Image Analysis in Earth Sciences is a graduate level textbook for researchers and students interested in the quantitative microstructure and texture analysis of earth materials. Methods of analysis and applications are introduced using carefully worked examples. The input images are typically derived from earth materials, acquired at a wide range of scales, through digital photography, light and electron microscopy. The book focuses on image acquisition, pre- and post-processing, on the extraction of objects (segmentation), the analysis of volumes and grain size distributions, on shape fabric analysis (particle and surface fabrics) and the analysis of the frequency domain (FFT and ACF). The last chapters are dedicated to the analysis of crystallographic fabrics and orientation imaging. Throughout the book the free software Image SXM is used.

Part I Looking at Images

1 Images and Microstructures 3

1.1 Images and Microstructures 3

1.2 Image Analysis 6

      1.2.1 Direct Image Analysis 8

      1.2.2 Analysis of Image Segments 9

      1.2.3 Analysis of Best-fit Ellipses 10

      1.2.4 Analysis of Digitized Outlines 10

1.3 Segmentation 11

1.4 Image Models 12

2 Acquiring Images 15

2.1 Photography 15

      2.1.1 Field Photography 15

      2.1.2 Photomacrography 17

2.2 Optical Scanners 19

2.3 Light Microscopy 19

      2.3.1 Modes of Polarization Microscopy 19

      2.3.2 Illumination 23

      2.3.3 Magnification and Resolution 24

2.4 Digital Cameras 27

2.5 Electron Microscopy 29

      2.5.1 Scanning Electron Microscopy (SEM) 29

      2.5.2 Transmission Electron Microscopy (TEM) 30

References 30

3 Digital Image Processing 31

3.1 The Digital Image 31

      3.1.1 Bit and Bytes 31

      3.1.2 Gray Values 33

      3.1.3 Color 33

3.2 Stacks 36

      3.2.1 R-G-B Stacks 36

      3.2.2 X-Y-Z Stacks 37

      3.2.3 X-Y-t Stacks 37

      3.2.4 X-Y-a Stacks 39

3.3 Format and Compression 39

3.4 Image SXM 42

      3.4.1 Quick Start 43

      3.4.2 LUT Window 43

      3.4.3 Map Window 44

      3.4.4 Info Window 44

      3.4.5 Tools 45

3.5 Preparing the Data 49

      3.5.1 Exploring the Image 49

      3.5.2 Scale and Calibrate 50

      3.5.3 Using Color 51

      3.5.4 Presenting the Data: The Beauty Case 53

References 56

4 Pre-processing 59

4.1 Comparing Images 59

4.2 Background Corrections 60

      4.2.1 Direct Background Correction 61

      4.2.2 Background Correction Using a Model Background 64

      4.2.3 Background Correction Using a Background Image 64

4.3 Re-sizing 67

4.3.1 Nearest Neighbor 67

4.3.2 Bilinear 68

4.3.3 Bicubic 68

4.4 Noise Removal 72

      4.4.1 Median Filtering 72

      4.4.2 Fourier Filtering 73

References 73

Part II Segmentation: Finding and Defining the Object

5 Segmentation by Point Operations 77

5.1 Look-Up Tables 77

      5.1.1 Changing the Contrast: Linear LUTs 77

      5.1.2 Non-linear LUTs 78

      5.1.3 Special LUTs 78

5.2 Macros 78

      5.2.1 Using Macros 78

      5.2.2 Lazy LUTs Macro 80

      5.2.3 From LUT to Point Operation 86

5.3 Segmentation by Point Operations 88

      5.3.1 Segmentation by Thresholding 90

      5.3.2 Segmentation by Gray Level Slicing 90

References 94

6 Post-processing 95

6.1 Ranking Filters 95

      6.1.1 Minimum: Median: Maximum 95

      6.1.2 Erosion: Dilation 97

      6.1.3 Opening: Closing 99

6.2 Copy Modes 100

      6.2.1 Logical Operations 100

      6.2.2 Combining Images 100

6.3 Structural Filtering 102

