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Digital Image Processing, Third Edition

by Rafael C. Gonzalez; Richard E. Woods

Publisher: Prentice Hall

Copyright Year: 2008

Publishing Date: 2007/08/21

eText ISBN-10: 0-13-604189-2

eText ISBN-13: 978-0-13-604189-4

Print ISBN-10: 0-13-168728-X

Print ISBN-13: 978-0-13-168728-8

Course: Electrical & Electronics Engineering, Computer Graphics

Pages: 976

eTextbook $79.50

(180 day subscription)

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Table of Contents | Description

Instructor Resources | Student Resources

ABOUT THIS TITLE - TABLE OF CONTENTS

Acknowledgments, xix

The Book Web Site, xx

About the Authors, xxi

1. Introduction, 1

1.1. What Is Digital Image Processing?, 1

1.2. The Origins of Digital Image Processing, 3

1.3. Examples of Fields that Use Digital Image Processing, 7

1.3.1. Gamma-Ray Imaging, 8

1.3.2. X-Ray Imaging, 9

1.3.3. Imaging in the Ultraviolet Band, 11

1.3.4. Imaging in the Visible and Infrared Bands, 12

1.3.5. Imaging in the Microwave Band, 18

1.3.6. Imaging in the Radio Band, 20

1.3.7. Examples in which Other Imaging Modalities Are Used, 20

1.4. Fundamental Steps in Digital Image Processing, 25

1.5. Components of an Image Processing System, 28

References and Further Reading, 31

2. Digital Image Fundamentals, 35

2.1. Elements of Visual Perception, 36

2.1.1. Structure of the Human Eye, 36

2.1.2. Image Formation in the Eye, 38

2.1.3. Brightness Adaptation and Discrimination, 39

2.2. Light and the Electromagnetic Spectrum, 43

2.3. Image Sensing and Acquisition, 46

2.3.1. Image Acquisition Using a Single Sensor, 48

2.3.2. Image Acquisition Using Sensor Strips, 48

2.3.3. Image Acquisition Using Sensor Arrays, 50

2.3.4. A Simple Image Formation Model, 50

2.4. Image Sampling and Quantization, 52

2.4.1. Basic Concepts in Sampling and Quantization, 52

2.4.2. Representing Digital Images, 55

2.4.3. Spatial and Intensity Resolution, 59

2.4.4. Image Interpolation, 65

2.5. Some Basic Relationships between Pixels, 68

2.5.1. Neighbors of a Pixel, 68

2.5.2. Adjacency, Connectivity, Regions, and Boundaries, 68

2.5.3. Distance Measures, 71

2.6. An Introduction to the Mathematical Tools Used in Digital Image Processing, 72

2.6.1. Array versus Matrix Operations, 72

2.6.2. Linear versus Nonlinear Operations, 73

2.6.3. Arithmetic Operations, 74

2.6.4. Set and Logical Operations, 80

2.6.5. Spatial Operations, 85

2.6.6. Vector and Matrix Operations, 92

2.6.7. Image Transforms, 93

2.6.8. Probabilistic Methods, 96

References and Further Reading, 98

3. Intensity Transformations and Spatial Filtering, 104

3.1. Background, 105

3.1.1. The Basics of Intensity Transformations and Spatial Filtering, 105

3.1.2. About the Examples in This Chapter, 107

3.2. Some Basic Intensity Transformation Functions, 107

3.2.1. Image Negatives, 108

3.2.2. Log Transformations, 109

3.2.3. Power-Law (Gamma) Transformations, 110

3.2.4. Piecewise-Linear Transformation Functions, 115

3.3. Histogram Processing, 120

3.3.1. Histogram Equalization, 122

3.3.2. Histogram Matching (Specification), 128

3.3.3. Local Histogram Processing, 139

3.3.4. Using Histogram Statistics for Image Enhancement, 139

3.4. Fundamentals of Spatial Filtering, 144

3.4.1. The Mechanics of Spatial Filtering, 145

3.4.2. Spatial Correlation and Convolution, 146

3.4.3. Vector Representation of Linear Filtering, 150

3.4.4. Generating Spatial Filter Masks, 151

3.5. Smoothing Spatial Filters, 152

3.5.1. Smoothing Linear Filters, 152

3.5.2. Order-Statistic (Nonlinear) Filters, 156

3.6. Sharpening Spatial Filters, 157

3.6.1. Foundation, 158

3.6.2. Using the Second Derivative for Image Sharpening—The Laplacian, 160

3.6.3. Unsharp Masking and Highboost Filtering, 162

