Hyperbolic wavelet transform: an efficient tool for multifractal analysis of anisotropic textures

TL;DR

This paper introduces a hyperbolic wavelet transform method for analyzing the multifractal properties of anisotropic textures, capturing both scale invariance and directional regularities within a unified framework.

Contribution

It presents a novel multifractal analysis approach using hyperbolic wavelet bases to characterize anisotropic regularities in functions.

Findings

Effective characterization of local and directional regularities.

Joint analysis of scale invariance and anisotropy.

In-depth study of multifractal properties.

Abstract

Global and local regularities of functions are analyzed in anisotropic function spaces, under a common framework, that of hyperbolic wavelet bases. Local and directional regularity features are characterized by means of global quantities constructed upon the coefficients of hyperbolic wavelet decompositions. A multifractal analysis is introduced, that jointly accounts for scale invariance and anisotropy. Its properties are studied in depth.