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

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.