MATLAB-based Image Multifractal Analysis Program

This text introduces a MATLAB-based image multifractal analysis program capable of directly computing and generating the multifractal spectrum of images. The program utilizes box-counting methodology combined with statistical moment calculations to quantify the complexity and fractal characteristics of images through parameters like singularity strength and fractal dimension. Key functions include image preprocessing, partition function computation, and Legendre transformation implementation for spectrum derivation. This implementation simplifies multifractal spectrum calculation by automating the entire workflow, eliminating the need for tedious manual computations. Through this program, researchers can effectively analyze and understand various types of images, making it particularly valuable in image processing, pattern recognition, and complex system analysis applications where quantitative characterization of texture complexity is required. The algorithm efficiently handles grayscale image data by calculating probability measures across different scaling levels and generates the multifractal spectrum curve showing the relationship between Hölder exponent and fractal dimension.