Image Processing for Computer Graphics and Vision (eBook)

Preface 6
Contents 8
Introduction 15
Computer Graphics 15
Abstraction Paradigms 17
About This Book 19
Comments and References 22
Signal Theory 26
Abstraction Paradigms 26
Levels of Abstraction 27
Mathematical Models for Signals 28
Approximation of Signals 29
Functional Models and Abstraction Levels 31
The Spatial Model 32
The Frequency Model 35
Linear Representation of Signals 40
Existence of Exact Representations 42
Operations on Signals 45
Filters 45
Transforms 46
Filtering and Frequencies 47
Sampling Theory 48
Uniform Point Sampling 49
Point Sampling and the Fourier Transform 51
The Sampling Theorem 54
Extensions of the Sampling Theorem 57
Operations in the Discrete Domain 59
Discrete Convolution 60
The Discrete Fourier Transform 60
The Inverse Discrete Transform 63
Properties of the DFT 63
The Discrete Transform on the Interval [0,A] 64
Matrix Representation of the DFT 65
The Fast Fourier Transform 65
Finite Transform 66
Comments and References 66
Random Processes 69
Random Variables 69
Stochastic Processes 75
Point Processes 77
Homogeneous Processes with Independence 77
Inhomogeneity and/or Dependence 80
Comments and References 84
Fundamentals of Color 86
Paradigms in the Study of Color 86
The Physical Universe of Color 87
Color Formation 87
Photometry and Colorimetry 89
The Mathematical Universe of Color 90
The Representation Universe of Color 91
Color Sampling 91
Color Reconstruction 94
Computation of Primary Components 96
CIE-RGB Representation 99
Color Matching Experiments 101
Luminance and Chrominance 102
The Color Solid 106
Chromaticity Space 106
Grassmann's Laws 109
Comments and References 111
Color Systems 113
Preliminary Notions 113
Changing Between Color Systems 114
Color Systems and Computer Graphics 116
Standard Color Systems 116
The CIE-RGB Standard 117
The CIE-XYZ Standard 118
Changing Between the CIE-RGB and CIE-XYZSystems 120
Complementary Color Systems 125
Uniform Color Systems 126
Device Color Systems 127
The Monitor RGB System 127
Monitor-Complementary Systems 129
Component Video Systems 130
Composite Video Systems 134
Color Interface Systems 135
The HSV System 137
The HSL System 139
The Munsell System 139
The Pantone System 141
Computational Color Systems 142
Color Transformations 143
Comments and References 143
Digital Images 145
Abstraction Paradigms for Images 145
The Spatial Model 146
Continuous Images 146
Image Representation 148
Digital Images 149
Digital Topology 151
Pixel Shape 152
Comments and References 155
Operations on Images 157
Arithmetic Operations 157
Filters 159
Classification 160
Morphological Filters 162
Spatially Invariant Filters 164
Spatially Invariant Linear Filters 165
Discrete Filters 167
Extending the Domain of the Image 172
Examples of Linear Filters 176
Edge Enhancement Operations 189
Laplacian Addition 189
Unsharp Masking 192
Difference of Gaussians 193
Comments and References 194
Sampling and Reconstruction 197
Sampling 197
Time-Domain Viewpoint 197
Frequency-Domain Viewpoint 198
Reconstruction 198
Frequency Domain Viewpoint 198
Time-Domain Viewpoint 199
Aliasing 201
Aliasing in Computer-Generated Images 204
Reconstruction Problems 206
Reconstruction Using a Box Filter 207
Analysis of Reconstruction Problems 208
Some Classical Reconstruction Filters 210
A Study of Reconstruction Problems 213
Reconstructing After Aliasing 221
A Case Study 223
Comments and References 225
Multiscale Analysis and Wavelets 227
The Wavelet Transform 227
Inverse of the Wavelet Transform 228
Image of the Wavelet Transform 229
Filtering and the Wavelet Transform 230
The Discrete Wavelet Transform 234
Function Representation 236
Multiresolution Representation 238
