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

摘要

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