3.6.4. Using First-Order Derivatives for (Nonlinear) Image Sharpening—The Gradient, 165

3.7. Combining Spatial Enhancement Methods, 169

3.8. Using Fuzzy Techniques for Intensity Transformations and Spatial Filtering, 173

3.8.1. Introduction, 173

3.8.2. Principles of Fuzzy Set Theory, 174

3.8.3. Using Fuzzy Sets, 178

3.8.4. Using Fuzzy Sets for Intensity Transformations, 186

3.8.5. Using Fuzzy Sets for Spatial Filtering, 189

References and Further Reading, 192

4. Filtering in the Frequency Domain, 199

4.1. Background, 200

4.1.1. A Brief History of the Fourier Series and Transform, 200

4.1.2. About the Examples in this Chapter, 201

4.2. Preliminary Concepts, 202

4.2.1. Complex Numbers, 202

4.2.2. Fourier Series, 203

4.2.3. Impulses and Their Sifting Property, 203

4.2.4. The Fourier Transform of Functions of One Continuous Variable, 205

4.2.5. Convolution, 209

4.3. Sampling and the Fourier Transform of Sampled Functions, 211

4.3.1. Sampling, 211

4.3.2. The Fourier Transform of Sampled Functions, 212

4.3.3. The Sampling Theorem, 213

4.3.4. Aliasing, 217

4.3.5. Function Reconstruction (Recovery) from Sampled Data, 219

4.4. The Discrete Fourier Transform (DFT) of One Variable, 220

4.4.1. Obtaining the DFT from the Continuous Transform of a Sampled Function, 221

4.4.2. Relationship Between the Sampling and Frequency Intervals, 223

4.5. Extension to Functions of Two Variables, 225

4.5.1. The 2-D Impulse and Its Sifting Property, 225

4.5.2. The 2-D Continuous Fourier Transform Pair, 226

4.5.3. Two-Dimensional Sampling and the 2-D Sampling Theorem, 227

4.5.4. Aliasing in Images, 228

4.5.5. The 2-D Discrete Fourier Transform and Its Inverse, 235

4.6. Some Properties of the 2-D Discrete Fourier Transform, 236

4.6.1. Relationships Between Spatial and Frequency Intervals, 236

4.6.2. Translation and Rotation, 236

4.6.3. Periodicity, 237

4.6.4. Symmetry Properties, 239

4.6.5. Fourier Spectrum and Phase Angle, 245

4.6.6. The 2-D Convolution Theorem, 249

4.6.7. Summary of 2-D Discrete Fourier Transform Properties, 253

4.7. The Basics of Filtering in the Frequency Domain, 255

4.7.1. Additional Characteristics of the Frequency Domain, 255

4.7.2. Frequency Domain Filtering Fundamentals, 257

4.7.3. Summary of Steps for Filtering in the Frequency Domain, 263

4.7.4. Correspondence Between Filtering in the Spatial and Frequency Domains, 263

4.8. Image Smoothing Using Frequency Domain Filters, 269

4.8.1. Ideal Lowpass Filters, 269

4.8.2. Butterworth Lowpass Filters, 273

4.8.3. Gaussian Lowpass Filters, 276

4.8.4. Additional Examples of Lowpass Filtering, 277

4.9. Image Sharpening Using Frequency Domain Filters, 280

4.9.1. Ideal Highpass Filters, 281

4.9.2. Butterworth Highpass Filters, 284

4.9.3. Gaussian Highpass Filters, 285

4.9.4. The Laplacian in the Frequency Domain, 286

4.9.5. Unsharp Masking, Highboost Filtering, and High-Frequency-Emphasis Filtering, 288

4.9.6. Homomorphic Filtering, 289

4.10. Selective Filtering, 294

4.10.1. Bandreject and Bandpass Filters, 294

4.10.2. Notch Filters, 294

4.11. Implementation, 298

4.11.1. Separability of the 2-D DFT, 298

4.11.2. Computing the IDFT Using a DFT Algorithm, 299

4.11.3. The Fast Fourier Transform (FFT), 299

4.11.4. Some Comments on Filter Design, 303

References and Further Reading, 304

5. Image Restoration and Reconstruction, 311

5.1. A Model of the Image Degradation/Restoration Process, 312

5.2. Noise Models, 313

5.2.1. Spatial and Frequency Properties of Noise, 313

5.2.2. Some Important Noise Probability Density Functions, 314

5.2.3. Periodic Noise, 318

5.2.4. Estimation of Noise Parameters, 319

5.3. Restoration in the Presence of Noise Only—Spatial Filtering, 322

5.3.1. Mean Filters, 322

5.3.2. Order-Statistic Filters, 325

