Fractal and multifractal analysis: a review

Area of Science:

• Medical Signal Analysis
• Fractal Geometry
• Image Processing

Background:

• Fractal and multifractal geometries are increasingly utilized in medical signal analysis.
• Applications include pattern recognition, texture analysis, and segmentation of 1D, 2D, and 3D medical data.
• Accurate estimation of fractal features is crucial for these applications.

Purpose of the Study:

• To provide a comprehensive overview of algorithms used for estimating fractal dimension and multifractal spectra.
• To explain the working principles, benefits, and limitations of various estimation methods.
• To categorize these algorithms and discuss their specific applications in medical signal analysis.

Main Methods:

• Review and synthesis of existing literature on fractal dimension and multifractal spectral estimation algorithms.
• Categorization of algorithms based on their methodologies and underlying principles.
• Analysis of algorithm performance, including benefits and limitations in medical contexts.

Main Results:

• Identification and classification of diverse algorithms for fractal feature estimation.
• Detailed explanation of how each algorithm functions.
• Comparative analysis of the strengths and weaknesses of different methods for medical signal processing.

Conclusions:

• Fractal and multifractal geometry offers powerful tools for medical signal analysis.
• Understanding the nuances of different estimation algorithms is key to selecting the most appropriate method.
• This review serves as a guide for researchers and practitioners in the field.