Multiscale and Anisotropic Characterization of Images Based on Complexity: an Application to Turbulence

TL;DR

This paper introduces a multiscale, directional statistical method to characterize image anisotropy and complexity, validated on synthetic and turbulent velocity fields, revealing anisotropic features and isotropy in turbulence fluctuations.

Contribution

It presents a novel multiscale, anisotropic analysis framework based on skewness, flatness, entropy, and Gaussianity distance to characterize image and turbulence anisotropy.

Findings

Method detects anisotropy in synthetic and turbulent fields.

Turbulent velocity fluctuations are isotropic when mean velocity is removed.

Quantifies multiscale anisotropic properties in images and turbulence.

Abstract

This article presents a multiscale, non-linear and directional statistical characterization of images based on the estimation of the skewness, flatness, entropy and distance from Gaussianity of the spatial increments. These increments are characterized by their magnitude and direction; they allow us to characterize the multiscale properties directionally and to explore anisotropy. To describe the evolution of the probability density function of the increments with their magnitude and direction, we use the skewness to probe the symmetry, the entropy to measure the complexity, and both the flatness and distance from Gaussianity to describe the shape. These four quantities allow us to explore the anisotropy of the linear correlations and non-linear dependencies of the field across scales. First, we validate the methodology on two-dimensional synthetic scale-invariant fields with different multiscale properties and anisotropic characteristics. Then, we apply it on two synthetic turbulent velocity fields: a perfectly isotropic and homogeneous one, and a channel flow where boundaries induce inhomogeneity and anisotropy. Our characterization unambiguously detects the anisotropy in the second case, where our quantities report scaling properties that depend on the direction of analysis. Furthermore, we show in both cases that turbulent velocity fluctuations are always isotropic, when the mean velocity profile is adequately removed.