      6.3.1 Skeletonization 102

      6.3.2 Pruning 103

      6.3.3 Watershed 103

6.4 Cleaning Up Bitmaps 104

6.5 Phases, Grains and Boundaries 106

References 111

7 Segmentation by Neighborhood Operations 113

7.1 Neighborhood 113

7.2 Averaging Filters 114

      7.2.1 Gauss Filters 116

      7.2.2 Influence of Shape and Size 118

7.3 Gradient Filters 119

      7.3.1 Roberts Cross 123

      7.3.2 Sobel Edge Detection 126

      7.3.3 Laplace Filters 128

7.4 Edge Detection 130

References 135

8 Image Analysis 137

8.1 Image Segments and Best-Fit Ellipses 137

8.2 Deriving Size and Shape Descriptors 140

8.3 Example of Image Analysis 142

8.4 Digitizing Outlines 144

      8.4.1 Exporting Segment Boundaries 146

      8.4.2 Creating Polygonal Chains 147

      8.4.3 The Nature of the Square Grid 149

      8.4.4 From Discrete to Continuous 151

8.5 SCASMO 151

      8.5.1 How to Run SCASMO 152

8.6 The FABRIC Programs 156

References 156

9 Test Images 157

9.1 Numerical Simulations 157

      9.1.1 Ellipses 157

      9.1.2 Shape and Orientation Distributions 158

      9.1.3 Spatial Distributions 161

9.2 Synthetic Particle Fabrics 161

9.3 RANDOM 163

      9.3.1 How to Run RANDOM 164

9.4 MONTECARLO 166

      9.4.1 Random Sampling 167

      9.4.2 How to Run MONTECARLO 169

References 170

Part III Measuring Size and Volume

10 Volume Determinations 173

10.1 Measuring Area Fractions 173

      10.1.1 Measuring Areas in Image SXM 174

      10.1.2 Counting Pixels 175

      10.1.3 Estimating Areas 177

10.2 Estimating Volume Fractions 177

10.3 Determining Errors 179

      10.3.1 Errors Associated with Point Counting 179

      10.3.2 Errors Associated with Area Measurements 180

10.4 Practical Application 180

10.5 Surface Fractions 182

References 185

11 2-D Grain Size Distributions 187

11.1 Measures for Grain Size 187

11.2 Mean Grain Size 192

11.3 Grain Size Distribution 194

11.4 Grain Size Mapping 196

References 199

12 3-D Grain Size 201

12.1 Random Sectioning of a Single Sphere 201

12.2 From 3-D Spheres to 2-D Sections 205

      12.2.1 The Stereological Model 205

      12.2.2 Four Typical Distributions 207

12.3 From 2-D Sections to 3-D Spheres 207

12.4 STRIPSTAR 213

      12.4.1 How to Run STRIPSTAR 214

12.5 Practical Applications 215

      12.5.1 Particles in a Matrix 216

      12.5.2 Crystalline Aggregates 217

      12.5.3 Shortcuts 219

      12.5.4 The Influence of Shape: How Random is Random? 221

      12.5.5 Error Estimation 222

      12.5.6 Phi-Values and Logarithmic Binning 222

References 224

13 Fractal Grain Size Distributions 225

13.1 Fragmentation in Nature and Experiment 225

13.2 Fragmenting the Cube 227

      13.2.1 The Fractal Model for Sectioning 228

      13.2.2 Fractal Dimensions 229

      13.2.3 Fragmentation Numbers F > 8 or F < 8 231

      13.2.4 Continuous Fragmentation 232

13.3 Fragmentation Matrix 233

      13.3.1 Deriving the Fractal Dimension from the Matrix 234

      13.3.2 Fractal Dimension from the Matrix and from Grain Size Analysis 239

13.4 Visualizing Grain Size Distributions 241

      13.4.1 Preparing the Bitmap 242

      13.4.2 Gauss Filtering 243

      13.4.3 Converting the Matrix to the Fractal Dimension 245

13.5 Examples 249

References 249

Part IV Quantifying Shape and Orientation

14 Particle Fabrics 253

14.1 Projections of a Single Ellipse 254

14.2 Projections of Non-elliptical Shapes 255

