IMPLEMENTATION OF FAST CALCULATION OF THE MULTIFRACTAL SPECTRUM OF A THREE-DIMENSIONAL IMAGE

Abstract

This paper examines the algorithmic aspects of calculating multifractal characteristics using the box-counting method
for three-dimensional images. It is demonstrated that the application of prefix sums, fast exponentiation, and multithreaded
computing enables efficient analysis of large images (tens of gigavoxels) within a reasonable time frame (from tens of seconds
to several minutes) at the cost of increased RAM consumption. A methodology for selecting the optimal image size is proposed
to maximize the number of points on the graphs of generalized statistical sum dependencies on box size, thereby improving
calculation accuracy. Algorithmic solutions for efficient multithreaded data processing are also presented.