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Summary
Summary
Digital images have become mainstream of late notably within HDTV, cell phones, personal cameras, and many medical applications. The processing of digital images and video includes adjusting illumination, manufacturing enlargements/reductions, and creating contrast. This development has made it possible to take long forgotten, badly damaged photos and make them new again with image estimation. It can also help snapshot photographers with image restoration, a method of reducing the influence of an unsteady hand.
Dr. Woods has constructed a book for professionals and graduate students that will give them the thorough understanding of image and video processing that they need in order to contribute to this hot technology's future advances. Examples and problems at the end of each chapter help the reader digest what has just been read. Forged from a theoretical base, this exceptional book develops into an essential guide to hands-on endeavors in signal processing.
Table of Contents
Preface | p. xiii |
Acknowledgments | p. xvii |
1 Two-Dimensional Signals and Systems | p. 1 |
1.1 Two-Dimensional Signals | p. 2 |
1.1.1 Separable Signals | p. 6 |
1.1.2 Periodic signals | p. 7 |
1.1.3 2-D Discrete-Space Systems | p. 9 |
1.1.4 Two-Dimensional Convolution | p. 11 |
1.1.5 Stability of 2-D Systems | p. 13 |
1.2 2-D Discrete-Space Fourier Transform | p. 14 |
1.2.1 Inverse 2-D Fourier Transform | p. 18 |
1.2.2 Fourier Transform of 2-D or Spatial Convolution | p. 19 |
1.2.3 Symmetry Properties of Fourier Transform | p. 26 |
1.2.4 Continuous-Space Fourier Transform | p. 28 |
1.3 Conclusions | p. 31 |
1.4 Problems | p. 31 |
References | p. 33 |
2 Sampling in Two Dimensions | p. 35 |
2.1 Sampling Theorem-Rectangular Case | p. 36 |
2.1.1 Reconstruction Formula | p. 40 |
2.1.2 Ideal Rectangular Sampling | p. 43 |
2.2 Sampling Theorem-General Regular Case | p. 48 |
2.2.1 Hexagonal Reconstruction Formula | p. 52 |
2.3 Change of Sample Rate | p. 57 |
2.3.1 Downsampling by Integers M[subscript 1] x M[subscript 2] | p. 57 |
2.3.2 Ideal Decimation | p. 58 |
2.3.3 Upsampling by Integers L[subscript 1] x L[subscript 2] | p. 61 |
2.3.4 Ideal Interpolation | p. 62 |
2.4 Sample-Rate Change-General Case | p. 64 |
2.4.1 General Downsampling | p. 64 |
2.5 Conclusions | p. 66 |
2.6 Problems | p. 66 |
References | p. 70 |
3 Two-Dimensional Systems and Z-Transforms | p. 71 |
3.1 Linear Spatial or 2-D Systems | p. 72 |
3.2 Z-Transforms | p. 76 |
3.3 Regions of Convergence | p. 79 |
3.3.1 More General Case | p. 82 |
3.4 Some Z-Transform Properties | p. 83 |
3.4.1 Linear Mapping of Variables | p. 84 |
3.4.2 Inverse Z-Transform | p. 85 |
3.5 2-D Filter Stability | p. 89 |
3.5.1 First-Quadrant Support | p. 91 |
3.5.2 Second-Quadrant Support | p. 91 |
3.5.3 Root Maps | p. 96 |
3.5.4 Stability Criteria for NSHP Support Filters | p. 98 |
