Fractals : Applications in Biological Signalling and Image Processing

The book provides an insight into the advantages and limitations of the use of fractals in biomedical data. It begins with a brief introduction to the concept of fractals and other associated measures and describes applications for biomedical signals and images. Properties of biological data in relations to fractals and entropy, and the association with health and ageing are also covered. The book provides a detailed description of new techniques on physiological signals and images based on the fractal and chaos theory. The aim of this book is to serve as a comprehensive guide for researchers and readers interested in biomedical signal and image processing and feature extraction for disease risk analyses and rehabilitation applications. While it provides the mathematical rigor for those readers interested in such details, it also describes the topic intuitively such that it is suitable for audience who are interested in applying the methods to healthcare and clinical applications. The book is the outcome of years of research by the authors and is comprehensive and includes other reported outcomes. Content: Introduction Introduction History of Fractal Analysis Fundamentals of fractals Definition of Fractal Complexity of biological systems Fractal Dimension Summary of this book References Physiology, Anatomy and Fractal Properties Introduction Conceptual understanding Chaos, Complexity, Fractals and entropy Chaos Theory Complex Systems Entropy Fractal and fractal dimension Computing Fractal dimension Relationship of Fractals and Self-similarity Fractals in Biology Properties of natural and synthetic objects Human physiology Summary References Fractal Dimension of Biosignals Introduction Fractal Dimension and Self-similarity Different methods to estimate fractal dimension of a waveform Fractals and Electrocardiogram (ECG), Electromyogram (EMG) and Electroencephalogram (EEG) Fractal dimension for Gait Analysis Summary References Fractals analysis of electrocardiogram Heart activity and fractal properties Heart rate variability Fractal properties of ECG An Example Poincare plot of heart-rate variability Application - ECG and Heart rate variability Summary References Fractals analysis of Surface Electromyogram Introduction Surface Electromyogram (sEMG) Fractal analysis of sEMG Summary References Fractals analysis of Electroencephalogram Electroencephalogram Techniques for EEG Analysis Fractal properties of EEG An example - Measuring alertness using Fractal properties of EEG References Fractal analysis of biomedical images Introduction Fractal geometry and self-similarity Entropy, fractals and tortuosity Binary Box-count Fractal dimension Differential (3D) Box-counting dimension Spectral fractal dimension Higuchi's fractal dimension Summary References Fractal Dimension of Retinal Vasculature Introduction to human eye anatomy Eye fundus retinopathy - Disease manifestation in retina FD and age related changes of retinal vasculature FD and Hypertensive retinopathy FD and risk of stroke event FD and Diabetic retinopathy Summary References Fractal Dimension of Mammograms Introduction Mammography and Properties of breast tissue Fractal irregularities of breast tissues Fractal based detection of Breast cancer and the tumor types Summary References Fractal Dimension of Skin Lesions Introduction Fundamentals of Skin Skin legions and abnormalities Skin cancer and associated changes to FD FD of the ageing skin Summary References Case study I: Age associated change of complexity Background Physiological basis Ageing muscles and fractal properties Ageing heart and changes to ECG Ageing eyes and FD of eye-fundus images Summary References Case study 2: Health, well-being and Fractal properties Introduction Risk of stroke and retinal fractal Muscle fatigue and fractal properties Summary References Cover -- Half Title -- Title Page -- Copyright Page -- Preface -- Table of Contents -- List of Figures -- 1: Introduction -- Abstract -- 1.1 Introduction -- 1.2 History of Fractal Analysis -- 1.3 Fundamentals of Fractals -- 1.4 Definition of Fractal -- 1.5 Complexity of Biological Systems -- 1.6 Fractal Dimension -- 1.7 Summary of this Book -- References -- 2: Physiology, Anatomy and Fractal Properties -- Abstract -- 2.1 Introduction -- 2.2 Conceptual Understanding -- 2.3 Chaos, Complexity, Fractals and Entropy -- 2.4 Chaos Theory -- 2.5 Complex Systems -- 2.6 Entropy -- 2.7 Fractal and Fractal Dimension -- 2.8 Computing Fractal Dimension -- 2.8.1 Box-counting -- 2.8.2 Power spectrum fractal dimension -- 2.9 Relationship of Fractals and Self-similarity -- 2.9.1 Sierpinski triangle -- 2.9.2 Fractal dimension of the Menger Sponge -- 2.10 Fractals in Biology -- 2.11 Properties of Natural and Synthetic Objects -- 2.12 Human Physiology -- 2.12.1 Fractals and Electrocardiogram (ECG), Electromyogram (EMG) and Electroencephalogram (EEG) -- 2.12.2 Fractal dimension for human movement and gait analysis -- 2.13 Summary -- References -- 3: Fractal Dimension of Biosignals -- Abstract -- 3.1 Introduction -- 3.2 Fractal Dimension and Self-similarity -- 3.2.1 Self-similarity -- Exact self-similarity -- Approximate self-similarity -- Statistical self-similarity -- 3.2.2 Fractal dimension -- 3.3 Different Methods to Estimate Fractal Dimension of a Waveform -- 3.3.1 Box-counting method -- 3.3.2 Katz's algorithm -- 3.3.3 Higuchi's algorithm -- 3.3.4 Petrosian's algorithm -- 3.3.5 Sevcik's algorithm -- 3.3.6 Correlation dimension -- 3.3.7 Adapted box fractal dimension -- 3.3.8 Fractal dimension estimate based on power law function -- 3.4 Fractals and Electrocardiogram (ECG), Electromyogram (EMG) and Electroencephalogram (EEG) Chapter 1 Introduction -- chapter 2 Physiology, Anatomy and Fractal Properties -- chapter 3 Fractal Dimension of Biosignals -- chapter 4 Fractals Analysis of Electrocardiogram -- chapter 5 Fractals Analysis of Surface Electromyogram -- chapter 6 Fractals Analysis of Electroencephalogram -- chapter 7 Fractal Analysis of Biomedical Images -- chapter 8 Fractal Dimension of Retinal Vasculature -- chapter 9 Fractal Dimension of Mammograms -- chapter 10 Fractal Dimension of Skin Lesions -- chapter 11 Case Study I: Age Associated Change of Complexity -- chapter 12 Case Study 2: Health, Well-being and Fractal Properties