measurement relates to anisotropy

Mathematical proof of the connection between geometry and smoothness

Characterization of self-similar Gaussian fields' anisotropic properties

Abstract

In previous works, we proposed a method to characterize jointly self-similarity and anisotropy properties of a large class of self--similar Gaussian random fields. We provide here a mathematical analysis of our approach, proving that the sharpest way of measuring smoothness is related to these anisotropies and thus to the geometry of these fields.