5.3.3. Adaptive Filters, 330

5.4. Periodic Noise Reduction by Frequency Domain Filtering, 335

5.4.1. Bandreject Filters, 335

5.4.2. Bandpass Filters, 336

5.4.3. Notch Filters, 337

5.4.4. Optimum Notch Filtering, 338

5.5. Linear, Position-Invariant Degradations, 343

5.6. Estimating the Degradation Function, 346

5.6.1. Estimation by Image Observation, 346

5.6.2. Estimation by Experimentation, 347

5.6.3. Estimation by Modeling, 347

5.7. Inverse Filtering, 351

5.8. Minimum Mean Square Error (Wiener) Filtering, 352

5.9. Constrained Least Squares Filtering, 357

5.10. Geometric Mean Filter, 361

5.11. Image Reconstruction from Projections, 362

5.11.1. Introduction, 362

5.11.2. Principles of Computed Tomography (CT), 365

5.11.3. Projections and the Radon Transform, 368

5.11.4. The Fourier-Slice Theorem, 374

5.11.5. Reconstruction Using Parallel-Beam Filtered Backprojections, 375

5.11.6. Reconstruction Using Fan-Beam Filtered Backprojections, 381

References and Further Reading, 388

6. Color Image Processing, 394

6.1. Color Fundamentals, 395

6.2. Color Models, 401

6.2.1. The RGB Color Model, 402

6.2.2. The CMY and CMYK Color Models, 406

6.2.3. The HSI Color Model, 407

6.3. Pseudocolor Image Processing, 414

6.3.1. Intensity Slicing, 415

6.3.2. Intensity to Color Transformations, 418

6.4. Basics of Full-Color Image Processing, 424

6.5. Color Transformations, 426

6.5.1. Formulation, 426

6.5.2. Color Complements, 430

6.5.3. Color Slicing, 431

6.5.4. Tone and Color Corrections, 433

6.5.5. Histogram Processing, 438

6.6. Smoothing and Sharpening, 439

6.6.1. Color Image Smoothing, 439

6.6.2. Color Image Sharpening, 442

6.7. Image Segmentation Based on Color, 443

6.7.1. Segmentation in HSI Color Space, 443

6.7.2. Segmentation in RGB Vector Space, 445

6.7.3. Color Edge Detection, 447

6.8. Noise in Color Images, 451

6.9. Color Image Compression, 454

References and Further Reading, 456

7. Wavelets and Multiresolution Processing, 461

7.1. Background, 462

7.1.1. Image Pyramids, 463

7.1.2. Subband Coding, 466

7.1.3. The Haar Transform, 474

7.2. Multiresolution Expansions, 477

7.2.1. Series Expansions, 477

7.2.2. Scaling Functions, 479

7.2.3. Wavelet Functions, 483

7.3. Wavelet Transforms in One Dimension, 486

7.3.1. The Wavelet Series Expansions, 486

7.3.2. The Discrete Wavelet Transform, 488

7.3.3. The Continuous Wavelet Transform, 491

7.4. The Fast Wavelet Transform, 493

7.5. Wavelet Transforms in Two Dimensions, 501

7.6. Wavelet Packets, 510

References and Further Reading, 520

8. Image Compression, 525

8.1. Fundamentals, 526

8.1.1. Coding Redundancy, 528

8.1.2. Spatial and Temporal Redundancy, 529

8.1.3. Irrelevant Information, 530

8.1.4. Measuring Image Information, 531

8.1.5. Fidelity Criteria, 534

8.1.6. Image Compression Models, 536

8.1.7. Image Formats, Containers, and Compression Standards, 538

8.2. Some Basic Compression Methods, 542

8.2.1. Huffman Coding, 542

8.2.2. Golomb Coding, 544

8.2.3. Arithmetic Coding, 548

8.2.4. LZW Coding, 551

8.2.5. Run-Length Coding, 553

8.2.6. Symbol-Based Coding, 559

8.2.7. Bit-Plane Coding, 562

8.2.8. Block Transform Coding, 566

8.2.9. Predictive Coding, 584

8.2.10. Wavelet Coding, 604

8.3. Digital Image Watermarking, 614

References and Further Reading, 622

9. Morphological Image Processing, 627

9.1. Preliminaries, 628

9.2. Erosion and Dilation, 630

9.2.1. Erosion, 631

9.2.2. Dilation, 633

9.2.3. Duality, 635

9.3. Opening and Closing, 635

9.4. The Hit-or-Miss Transformation, 640

9.5. Some Basic Morphological Algorithms, 642

9.5.1. Boundary Extraction, 642

9.5.2. Hole Filling, 643

9.5.3. Extraction of Connected Components, 645

9.5.4. Convex Hull, 647

9.5.5. Thinning, 649

9.5.6. Thickening, 650

