Image-based fractal description of microstructures / by J.M. Li ... [and others].

Format:

Book

Contributor:

Li, J. M.

Language:

English

Subjects (All):

Microstructure.

Image processing.

Fractals.

Physical Description:

xii, 272 pages : illustrations ; 25 cm

Place of Publication:

Boston : Kluwer Academic Publishers, [2003]

Summary:

Fractal analysis has rapidly become an important field in materials science and engineering with broad applications to theoretical analysis and quantitative description of microstructures of materials. Fractal methods have thus far shown great potential in engineering applications in quantitative microscopic analysis of materials using commercial microscopes. This book attempts to introduce the fundamentals and the basis methods of fractal description of microstructures in combination with digital imaging and computer technologies. Basic concepts are given in the form of mathematical expressions. Detailed algorithms in practical applications are also provided. Fractal measurement, error analysis and fractal description of cluster growth, thin films and surfaces are emphasized in this book. Image-Based Fractal Description of Microstructures provides a comprehensive approach to materials characterization by fractal from theory to application.

Contents:

1.1 Classification of basic elements in microstructures 1

1.2 Image and image processing 6

1.2.2 Image processing 8

1.3 Image-based measurement of basic elements 9

1.4 Parameter estimation 11

1.5 Relationship between properties and irregularity of microstructures of materials 12

Chapter 2 Digital Images of Microstructures 13

2.1 Light optical microscope 13

2.2 Scanning electron microscope 16

2.2.1 Topographical contrast 16

2.2.2 Atomic number (compositional) contrast 18

2.2.3 Crystallographic orientation contrast 18

2.2.4 X-ray contrast 18

2.3 Transmission electron microscope 18

2.3.1 Mass-thickness contrast 20

2.3.2 Diffraction contrast 20

2.3.3 Phase contrast 20

2.4 Scanning tunnelling microscope 21

2.5 Atomic force microscope 22

2.6 Magnetic force microscope 23

Chapter 3 Image Processing 25

3.1 Image pre-processing 25

3.1.1 Brightness and contrast transformations 25

3.1.2 Image enhancement 28

3.1.3 Fourier-based spatial frequency transform 29

3.1.4 Non-uniform illumination correction 33

3.1.5 Noise and filtration 36

3.2 Object abstraction 40

3.2.1 Edge detection 40

3.2.1.1 Roberts operator 44

3.2.1.2 Sobel Operator 44

3.2.1.3 Kirsch operator 46

3.2.1.4 Laplacian operator 46

3.2.2 Microstructural segmentation and classification 47

3.2.2.1 Thresholding operation 47

3.2.2.2 K-average dynamic classification 48

3.3 Image post-processing 51

3.3.1 Distance, perimeter, area and center of mass 51

3.3.2 Thinning 52

3.3.3 Dilation and erosion 53

Chapter 4 Fundamental Statistics 57

4.1 Populations, sampling and probability 57

4.2 Statistical measures for population 58

4.2.1 Mean 58

4.2.2 Variance 58

4.2.3 Standard deviation 59

4.2.4 Coefficient of correlation 59

4.2.5 Errors 60

4.2.5.1 Absolute deviation 60

4.2.5.2 Relative deviation 60

4.2.5.3 Residual deviation 60

4.2.5.4 Average deviation 60

4.2.5.5 Standard deviation 61

4.3 Probability distribution 61

4.3.1 Normal distribution 61

4.3.2 x[superscript 2] distribution 63

4.3.3 t-distribution 64

4.3.4 F-distribution 66

4.4 Some useful theorems 67

4.4.1 Chebyshev's inequality 67

4.4.2 Law of large numbers 67

4.4.3 Central limit theorem 68

4.5 Simple linear regression analysis 68

4.5.1 Line-fitting to data: Least-squares regression method 69

4.5.2 Curve-fitting to data 71

4.5.3 Coefficient of correlation of the linear regression 72

4.5.4 Error analysis 72

4.5.5 Tests of hypothesis 74

Chapter 5 Fractal Fundamentals 79

5.2 Dimension 80

5.2.1 Euclidean space 80

5.2.2 Topological dimension 81

5.2.3 Hausdorff dimension 82

5.2.4 Generalized dimension 84

5.3 Properties of a fractal set 85

5.3.1 Self-similarity 85

5.3.2 Self-affinity 86

5.4 Examples of fractals 87

5.4.1 Cantor set 87

