Table of contents for Digital image processing / Rafael C. Gonzalez, Richard E. Woods.


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What Is Digital Image Processing? 15
The Origins of Digital Image Processing 17
Examples of Fields that Use Digital Image Processing 21
1.3.1 Gamma-Ray Imaging 22
1.3.2 X-ray Imaging 23
1.3.3 Imaging in the Ultraviolet Band 25
1.3.4 Imaging in the Visible and Infrared Bands 26
1.3.5 Imaging in the Microwave Band  32
1.3.6 Imaging in the Radio Band 34
1.3.7 Examples in which Other Imaging Modalities Are Used 34
Fundamental Steps in Digital Image Processing 39
Components of an Image Processing System 42
Summary 44
References and Further Reading 45


Digital Image Fundamentals 34
Elements of Visual Perception 34
2.1.1 Structure of the Human Eye 35
2.1.2 Image Formation in the Eye 37
2.1.3 Brightness Adaptation and Discrimination 38
Light and the Electromagnetic Spectrum 42
Image Sensing and Acquisition 45
2.3.1 Image Acquisition Using a Single Sensor 47
2.3.2 Image Acquisition Using Sensor Strips 48
2.3.3 Image Acquisition Using Sensor Arrays 49
2.3.4 A Simple Image Formation Model 50
Image Sampling and Quantization 52
12.4.1 Basic Concepts in Sampling and Quantization 52
2.4.2 Representing Digital Images 54
2.4.3 Spatial and Gray-Level Resolution  57
2.4.4 Aliasing and Moire Patterns 62
2.4.5 Zooming and Shrinking Digital Images 64



Background 76
Some Basic Gray Level Transformations 78
3.2.1 Image Negatives 78
3.2.2 Log Transformations 79
3.2.3 Power-Law Transformations 80
3.2.4 Piecewise-Linear Transformation Functions 85
Histogram Processing 88
3.3.1 Histogram Equalization 91
3.3.2 Histogram Matching (Specification) 94
3.3.3 Local Enhancement 103
3.3.4 Use of Histogram Statistics for Image Enhancement 103
Enhancement Using Arithmetic/Logic Operations 108
3.4.1 Image Subtraction 110
3.4.2 Image Averaging  112
Basics of Spatial Filtering 116
Smoothing Spatial Filters 119
3.6.1 Smoothing Linear Filters 119
3.6.2 Order-Statistics Filters 123
Sharpening Spatial Filters 125
3.7.1 Foundation 125
3.7.2 Use of Second Derivatives for Enhancement-
     The Laplacian 128
3.7.3 Use of First Derivatives for Enhancement-The Gradient 134
Combining Spatial Enhancement Methods 137
Summary   141
References and Further Reading 142
Problems 142



Image Enhancement in the Frequency
Domain 147
Background 148



Introduction to the Fourier Transform and the Frequency
Domain 149
4.2.1 The One-Dimensional Fourier Transform and its Inverse 150
4.2.2 The Two-Dimensional DFT and Its Inverse 154
4.2.3 Filtering in the Frequency Domain  156
4.2.4 Correspondence between Filtering in the Spatial
      and Frequency Domains 161
Smoothing Frequency-Domain Filters 167
4.3.1 Ideal Lowpass Filters 167
4.3.2 Butterworth Lowpass Filters 173
4.3.3 Gaussian Lowpass Filters 175
4.3.4 Additional Examples of Lowpass Filtering 178
Sharpening Frequency Domain Filters 180
4.4.1 Ideal Highpass Filters 182
4.4.2 Butterworth Highpass Filters 183
4.4.3 Gaussian Highpass Filters 184
4.4.4 The Laplacian in the Frequency Domain  185
4.4.5 Unsharp Masking, High-Boost Filtering,
      and High-Frequency Emphasis Filtering 187
Homomorphic Filtering 191
Implementation 194
4.6.1 Some Additional Properties of the 2-D Fourier Transform  194
4.6.2 Computing the Inverse Fourier Transform Using a Forward
      Transform Algorithm 198
4.6.3 More on Periodicity: the Need for Padding  199
4.6.4 The Convolution and Correlation Theorems 205
4.6.5 Summary of Properties of the 2-D Fourier Transform  208
4.6.6 The Fast Fourier Transform  208
4.6.7 Some Comments on Filter Design  213
Summary 214
References 214
Problems 215