3.6 Conclusions | p. 100 |
3.7 Problems | p. 101 |
References | p. 103 |
4 Two-Dimensional Discrete Transforms | p. 105 |
4.1 Discrete Fourier Series | p. 106 |
4.1.1 Properties of the DFS Transform | p. 109 |
4.1.2 Periodic Convolution | p. 111 |
4.1.3 Shifting or Delay Property | p. 112 |
4.2 Discrete Fourier Transform | p. 113 |
4.2.1 DFT Properties | p. 115 |
4.2.2 Relation of DFT to Fourier Transform | p. 120 |
4.2.3 Effect of Sampling in Frequency | p. 121 |
4.2.4 Interpolating the DFT | p. 122 |
4.3 2-D Discrete Cosine Transform | p. 123 |
4.3.1 Review of 1-D DCT | p. 125 |
4.3.2 Some 1-D DCT Properties | p. 128 |
4.3.3 Symmetric Extension in 2-D DCT | p. 131 |
4.4 Subband/Wavelet Transform (SWT) | p. 132 |
4.4.1 Ideal Filter Case | p. 132 |
4.4.2 1-D SWT with Finite-Order Filter | p. 135 |
4.4.3 2-D SWT with FIR Filters | p. 137 |
4.4.4 Relation of SWT to DCT | p. 138 |
4.4.5 Relation of SWT to Wavelets | p. 138 |
4.5 Fast Transform Algorithms | p. 140 |
4.5.1 Fast DFT Algorithm | p. 140 |
4.5.2 Fast DCT Methods | p. 141 |
4.6 Sectioned Convolution Methods | p. 142 |
4.7 Conclusions | p. 143 |
4.8 Problems | p. 144 |
References | p. 147 |
5 Two-Dimensional Filter Design | p. 149 |
5.1 FIR Filter Design | p. 150 |
5.1.1 FIR Window Function Design | p. 150 |
5.1.2 Design by Transformation of 1-D Filter | p. 156 |
5.1.3 Projection-Onto-Convex-Sets Method | p. 161 |
5.2 IIR Filter Design | p. 165 |
5.2.1 2-D Recursive Filter Design | p. 165 |
5.2.2 Fully Recursive Filter Design | p. 171 |
5.3 Subband/Wavelet Filter Design | p. 174 |
5.3.1 Wavelet (Biorthogonal) Filter Design Method | p. 178 |
5.4 Conclusions | p. 182 |
5.5 Problems | p. 182 |
References | p. 187 |
6 Introductory Image Processing | p. 189 |
6.1 Light and Luminance | p. 190 |
6.2 Still Image Visual Properties | p. 194 |
6.2.1 Weber's Law | p. 195 |
6.2.2 Contrast Sensitivity Function | p. 196 |
6.2.3 Local Contrast Adaptation | p. 198 |
6.3 Time-Variant Human Visual System Properties | p. 199 |
6.4 Image Sensors | p. 201 |
6.4.1 Electronic | p. 201 |
6.4.2 Film | p. 203 |
6.5 Image and Video Display | p. 204 |
6.5.1 Gamma | p. 205 |
6.6 Simple Image Processing Filters | p. 206 |
6.6.1 Box Filter | p. 206 |
6.6.2 Gaussian Filter | p. 207 |
6.6.3 Prewitt Operator | p. 208 |
6.6.4 Sobel Operator | p. 208 |
6.6.5 Laplacian Filter | p. 209 |
6.7 Conclusions | p. 211 |
6.8 Problems | p. 211 |
References | p. 213 |
7 Image Estimation and Restoration | p. 215 |
7.1 2-D Random Fields | p. 216 |
7.1.1 Filtering a 2-D Random Field | p. 218 |
7.1.2 Autoregressive Random Signal Models | p. 222 |
7.2 Estimation for Random Fields | p. 224 |
7.2.1 Infinite Observation Domain | p. 225 |
7.3 2-D Recursive Estimation | p. 229 |
7.3.1 1-D Kalman Filter | p. 229 |
7.3.2 2-D Kalman Filtering | p. 233 |
7.3.3 Reduced Update Kalman Filter | p. 235 |
