The multi-billion dollar industry of digital imaging technology is an active research area with applications in our everyday lives in products such as digital cameras, scanners, printers and display systems. This book presents an introduction to the fundamentals of digital imaging, with emphasis on the basic operations of image capture and display of monochrome and colour images. The authors balance the mathematical description of real problems with practical examples. With a colour-plate section and real-world applications, this book is suitable for graduate students taking courses in digital imaging in electrical engineering and computer science departments. It will also be a useful reference for practitioners in industry.
Author(s): H. J. Trussell, M. J. Vrhel
Publisher: Cambridge University Press
Year: 2008
Language: English
Pages: 552
Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Deadication......Page 7
Contents......Page 9
Preface......Page 17
Acknowledgments......Page 20
1.1 Digital imaging: overview......Page 21
1.2 Digital imaging: short history......Page 22
1.4 Methodology......Page 24
1.5 Prerequisite knowledge......Page 25
1.6 Overview of the book......Page 26
2.1 Images as functions......Page 28
2.1.2 Deterministic vs. stochastic......Page 31
2.1.3 Philosophical aspects of the problem......Page 32
Similarities of 1-D and 2-D functions......Page 33
2.2 Systems and operators......Page 34
2.2.1 Amplitude scaling......Page 35
2.2.3 Spatial scaling......Page 36
2.3 Linear systems (operators)......Page 37
2.4 Sampling representation......Page 40
2.5.3 Discrete convolution......Page 42
2.8 Problems......Page 52
3 Elementary display of images......Page 65
3.2 Contour plots......Page 66
3.3 Grayscale graphs......Page 67
3.3.1 Comparative display......Page 69
3.3.2 Grayscale inclusion......Page 73
3.3.3 Display of processed and nonpictorial images......Page 74
3.3.4 Nonlinear mappings and monitor adjustments......Page 76
3.4 Problems......Page 78
4.1 Appropriate quantization spaces......Page 81
4.2 Basic quantization......Page 84
4.2.2 Optimal quantization......Page 85
4.3 Companding quantizer......Page 86
4.3.1 Visual quantization......Page 87
4.4 Vector quantization......Page 88
4.4.1 Full search vector quantization......Page 89
4.4.2 LBG algorithm (generalized Lloyd)......Page 90
4.5 Quantization noise......Page 91
4.6 Problems......Page 95
5 Frequency domain representation......Page 97
5.1.1 One-dimensional transform......Page 98
Properties of Fourier transforms (1-D)......Page 99
5.1.2 Two-dimensional transform......Page 100
5.1.3 Examples of two-dimensional sinusoids......Page 101
5.2 Properties of 2-D Fourier transforms......Page 103
5.2.1 Relation between analog Fourier transforms and Fourier series......Page 105
5.3 Derivation of DFT from Fourier transform......Page 108
5.4 Two-dimensional discrete Fourier transform......Page 112
5.4.1 Common DFT pairs......Page 113
5.5 Discrete Fourier transform convolution using matrices......Page 114
5.6 Computation of 2-D DFT and the FFT......Page 116
One-dimensional transforms......Page 117
Two-dimensional transforms......Page 119
5.8 Problems......Page 130
6 Spatial sampling......Page 134
6.1.1 Ideal sampling, 1-D......Page 135
6.1.2 Ideal sampling, 2-D......Page 139
6.2 Sampling on nonrectangular lattices......Page 147
6.3 Sampling using finite apertures......Page 149
6.4 Ideal reconstruction of deterministic images......Page 151
6.5 Sampling and reconstruction of stochastic images......Page 152
6.6.1 One-dimensional reconstruction......Page 154
6.6.2 Two-dimensional reconstruction......Page 158
6.7 Problems......Page 163
7.1 Deterministic properties......Page 166
Region of support......Page 167
Range and histogram......Page 168
Color range and saturation......Page 170
7.1.2 Bandwidth......Page 171
7.1.3 Subspace concepts......Page 174