Image Restoration         220
A Model of the Image Degradation/Restoration Process 221
Noise Models 222
5.2.1 Spatial and Frequency Properties of Noise 222
5.2.2 Some Important Noise Probability Density Functions 222
5.2.3 Periodic Noise 227
5.2.4 Estimation of Noise Parameters 227
Restoration in the Presence of Noise Only-Spatial Filtering 230
5.3.1 Mean Filters 231
5.3.2 Order-Statistics Filters 233
5.3.3 Adaptive Filters 237



Periodic Noise Reduction by Frequency Domain Filtering 243
5.4.1 Bandreject Filters 244
5.4.2 Bandpass Filters 245
5.4.3 Notch Filters 246
5.4.4 Optimum Notch Filtering 248
Linear, Position-Invariant Degradations 254
Estimating the Degradation Function 256
5.6.1 Estimation by Image Observation 256
5.6.2 Estimation by Experimentation 257
5.6.3 Estimation by Modeling 258
Inverse Filtering 261
Minimum Mean Square Error (Wiener) Filtering 262
Constrained Least Squares Filtering 266
Geometric Mean Filter 270
Geometric Transformations 270
5.11.1 Spatial Transformations 271
5.11.2 Gray-Level Interpolation 272
Summary 276
References and Further Reading 277
Problems 278



Color Image Processing 282
Color Fundamentals 283
Color Models 289
6.2.1 The RGB Color Model 290
6.2.2 The CMY and CMYK Color Models 294
6.2.3 The HSI Color Model 295
Pseudocolor Image Processing 302
6.3.1 Intensity Slicing 303
6.3.2 Gray Level to Color Transformations 308
Basics of Full-Color Image Processing 313
Color Transformations 315
6.5.1 Formulation 315
6.5.2 Color Complements 318
6.5.3 Color Slicing 320
6.5.4 Tone and Color Corrections 322
6.5.5 Histogram Processing 326
Smoothing and Sharpening 327
6.6.1 Color Image Smoothing 328
6.6.2 Color Image Sharpening 330
Color Segmentation 331
6.7.1 Segmentation in HSI Color Space 331
6.7.2 Segmentation in RGB Vector Space 333
6.7.3 Color Edge Detection 335



Noise in Color Images 339
Color Image Compression 342
Summary 343
References and Further Reading 344
Problems 344



Wavelets and Multiresolution Processing             349
Background 350
7.1.1 Image Pyramids 351
7.1.2 Subband Coding  354
7.1.3 The Haar Transform 360
Multiresolution Expansions 363
7.2.1 Series Expansions 364
7.2.2 Scaling Functions 365
7.2.3 Wavelet Functions 369
Wavelet Transforms in One Dimension 372
7.3.1 The Wavelet Series Expansions 372
7.3.2 The Discrete Wavelet Transform 375
7.3.3 The Continuous Wavelet Transform 376
The Fast Wavelet Transform 379
Wavelet Transforms in Two Dimensions 386
Wavelet Packets 394
Summary 402
References and Further Reading 404
Problems 404



Image Compression 409
Fundamentals 411
8.1.1 Coding Redundancy 412
8.1.2 Interpixel Redundancy 414
8.1.3 Psychovisual Redundancy 417
8.1.4 Fidelity Criteria 419
Image Compression Models 421
8.2.1 The Source Encoder and Decoder 421
8.2.2 The Channel Encoder and Decoder 423
Elements of Information Theory 424
8.3.1 Measuring Information 424
8.3.2 The Information Channel 425
8.3.3 Fundamental Coding Theorems 430
8.3.4 Using Information Theory 437
Error-Free Compression 440
8.4.1 Variable-Length Coding 440



