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Copyright, ii
Preface, xv
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
Summary, 31
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
Summary, 98
References and Further Reading, 98
Problems, 99
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
Summary, 192
References and Further Reading, 192
Problems, 193
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
Summary, 303
References and Further Reading, 304
Problems, 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
Summary, 387
References and Further Reading, 388
Problems, 389
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
Summary, 455
References and Further Reading, 456
Problems, 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
Summary, 520
References and Further Reading, 520
Problems, 521
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
Summary, 621
References and Further Reading, 622
Problems, 623
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
Summary, 679
References and Further Reading, 679
Problems, 680
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
Summary, 785
References and Further Reading, 785
Problems, 787
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
Summary, 856
References and Further Reading, 856
Problems, 857
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
Summary, 906
References and Further Reading, 906
Problems, 907
Appendix A. Coding Tables for Image Compression, 910
Bibliography, 915
Index, 943

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