Subspaces of vector spaces......Page 175
Inner products and orthonormal expansions......Page 176
Subspace operations......Page 177
7.2 Stochastic properties......Page 182
Mean......Page 183
Autocovariance, autocorrelation and power spectrum......Page 184
7.2.2 Bandwidth......Page 186
7.2.3 Noise......Page 188
Signal-to-noise ratios......Page 191
Examples of noise in images......Page 192
NonFourier basis functions......Page 195
7.3 Models for generation of images......Page 197
Finite impulse response models......Page 199
7.4 Two-dimensional stochastic image models......Page 200
7.4.2 Determining prediction coefficients......Page 201
7.4.3 Filtered noise......Page 204
7.5 Problems......Page 206
8 Photometry and colorimetry......Page 211
8.1 Fundamentals of the eye......Page 212
8.2 Radiometry and photometry......Page 214
8.3 Mathematics of color matching......Page 221
8.3.1 Background......Page 223
8.3.2 Mathematical definition of color matching......Page 224
Property 1 (existence of color match)......Page 228
Property 3 (dependence of color on A)......Page 229
Property 4 (transformation of primaries)......Page 230
Property 6 (metamers and the human visual subspace)......Page 233
Property 7 (effect of illumination)......Page 235
Property 8 (ideal color recording)......Page 236
8.4 Mathematics of color reproduction......Page 237
8.4.1 Additive color systems......Page 238
8.4.2 Subtractive color systems......Page 240
8.5.1 Uniform color spaces......Page 243
8.5.2 Device independent and dependent spaces......Page 247
8.5.3 Pseudo-device independent spaces......Page 248
8.6 Color temperature......Page 249
8.7 Color measurement instruments......Page 250
8.7.1 Spectroradiometer......Page 252
8.7.2 Spectrophotometer......Page 254
8.7.3 Colorimeter......Page 256
8.7.4 Densitometer......Page 258
8.8 Problems......Page 261
9.1 Sampling for color reproduction......Page 265
9.2 Color aliasing......Page 268
9.3 Sampling for color computation......Page 269
9.3.1 Characteristics of color signals......Page 270
Sensors......Page 271
Reflectances and transmissivities......Page 272
Illuminations......Page 273
9.3.2 Color operations......Page 277
Aliasing......Page 280
Lowpass filtering......Page 281
9.3.4 Significance of the errors......Page 282
9.4 Problems......Page 283
10.1 Scanners......Page 286
10.1.1 Optical issues......Page 290
10.2.1 Pipeline......Page 293
10.2.2 The sensor......Page 297
10.2.3 Color separation......Page 298
10.2.4 Demosaicking......Page 299
10.2.5 White balance......Page 301
10.2.6 Appearance......Page 304
10.3 Multispectral and hyperspectral imaging......Page 305
10.4 Problems......Page 306
11.1 Cathode ray tube monitors......Page 309
11.2 Flat panel displays......Page 312
11.3.1 Monochromatic film......Page 320
11.3.3 Photographic prints......Page 322
11.4 Commercial printing......Page 324
11.5 Halftone reproduction......Page 326
Digital halftone......Page 328
Error diffusion......Page 335
Iterative and search-based methods......Page 341
Color halftone......Page 344
11.6 Ink-jet devices......Page 352
11.7 Electrophotographic imaging......Page 356
11.8 Dye sublimation......Page 360
11.9 Problems......Page 361
12.1 Goal of characterization......Page 364
12.2 Monochrome......Page 365
Scanners......Page 367
Cameras......Page 368
12.2.2 Output devices......Page 369
12.3 Color......Page 373
12.3.1 Device gamut......Page 377
12.3.2 Selection of interchange color space......Page 378
12.3.3 Calibration and profiling......Page 381
Densitometric approach......Page 383
Calibration mapping......Page 384
12.3.4 Color management systems......Page 385
12.3.5 Models......Page 386
Scanners......Page 387
Digital cameras......Page 389
12.3.7 Profiling of display devices......Page 390
Cathode ray tubes......Page 391
Printers......Page 392
12.3.8 Undercolor removal......Page 394