7.3.4 Approximate RUKF | p. 236 |
7.3.5 Steady-State RUKF | p. 236 |
7.3.6 LSI Estimation and Restoration Examples with RUKF | p. 237 |
7.4 Inhomogeneous Gaussian Estimation | p. 241 |
7.4.1 Inhomogeneous Estimation with RUKF | p. 243 |
7.5 Estimation in the Subband/Wavelet Domain | p. 244 |
7.6 Bayesian and MAP Estimation | p. 248 |
7.6.1 Gauss Markov Image Models | p. 249 |
7.6.2 Simulated Annealing | p. 253 |
7.7 Image Identification and Restoration | p. 257 |
7.7.1 Expectation-Maximization Algorithm Approach | p. 258 |
7.7.2 EM Method in the Subband/Wavelet Domain | p. 262 |
7.8 Color Image Processing | p. 263 |
7.9 Conclusions | p. 263 |
7.10 Problems | p. 263 |
References | p. 266 |
8 Digital Image Compression | p. 269 |
8.1 Introduction | p. 270 |
8.2 Transformation | p. 272 |
8.2.1 DCT | p. 272 |
8.2.2 SWT | p. 274 |
8.2.3 DPCM | p. 275 |
8.3 Quantization | p. 276 |
8.3.1 Uniform Quantization | p. 278 |
8.3.2 Optimal MSE Quantization | p. 278 |
8.3.3 Vector Quantization | p. 280 |
8.3.4 LBG Algorithm [7] | p. 282 |
8.4 Entropy Coding | p. 284 |
8.4.1 Huffman Coding | p. 285 |
8.4.2 Arithmetic Coding | p. 286 |
8.4.3 ECSQ and ECVQ | p. 287 |
8.5 DCT Coder | p. 289 |
8.6 SWT Coder | p. 292 |
8.6.1 Multiresolution SWT Coding | p. 298 |
8.6.2 Nondyadic SWT Decompositions | p. 300 |
8.6.3 Fully Embedded SWT Coders | p. 300 |
8.6.4 Embedded Zero-Tree Wavelet (EZW) Coder | p. 301 |
8.6.5 Set Partitioning in Hierarchical Trees (SPIHT) Coder | p. 304 |
8.6.6 Embedded Zero Block Coder (EZBC) | p. 306 |
8.7 JPEG 2000 | p. 308 |
8.8 Color Image Coding | p. 309 |
8.8.1 Scalable Coder Results Comparison | p. 311 |
8.9 Robustness Considerations | p. 311 |
8.10 Conclusions | p. 312 |
8.11 Problems | p. 312 |
References | p. 315 |
9 Three-Dimensional and Spatiotemporal Processing | p. 317 |
9.1 3-D Signals and Systems | p. 318 |
9.1.1 Properties of 3-D Fourier Transform | p. 320 |
9.1.2 3-D Filters | p. 321 |
9.2 3-D Sampling and Reconstruction | p. 321 |
9.2.1 General 3-D Sampling | p. 323 |
9.3 Spatiotemporal Signal Processing | p. 325 |
9.3.1 Spatiotemporal Sampling | p. 325 |
9.3.2 Spatiotemporal Filters | p. 326 |
9.3.3 Intraframe Filtering | p. 328 |
9.3.4 Intraframe Wiener Filter | p. 328 |
9.3.5 Interframe Filtering | p. 330 |
9.3.6 Interframe Wiener Filter | p. 331 |
9.4 Spatiotemporal Markov Models | p. 332 |
9.4.1 Causal and Semicausal 3-D Field Sequences | p. 333 |
9.4.2 Reduced Update Spatiotemporal Kalman Filter | p. 335 |
9.5 Conclusions | p. 338 |
9.6 Problems | p. 338 |
References | p. 339 |
10 Digital Video Processing | p. 341 |
10.1 Interframe Processing | p. 342 |
10.2 Motion Estimation and Motion Compensation | p. 348 |
10.2.1 Block Matching Method | p. 350 |
10.2.2 Hierarchical Block Matching | p. 353 |
10.2.3 Overlapped Block Motion Compensation | p. 354 |
10.2.4 Pel-Recursive Motion Estimation | p. 355 |
10.2.5 Optical flow methods | p. 356 |