14.3 Best-Fit Ellipses and Convex Hulls 256

14.4 Projections of Sets of Ellipses 261

14.5 PAROR 263

      14.5.1 How to Run PAROR 264

      14.5.2 The Monitor Printout File 265

      14.5.3 The B(a) File 268

      14.5.4 The Axes Orientation File 269

      14.5.5 The Particle Data File 270

14.6 PAROR Analysis of Particles in a Matrix 270

14.7 PAROR Analysis of Crystalline Aggregates 272

14.8 PAROR Analysis of Surfaces 274

14.9 Restoring the Input 276

14.10 PAROR Analysis Within Image SXM 279

References 280

15 Surface Fabrics 283

15.1 Projection of Line Segments 283

15.2 Straight Line Segments 284

15.3 SURFOR 285

      15.3.1 How to Run SURFOR 287

      15.3.2 The Monitor Printout File 287

      15.3.3 The A(a) File 289

      15.3.4 The Surface Orientation File 289

      15.3.5 The Characteristic Shape File 289

15.4 SURFOR Analysis of Lines Segments 289

15.5 SURFOR Analysis of Closed Outlines 293

15.6 SURFOR Versus PAROR Analysis 294

15.7 SURFOR Analysis of Incomplete Outlines 297

15.8 SURFOR Analysis of Open Lines 298

15.9 SURFOR Analysis Within Image SXM 301

References 303

16 Strain Fabrics 305

16.1 Fabrics and Strain 305

      16.1.1 Strain Markers 305

      16.1.2 The Geometry of Strain 306

16.2 Measuring Strain with SURFOR 308

16.3 Testing for Strain 312

16.4 Practical Examples 314

16.5 SURFOR and PAROR Versus the Rf–j Method 317

References 320

17 Shape Descriptors 323

17.1 Shape Descriptors 323

      17.1.1 Deviation from the Circular Form: Classical Shape Factors 324

      17.1.2 Aspect Ratios 326

      17.1.3 Convexity: Concavity 328

      17.1.4 Excess Perimeter and Defect Area 329

      17.1.5 Angularity 331

17.2 iSHAPES 335

17.2.1 How to Run iSHAPES 335

17.3 Manual and Automatic Digitization 337

17.4 Applications of iSHAPES 339

17.4.1 Fault Rock Microstructures 339

17.4.2 Grain Boundary Migration Microstructures 342

17.4.3 Annealing Microstructures 344

References 347

Part V Spatial Relationships

18 Spatial Distributions 351

18.1 Basic Concepts 351

      18.1.1 Spatial Distributions 352

      18.1.2 Random Mixing 354

      18.1.3 Volume Model and Surface Model 356

18.2 What to Measure 356

18.3 Test Samples 357

18.4 Analysis of a Polyphase Material 359

      18.4.1 Focusing on One Phase 361

      18.4.2 Selecting Two Phases 363

18.5 Errors 365

18.6 Orientation Dependent Analysis 366

References 368

19 Spatial Frequencies 369

19.1 Spatial Frequencies 369

19.2 Fourier Transforms 372

      19.2.1 One-Dimensional Fourier Transform 372

      19.2.2 Two-Dimensional Fourier Transform 373

      19.2.3 Discrete Fourier Transforms 373

      19.2.4 Fast Fourier Transform 375

19.3 Interpreting Fourier Transform Images 376

19.4 Frequency Filtering 377

19.4.1 Selecting Frequencies 378

19.4.2 High-Pass and Low-Pass Filtering 379

19.5 Practical Applications 385

References 388

20 Autocorrelation Function 389

20.1 Principles of Autocorrelation 389

      20.1.1 Mathematical Definition 390

      20.1.2 Autocorrelation Function of Single Shapes 391

      20.1.3 Autocorrelation Function of Sets of Shapes 392

20.2 Analysis of Autocorrelation Functions 397

20.3 Practical Applications of Autocorrelation Functions 398

      20.3.1 Lazy ACF Tiling Macro 400

      20.3.2 Bulk ACF 402

      20.3.3 Local ACFs 403

20.4 Autocorrelation Functions and Strain Analysis 405

      20.4.1 Heterogeneous Strain 405

      20.4.2 Autocorrelation of Center Points 407