9.5.7. Skeletons, 651

9.5.8. Pruning, 654

9.5.9. Morphological Reconstruction, 656

9.5.10. Summary of Morphological Operations on Binary Images, 662

9.6. Gray-Scale Morphology, 665

9.6.1. Erosion and Dilation, 666

9.6.2. Opening and Closing, 668

9.6.3. Some Basic Gray-Scale Morphological Algorithms, 670

9.6.4. Gray-Scale Morphological Reconstruction, 676

References and Further Reading, 679

10. Image Segmentation, 689

10.1. Fundamentals, 690

10.2. Point, Line, and Edge Detection, 692

10.2.1. Background, 692

10.2.2. Detection of Isolated Points, 696

10.2.3. Line Detection, 697

10.2.4. Edge Models, 700

10.2.5. Basic Edge Detection, 706

10.2.6. More Advanced Techniques for Edge Detection, 714

10.2.7. Edge Linking and Boundary Detection, 725

10.3. Thresholding, 738

10.3.1. Foundation, 738

10.3.2. Basic Global Thresholding, 741

10.3.3. Optimum Global Thresholding Using Otsu’s Method, 742

10.3.4. Using Image Smoothing to Improve Global Thresholding, 747

10.3.5. Using Edges to Improve Global Thresholding, 749

10.3.6. Multiple Thresholds, 752

10.3.7. Variable Thresholding, 756

10.3.8. Multivariable Thresholding, 761

10.4. Region-Based Segmentation, 763

10.4.1. Region Growing, 763

10.4.2. Region Splitting and Merging, 766

10.5. Segmentation Using Morphological Watersheds, 769

10.5.1. Background, 769

10.5.2. Dam Construction, 772

10.5.3. Watershed Segmentation Algorithm, 774

10.5.4. The Use of Markers, 776

10.6. The Use of Motion in Segmentation, 778

10.6.1. Spatial Techniques, 778

10.6.2. Frequency Domain Techniques, 782

References and Further Reading, 785

11. Representation and Description, 795

11.1. Representation, 796

11.1.1. Boundary (Border) Following, 796

11.1.2. Chain Codes, 798

11.1.3. Polygonal Approximations Using Minimum-Perimeter Polygons, 801

11.1.4. Other Polygonal Approximation Approaches, 807

11.1.5. Signatures, 808

11.1.6. Boundary Segments, 810

11.1.7. Skeletons, 812

11.2. Boundary Descriptors, 815

11.2.1. Some Simple Descriptors, 815

11.2.2. Shape Numbers, 816

11.2.3. Fourier Descriptors, 818

11.2.4. Statistical Moments, 821

11.3. Regional Descriptors, 822

11.3.1. Some Simple Descriptors, 822

11.3.2. Topological Descriptors, 823

11.3.3. Texture, 827

11.3.4. Moment Invariants, 839

11.4. Use of Principal Components for Description, 842

11.5. Relational Descriptors, 852

References and Further Reading, 856

12. Object Recognition, 861

12.1. Patterns and Pattern Classes, 861

12.2. Recognition Based on Decision-Theoretic Methods, 866

12.2.1. Matching, 866

12.2.2. Optimum Statistical Classifiers, 872

12.2.3. Neural Networks, 882

12.3. Structural Methods, 903

12.3.1. Matching Shape Numbers, 903

12.3.2. String Matching, 904

References and Further Reading, 906

Appendix A. Coding Tables for Image Compression, 910

Bibliography, 915

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ABOUT THIS TITLE - DESCRIPTION

For courses in Image Processing and Computer Vision. Completely self-contained–and heavily illustrated–this introduction to basic concepts and methodologies for digital image processing is written at a level that truly is suitable for seniors and first-year graduate students in almost any technical discipline. The leading textbook in its field for more than twenty years, it continues its cutting-edge focus on contemporary developments in all mainstream areas of image processing–e.g., image fundamentals, image enhancement in the spatial and frequency domains, restoration, color image processing, wavelets, image compression, morphology, segmentation, image description, and the fundamentals of object recognition. It focuses on material that is fundamental and has a broad scope of application.

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