Multifractal analysis of three-dimensional grayscale images: Estimation of generalized fractal dimension and singularity spectrum

TL;DR

This paper introduces methods for multifractal analysis of 3D grayscale images, including synthetic image generation and estimation of generalized fractal dimensions and singularity spectra to characterize complex systems.

Contribution

It presents new procedures for generating 3D synthetic images and evaluates two approaches for calculating multifractal properties of complex 3D structures.

Findings

Effective methods for estimating generalized fractal dimensions.

Two approaches for singularity spectrum evaluation demonstrated.

Application to complex 3D systems enhances understanding of multifractal behavior.

Abstract

A multifractal analysis is performed on a three-dimensional grayscale image associated with a complex system. First, a procedure for generating 3D synthetic images (2D image stacks) of a complex structure exhibiting multifractal behaviour is described. Then, in order to characterize the 3D system, the theoretical calculation of the generalized fractal dimension and two different approaches for evaluating the singularity spectrum are presented.