12.3.9 Perceptual issues......Page 396
12.3.10 Gamut mapping......Page 400
12.4 Problems......Page 406
13.1 Image formation models......Page 410
13.2 Estimation of sensor response......Page 411
13.3 Estimation of noise statistics......Page 413
13.3.1 Estimation of noise variance from experiments......Page 414
13.3.2 Estimation of noise variance from recoded data......Page 415
13.4 Estimation of the point spread function......Page 417
13.4.1 Estimation of the point spread function from a line spread function......Page 418
13.4.3 Estimation of the point spread function by spectral analysis......Page 419
Definition of the cepstrum......Page 420
13.5 Modeling point spread functions......Page 421
13.5.1 Optical apertures......Page 423
13.5.2 Motion point spread functions......Page 425
13.5.3 Distortions by imaging medium......Page 426
13.6 Problems......Page 428
14 Image restoration......Page 432
14.1 Restoration of spatial blurs......Page 433
14.1.1 Inverse filter......Page 434
Wiener filter......Page 436
Practical aspects......Page 437
Finite impulse response implementation......Page 438
14.1.5 Power spectral estimation......Page 439
14.1.6 Maximum a posteriori (MAP) restoration......Page 440
14.1.7 Constrained least squares (CLS) restoration......Page 441
14.1.8 Projection onto convex sets......Page 442
14.1.9 Examples of restoration of blurred images......Page 445
14.1.10 Estimation of scanner response......Page 454
14.2 Color and spectral correction......Page 455
14.2.2 Constrained estimation......Page 456
14.2.3 Minimum mean square error estimation......Page 457
14.3 Tristimulus value (color) correction......Page 458
14.4 Illuminant color correction......Page 459
14.5 Color photographic film exposure......Page 461
14.6 Problems......Page 462
A.1 Basic definition......Page 465
A.3 Frequency effects of sampling, 1-D......Page 467
A.4 Sampling, 2-D......Page 468
A.6 Generalized sampling......Page 470
B.2 Kronecker product......Page 474
B.2.1 Properties of the Kronecker product......Page 475
B.4 Matrix derivatives......Page 476
B.5 Generalized inverse (pseudoinverse)......Page 477
Derived properties......Page 478
B.5.1 Computing A+......Page 479
B.5.2 Relation to signal recovery......Page 480
B.6 Ill-conditioned matrices (systems)......Page 481
B.7 Properties of DFT matrices......Page 482
C.1 Basic probability definitions......Page 484
C.1.3 Central limit theorem......Page 485
C.2 Histograms......Page 486
C.3 Basic joint probability definitions......Page 487
C.3.2 Correlation and covariance......Page 488
C.4 Stochastic processes......Page 489
Stochastic images......Page 490
C.4.1 Stationary processes......Page 491
C.5 Transformations of stochastic signals......Page 493
C.7 Stochastic image models......Page 494
C.7.1 Estimation of stochastic parameters......Page 495
C.7.3 One-dimensional models......Page 496
Infinite impulse response models......Page 497
C.7.5 Maximum entropy extension of ryy(m)......Page 498
C.7.6 Problems with AR, MA and ARMA model identification......Page 499
C.8.2 Semicausal prediction......Page 500
C.9.1 Minimum variance prediction......Page 501
C.10.1 Solving for finite a(m,n)......Page 504
C.10.2 High resolution spectral estimation......Page 505
D.2 Mathematics of MLUTs......Page 506
D.2.1 Sample points......Page 507
D.3.1 Finding the cube index......Page 508
D.3.2 Finding subindices and weights......Page 509
D.3.3 Interpolation methods......Page 510
D.4 Creation of input device MLUTs......Page 511
D.5 Creation of output device MLUTs......Page 514
E.1 Optical system......Page 519
E.2 Sensing elements......Page 521
E.3 Processing elements......Page 522
E.4 Mathematical modeling......Page 524
E.4.1 Weber's law......Page 525
E.4.2 Spatial-color properties and opponent color spaces......Page 526
E.4.3 sCIELAB......Page 529
References......Page 532
Index......Page 547