10.3 Motion-Compensated Filtering | p. 358 |
10.3.1 MC-Wiener Filter | p. 358 |
10.3.2 MC-Kalman Filter | p. 360 |
10.3.3 Frame-Rate Conversion | p. 363 |
10.3.4 Deinterlacing | p. 365 |
10.4 Bayesian Method for Estimating Motion | p. 371 |
10.4.1 Joint Motion Estimation and Segmentation | p. 373 |
10.5 Conclusions | p. 377 |
10.6 Problems | p. 378 |
References | p. 379 |
10.7 Appendix: Digital Video Formats | p. 380 |
SIF | p. 381 |
CIF | p. 381 |
ITU 601 Digital TV (aka SMPTE D1 and D5) | p. 381 |
ATSC Formats | p. 382 |
11 Digital Video Compression | p. 385 |
11.1 Intraframe Coding | p. 387 |
11.1.1 M-JPEG Pseudo Algorithm | p. 388 |
11.1.2 DV Codec | p. 391 |
11.1.3 Intraframe SWT Coding | p. 392 |
11.1.4 M-JPEG 2000 | p. 394 |
11.2 Interframe Coding | p. 395 |
11.2.1 Generalizing 1-D DPCM to Interframe Coding | p. 396 |
11.2.2 MC Spatiotemporal Prediction | p. 397 |
11.3 Interframe Coding Standards | p. 398 |
11.3.1 MPEG 1 | p. 399 |
11.3.2 MPEG 2-"a Generic Standard" | p. 401 |
11.3.3 The Missing MPEG 3-High-Definition Television | p. 403 |
11.3.4 MPEG 4-Natural and Synthetic Combined | p. 403 |
11.3.5 Video Processing of MPEG-Coded Bitstreams | p. 404 |
11.3.6 H.263 Coder for Visual Conferencing | p. 405 |
11.3.7 H.264/AVC | p. 405 |
11.3.8 Video Coder Mode Control | p. 408 |
11.3.9 Network Adaptation | p. 410 |
11.4 Interframe SWT Coders | p. 410 |
11.4.1 Motion-Compensated SWT Hybrid Coding | p. 412 |
11.4.2 3-D or Spatiotemporal Transform Coding | p. 413 |
11.5 Scalable Video Coders | p. 417 |
11.5.1 More on MCTF | p. 420 |
11.5.2 Detection of Covered Pixels | p. 421 |
11.5.3 Bidirectional MCTF | p. 423 |
11.6 Object-Based Video Coding | p. 426 |
11.7 Comments on the Sensitivity of Compressed Video | p. 428 |
11.8 Conclusions | p. 429 |
11.9 Problems | p. 430 |
References | p. 431 |
12 Video Transmission over Networks | p. 435 |
12.1 Video on IP Networks | p. 436 |
12.1.1 Overview of IP Networks | p. 437 |
12.1.2 Error-Resilient Coding | p. 440 |
12.1.3 Transport-Level Error Control | p. 442 |
12.1.4 Wireless Networks | p. 443 |
12.1.5 Joint Source-Channel Coding | p. 444 |
12.1.6 Error Concealment | p. 446 |
12.2 Robust SWT Video Coding (Bajic) | p. 447 |
12.2.1 Dispersive Packetization | p. 447 |
12.2.2 Multiple Description FEC | p. 453 |
12.3 Error-Resilience Features of H.264/AVC | p. 458 |
12.3.1 Syntax | p. 458 |
12.3.2 Data Partitioning | p. 459 |
12.3.3 Slice Interleaving and Flexible Macroblock Ordering | p. 459 |
12.3.4 Switching Frames | p. 459 |
12.3.5 Reference Frame Selection | p. 461 |
12.3.6 Intrablock Refreshing | p. 461 |
12.3.7 Error Concealment in H.264/AVC | p. 461 |
12.4 Joint Source-Network Coding | p. 463 |
12.4.1 Digital Item Adaptation (DIA) in MPEG 21 | p. 463 |
12.4.2 Fine-Grain Adaptive FEC | p. 464 |
12.5 Conclusions | p. 469 |
12.6 Problems | p. 469 |
References | p. 471 |
Index | p. 477 |