      20.4.3 Deformation and Reaction 408

References 409

Part VI Orientation Imaging

21 Crystal Orientation and Interference Color 413

21.1 Basic Concepts 414

21.2 Interference Colors 417

      21.2.1 Birefringence 417

      21.2.2 Optical Path 418

      21.2.3 Spectra of Interference Colors 419

      21.2.4 Color from Spectra 421

      21.2.5 First-Order Colors and Section Thickness 421

      21.2.6 Adding the Wave Plate 422

21.3 The Crystallographic Color Space 425

      21.3.1 Polstacks 426

      21.3.2 Polstack Sections 426

21.4 Color to Monochrome 428

      21.4.1 Finding the Best Filter 429

      21.4.2 Resolving the Azimuth 431

      21.4.3 Resolving the Inclination 433

21.5 LUTs for CIP 437

      21.5.1 Converting Intensity to Inclination 437

References 438

22 Computer-Integrated Polarization Microscopy 439

22.1 How CIP Works: The Basic Idea 441

22.2 Acquire the Input 443

22.2.1 The Structure of the Input Stack 444

22.2.2 The Micrographs 445

22.2.3 Circular Polarization 450

22.3 Prepare the Input Stack 451

22.4 Pre-process the Input Stack 456

      22.4.1 Calibration Files 456

      22.4.2 Image Calibration 457

      22.4.3 Lighting and Background Corrections 457

      22.4.4 Section Thickness 457

22.5 Do the CIP 460

22.6 Viewing the Result 467

22.7 Pole Figures 469

22.8 Refining the Calculation 469

References 475

23 Orientation and Misorientation Imaging 477

23.1 Orientation Imaging: Changing the Colors 477

23.2 Using EBSD Input 480

      23.2.1 Full Texture Versus c-Axis 480

      23.2.2 Euler Angles to c-Axes 480

23.3 Masking 481

      23.3.1 Selecting Regions 481

      23.3.2 Selecting Minerals 487

23.4 Misorientation Imaging 487

      23.4.1 Principal Misorientations 488

      23.4.2 Misorientation with Respect to Reference Direction 488

      23.4.3 From Misorientation to Orientation 488

      23.4.4 Misorientation Profiles 490

23.5 Segmentation in Orientation Space 493

      23.5.1 Grain Boundaries and Sub-grain Boundaries 494

      23.5.2 Flat Grains 497

23.6 Orientation Tracking 497

      23.6.1 Texture Domains 498

      23.6.2 Texture Domains of a Low-Strain Sample 498

      23.6.3 Texture Domains of a High-Strain Sample 501

      23.6.4 Domain Grain Size 503

23.7 Orientation Gradient Imaging 506

      23.7.1 Orientation Gradients 506

      23.7.2 Orientation Gradient Density 506

      23.7.3 Sharp Boundaries 507

23.8 Texture-Dependent Shape Analysis 509

References 512

Erratum to Chapter 13: Image Analysis in Earth Sciences E1

Index 515

Professor Renée Heilbronner has many years of experience in the field of image analysis and has developed several software packages for microstructure analysis for grain size, shape and strain determinations. She has also developed the CIP method for crystallographic texture determinations and orientation imaging based on polarization microscopy and digital image processing. She has contributed to the development of the freeware image analysis software (Image SXM, former NIH Image), and is a member of a growing group of international image analysis experts who are setting up workshops and building a network for microstructure and texture research involving mathematicians, material scientists and geologists. As an experienced teacher of image analysis at different levels ranging from general introductory courses to specialized texture workshops, she has taught at various universities all over the world.

中科院文献情报中心