5.4.2 Koch curve 89

5.4.3 Sierpinski graphics 91

5.4.4 Weierstrass-Mandelbrot curve 93

5.4.5 Fractal Brownian motion 94

5.4.5.2 Fractal Brownian motion 101

5.4.5.3 Simulation of FBM profile and surface 104

Chapter 6 Fractal Measurements of Projection Microstructures 111

6.2 Length of fractal curve 113

6.3 Perimeter-area and area-volume relations 117

6.4 Mass method 119

6.5 Box-counting method 123

6.6 Multifractal measurements of cluster growth 125

Chapter 7 Fractal Measurements of Topographical Images from 3D Surfaces 133

7.1 Fractal nature of material surfaces 133

7.2 Fractal-based methods for the description of surfaces 134

7.2.1 Slit island analysis 134

7.2.2 Profile analysis 135

7.2.3 3D surface analysis 137

7.2.3.1 Surface area method 137

7.2.3.2 FBM method 138

7.2.3.3 Dynamic scaling method 139

7.3 Variation-correlation method for the description of 3D surfaces 141

7.3.1 Algorithm of the variation method 141

7.3.2 Algorithm of the variation-correlation method 143

7.3.3 3D fractal model: the variation-correlation function and its properties 144

7.3.4 Fractal measure and estimation of fractal characteristic length 150

7.3.5 Physical meaning of fractal characteristic length 151

7.3.6 Physical meaning of fractal dimension 154

7.3.7 Saturated value of height variation of a surface 156

Chapter 8 Irregularity of Graphite Nodules 159

8.2 Measurement procedures 162

8.3 Quantitative analysis 162

8.3.1 Quantitative analysis of irregularity of graphite boundary 162

8.3.2 Quantitative analysis of the irregularity of the aggregated state of graphite nodules in 2D metallographic sections 166

8.3.3 Quantitative analysis of the irregularity of 3D surfaces of graphite nodules 169

8.3.4 A statistical method to analyze a group of graphite nodules 171

Chapter 9 Fractal Growth of Graphite Nodules 175

9.1 Growth of graphite nodules 175

9.2 Fractal growth of graphite nodules 178

9.2.1 Experimental observations and fractal measurements 178

9.2.2 Fractal characteristics 182

9.3 Fractal growth models of graphite nodules 183

9.3.1 Fractal-based model for diffusion-controlled growth 183

9.3.2 Fractal-based model for dissolution - controlled growth 185

9.4 Interpretation of fractal growth of graphite nodules 188

9.4.1 Thermodynamic growth of graphite nodules 188

9.4.2 Kinetic growth of graphite nodules 189

Chapter 10 Fractal-based Study of Magnetic Thin Films 193

10.1 Magnetic thin films 193

10.2 Preparation of magnetic thin films 194

10.3 Description of the surfaces of magnetic thin films 195

10.3.1 Theoretical analysis of the relationship between fractal dimension and surface energy of thin films 195

10.3.2 VCF-based quantitative analysis on the surfaces of magnetic thin films 201

10.4 Description of the magnetic microstructures of magnetic thin films 207

10.4.1 Irregular geometrical features of MFM magnetic microstructures 207

10.4.2 Relationship between fractal parameters and coercivity 210

10.4.3 Relationship between D[subscript cor] and ([delta]M)[subscript max] 213

Chapter 11 Fractal-based Study of Fracture Surfaces 215

11.1 Fractography 215

11.2 Fracture and fractals 216

11.3 Physical meaning of the secondary electron image 219

11.4 Influence of SEM parameters on D[subscript cor] 220

11.4.1 Brightness number 220

11.4.2 Contrast number 221

11.4.3 Working distance 222

11.4.4 Local current 222

11.4.5 Accelerating voltage 222

11.4.6 Tilt angle 224

11.4.7 Spot size number 225

11.5 Influence of noise on D[subscript cor] 226

11.6 Fractal characteristics and mechanical properties 229

11.6.1 Fractal characteristics with different fracture modes 229

11.6.2 Relationship between fractal dimension and mechanical properties 239

11.6.2.1 Brittle fracture 239

11.6.2.2 Ductile fracture 245

11.7 Quantitative fractography 250

11.7.1 VCF-Based edge detection on fracture surfaces 250

11.7.2 Segmentation of fracture surfaces 251.

Notes:

Includes bibliographical references (pages [255]-262) and index.

ISBN:

1402075073

OCLC:

52251454