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The purpose of this paper is to present a synthesis concerning the mathematical methods used in monofractal and multifractal analysis for the processing of biological and medical data and images. Different mathematical methods were proposed to estimate the monofractal dimension or multifractal spectrum of a fractal object. A brief overview of these algorithms, the way they work as well as their advantages and disadvantages are presented. Fractal and multifractal geometries provide noninvasive powerful tools that allow biologists, researchers and physicians the early detection and diagnosis of diseases, based on the analyses of biological and medical data and images. [ABSTRACT FROM AUTHOR]