Self-Similar Anisotropic Texture Analysis: the Hyperbolic Wavelet Transform Contribution

TL;DR

This paper introduces a hyperbolic wavelet transform method for jointly estimating anisotropy and self-similarity in image textures, providing confidence intervals and an isotropy test, applicable to various self-similar fields.

Contribution

It proposes a novel hyperbolic wavelet transform approach for accurate joint estimation of anisotropy and self-similarity, including rotation angle estimation and confidence interval construction.

Findings

Effective disentanglement of true anisotropy from superimposed anisotropic trends.

Robust estimation of anisotropy and self-similarity parameters across diverse textures.

Validation on various isotropic and anisotropic self-similar fields.

Abstract

Textures in images can often be well modeled using self-similar processes while they may at the same time display anisotropy. The present contribution thus aims at studying jointly selfsimilarity and anisotropy by focusing on a specific classical class of Gaussian anisotropic selfsimilar processes. It will first be shown that accurate joint estimates of the anisotropy and selfsimilarity parameters are performed by replacing the standard 2D-discrete wavelet transform by the hyperbolic wavelet transform, which permits the use of different dilation factors along the horizontal and vertical axis. Defining anisotropy requires a reference direction that needs not a priori match the horizontal and vertical axes according to which the images are digitized, this discrepancy defines a rotation angle. Second, we show that this rotation angle can be jointly estimated. Third, a non parametric bootstrap based procedure is described, that provides confidence interval in addition to the estimates themselves and enables to construct an isotropy test procedure, that can be applied to a single texture image. Fourth, the robustness and versatility of the proposed analysis is illustrated by being applied to a large variety of different isotropic and anisotropic self-similar fields. As an illustration, we show that a true anisotropy built-in self-similarity can be disentangled from an isotropic self-similarity to which an anisotropic trend has been superimposed.