Scale Spaces 239
Multiresolution Representation 242
A Pause to Think 243
Multiresolution Representation and Wavelets 245
A Pause... to See the Wavescape 248
Two Scale Relation 249
The Fast Wavelet Transform 250
Multiresolution Representation and Recursion 251
Two-Scale Relations and Inner Products 253
Wavelet Decomposition and Reconstruction 254
Decomposition 254
Reconstruction 255
The Fast Wavelet Transform Algorithm 256
Forward Transform 256
Inverse Transform 257
Complexity Analysis of the Algorithm 258
Boundary Conditions 259
Images and 2D-Wavelets 260
Tensor Product Extension 260
The 2D Algorithm 261
Comments and References 263
Probabilistic Image Models 265
Image Formation 265
Observed Data 266
Histograms and Estimation 271
Correlated Observations 286
Filtering 289
Classes 295
Comments and References 298
Color Quantization 303
Quantization Cells 305
Quantization and Perception 306
Overview of the Quantization Process 308
Quantization Error 309
Color Frequency Histograms 309
Uniform and Adaptive Quantization 310
Color Map Quantization 311
Test Images 311
Adaptive Quantization Methods 312
Quantization by Direct Selection 313
Quantization by Recursive Subdivision 313
Optimization Methods for Quantization 317
Optimal One-Dimensional Quantization 318
Optimal Quantization by Relaxation 319
Optimal Quantization by Simulated Annealing 320
Comments and References 320
Digital Halftoning 322
Dithering 322
Dithering by Random Modulation 326
A Classification of Dithering Algorithms 327
Periodic Dithering 329
Clustered Ordered Dithering 331
Dot Dispersion Ordered Dithering 336
Pattern Dithering 338
Nonperiodic Dithering 339
The Floyd--Steinberg Algorithm 339
Dithering with Space-Filling Curves 340
Comments and References 349
Image Compression 354
Image Encoding 354
Image Compression 358
Compression by Image Model 359
Compression by Image Representation 360
Compression and Multiscale Analysis 361
Two-Channel Encoding 362
Multiscale Representation of an Image 365
Comments and References 366
Combining Images 369
Preliminaries 369
Combining Images Algebraically 370
Mixing Images 371
Combining Images by Decomposing the Domain 372
Partitions of Unity and Decompositions 373
Image Compositing 374
Combining Images in the Discrete Domain 376
The Opacity Function 376
Discretization and Opacity Function 378
Computation of the Opacity Function 380
Compositing in the Discrete Domain 382
Compositing Using the Alpha Channel 382
Compositing Using Bitmasks 384
Compositing Operations 385
The Overlay Operator 386
The Inside Operator 388
The Outside Operator 388
The Atop Operator 389
The Xor Operator 390
The Clear Operator 391
The Set Operator 391
Comments and References 392
Warping and Morphing 394
Warping Filters 394
Warping in the Continuous Domain 395
Expansions and Contractions 396
Warping in the Discrete Domain 398
Resampling 399
Some Examples 401
Zooming 402
Warping in Practice 406
Approximating the Pixel Geometry 407
Warping Using the Direct Map 408
Warping Using the Inverse Map 410
Decomposable Transformations 411
Morphing 414
Continuous Families of Transformations 416
Comments and References 419
Image Systems 420
Image Characteristics 420
Matrix Representation of a Digital Image 421
Pixel Geometry 422
Image Display 423
Support Media 424
Tone Maps 424
Calibration 426
Cross Rendering 427
Gamut Transformations 427
Color Correction 428
Luminance Overflow 428
Unrealizable Colors 428
Display Models 429
Physical Reconstruction Function 431
Electronic Publishing Systems 433
Offset Printing 434
Comments and References 442
Appendix: Radiometry and Photometry 445
Radiometry 445
Radiometric Magnitudes 448
Spectral Distribution 450
Photometric Variables 452
Comments and References 455
Index 456