Image-Based Fractal Description of Microstructures

Abstract

Preface. Acknowledgements. 1: Introduction. 1.1. Classification of basic elements in microstructures. 1.2. Image and image processing. 1.3. Image-based measurement of basic elements. 1.4. Parameter estimation. 1.5. Relationship between properties and irregularity of microstructures of materials. 2: Digital Images of Microstructures. 2.1. Light optical microscope. 2.2. Scanning electron microscope. 2.3. Transmission electron microscope. 2.4. Scanning tunnelling microscope. 2.5. Atomic force microscope. 2.6. Magnetic force microscope. 3: Image Processing. 3.1. Image pre-processing. 3.2. Object abstraction. 3.3. Image post-processing. 4: Fundamental Statistics. 4.1. Populations, sampling and probability. 4.2. Statistical measures for population. 4.3. Probability distribution. 4.4. Some useful theorems. 4.5. Simple linear regression analysis. 5: Fractal Fundamentals. 5.1. Definitions of fractals. 5.2. Dimension. 5.3. Properties of a fractal set. 5.4. Examples of fractals. 6: Fractal Measurements of Projection Microstructures. 6.1. Fractal measurements. 6.2. Length of fractal curve. 6.3. Perimeter-area and area-volume relations. 6.4. Mass method. 6.5. Box-counting method. 6.6. Multifractal measurements of cluster growth. 7: Fractal Measurements of Topographical Images from 3D Surfaces. 7.1. Fractal nature of material surfaces. 7.2. Fractal-based methods for the description ofsurfaces. 7.3. Variation-correlation method for the description of 3D surfaces. 8: Irregularity of Graphite Nodules. 8.1. Conventional description of nodules. 8.2. Measurement procedures. 8.3. Quantitative analysis. 9: Fractal Growth of Graphite Nodules. 9.1. Growth of graphite nodules. 9.2. Fractal growth of graphite nodules. 9.3. Fractal growth models of graphite nodules. 9.4. Interpretation of fractal growth of graphite nodules. 10: Fractal-based Study of Magnetic Thin Films. 10.1. Magnetic thin films. 10.2. Preparation of magnetic thin films. 10.3. Description of the surfaces of magnetic thin films. 10.4. Description of the magnetic microstructures of magnetic thin films. 11: Fractal-based Study of Fracture Surfaces. 11.1. Fractography. 11.2. Fracture and fractals. 11.3. Physical meaning of the secondary electron image. 11.4. Influence of SEM parameters on Dcor. 11.5. Influence of noise on Dcor. 11.6. Fractal characteristics and mechanical properties. 11.7. Quantitative fractography. References. Index.