Objectives and outcomes
Acquiring knowledge about fractals and multifractals and applying multifractal and fractal analysis to
problems of high complexity. Ability to understand the basic algorithms used in multifractal analysis, as
well as the ability to expand knowledge by working on a specific problem in the field of doctoral
dissertation.
Lectures
Fractal theory. Fractal properties. Natural fractals. Euclidean and topological dimensions. Fractal
dimensions. Dimensions of similarity. Box-counting dimensions. Hausdorff dimension. Multifractal theory.
Measure theory. Multifractal analysis. Fine and rough theory. Sums of moments and Legendre
transformations. Multifractal based image processing. Digital image in shades of grey. Image
segmentation and texture classification. Methods for determining the multifractal spectrum.
Research work
Applying fractal and multifractal image analysis to medicine. Multifractal analysis of EEG signals for diagnosing
chronic diseases of the central nervous system. Application to the analysis of microscope, MRI and mammography
images in order to find primary tumours.