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

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