8.4.2 LZW Coding 446
8.4.3 Bit-Plane Coding 448
8.4.4 Lossless Predictive Coding 456
Lossy Compression 459
8.5.1 Lossy Predictive Coding 459
8.5.2 Transform Coding 467
8.5.3 Wavelet Coding 486
Image Compression Standards 492
8.6.1 Binary Image Compression Standards 493
8.6.2 Continuous Tone Still Image Compression Standards 498
8.6.3 Video Compression Standards 510
Summary 513
References and Further Reading 513
Problems 514



Morphological Image Processing             519
Preliminaries 520
9.1.1 Some Basic Concepts from Set Theory 520
9.1.2 Logic Operations Involving Binary Images 522
Dilation and Erosion 523
9.2.1 Dilation 523
9.2.2 Erosion 525
Opening and Closing 528
The Hit-or-Miss Transformation 532
Some Basic Morphological Algorithms 534
9.5.1 Boundary Extraction  534
9.5.2 Region Filling 535
9.5.3 Extraction of Connected Components 536
9.5.4 Convex Hull 539
9.5.5 Thinning 541
9.5.6 Thickening 541
9.5.7 Skeletons 543
9.5.8 Pruning 545
9.5.9 Summary of Morphological Operations on Binary Images 547
Extensions to Gray-Scale Images 550
9.6.1 Dilation 550
9.6.2 Erosion 552
9.6.3 Opening and Closing 554
9.6.4 Some Applications of Gray-Scale Morphology 556
Summary 560
References and Further Reading 560
Problems 560



Detection of Discontinuities 568
10.1.1 Point Detection 569
10.1.2 Line Detection 570
10.1.3 Edge Detection 572
Edge Linking and Boundary Detection 585
10.2.1 Local Processing 585
10.2.2 Global Processing via the Hough Transform  587
10.2.3 Global Processing via Graph-Theoretic Techniques 591
Thresholding 595
10.3.1 Foundation  595
10.3.2 The Role of Illumination 596
10.3.3 Basic Global Thresholding 598
10.3.4 Basic Adaptive Thresholding 600
10.3.5 Optimal Global and Adaptive Thresholding  602
10.3.6 Use of Boundary Characteristics for Histogram Improvement
     and Local Thresholding 608
10.3.7 Thresholds Based on Several Variables 611
Region-Based Segmentation 612
10.4.1 Basic Formulation 612
10.4.2 Region Growing 613
10.4.3 Region Splitting and Merging 615
Segmentation by Morphological Watersheds 617
10.5.1 Basic Concepts 617
10.5.2 Dam Construction 620
10.5.3 Watershed Segmentation Algorithm  622
10.5.4 The Use of Markers 624
The Use of Motion in Segmentation 626
10.6.1 Spatial Techniques 626
10.6.2 Frequency Domain Techniques 630
Summary 634
References and Further Reading 634
Problems 636



Representation and Description 643
Representation 644
11.1.1 Chain Codes 644
11.1.2 Polygonal Approximations 646
11.13 Signatures 648
11.1.4 Boundary Segments 649
11.1.5 Skeletons 650



Boundary Descriptors 653
11.2.1 Some Simple Descriptors 653
11.2.2 Shape Numbers 654
11.2.3 Fourier Descriptors 655
11.2.4 Statistical Moments 659
i Regional Descriptors 660
11.3.1 Some Simple Descriptors 661
11.3.2 Topological Descriptors 661
11.3.3 Texture 665
11.3.4 Moments of Two-Dimensional Functions 672
Use of Principal Components for Description  675
Relational Descriptors 683
Summary 687
References and Further Reading 687
Problems 689



Object Recognition 693
Patterns and Pattern Classes 693
Recognition Based on Decision-Theoretic Methods 698
12.2.1 Matching 698
12.2.2 Optimum Statistical Classifiers 704
12.2.3 Neural Networks 712
Structural Methods 732
12.3.1 Matching Shape Numbers 732
12.3.2 String Matching 734
12.3.3 Syntactic Recognition of Strings 735
12.3.4 Syntactic Recognition of Trees 740
Summary 750
References and Further Reading 750
Problems 750








Library of Congress subject headings for this publication: Image processing Digital techniques