多维数字信号处理

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二维 多维 数字信号 图像 视频 国外研究生教材
MULTIDIMENSIONAL SIGNAL IMAGE AND VIDEO PROCESSING AND CODING John W WOODS Rensselaer polytechnic Institute Troy, New York AMSTERDAM· BOSTON· HEDELB W YORK·OXH()RD· PARIS·SAND N(亚 委业 SAN FRANCISCO· SINGAPORE· SYINEY·1OKYO ACADEMIC Acade mic Press is an inprint of elsevier of Evc frames of the author's dog he CONTENTS inning in the back yard, as captured by a DV camcorder at 30 tps. The actual displayed"trame rate here though is rather low and not recommended except to use as cover art 30 Corpora te Drive, Suite 400, Burlington, MA O1803, USA 2.5 B Street, Su te 1900, San DieyU, CalilOrnia 92101-4495, USA 84 Theobald's Road London WCIX BRR. UK 的 Copyright 2006, Flscvicr Inc All rights rescrved Preface xiii Acknowleds or mechanical, including photocopy, recording, or any information storage and retrieval systo out permission in writing from the publisher. 1 Two-DIMENSIONAL SIGNALS AND SYSTEMS 1 Permissions may be sought directly from Elscvicr's Scienee techn 1.1 Two-Dimensional Signals 2. ford,UK:phone:(+44)1865843830,fax:(-44)18G5853333,E-mail:permissions@elsevier.com.You 1. 1. 1 Scparable Signals 6 Illay also complete your t'equest Onl-line via the Elsevier homepage(hup: // com), by selecting 1.1.2 Periodic signals 7 Support Conract"rhen"C.opyrighr and Permission"and then"Obtaining Permissions. 1.1.3 2-D Discrctc-Space Systems 9 1.1.4 Two-Dimensional Convolution 11 Application submitted, oging-in-Publication Data Library of Congress 1.1.5 Stability of 2-D Systcms 13 1. 2 2-D Discrete-Space Fourier Transform 14 1. 2. 1 Inverse 2-D) Fourier 'transform 1 British [ibrary Cataloguing-in-Publication Data 1.2.2 Fourier Transform of 2-D or Spatial Convolution 19 A catalogue record for this book is available from the british libra 1.2.3 Symmetry Properties of Fourier'Iranisform 26 1.2.4 Continuous-Spatc Fourier Transform 2 SBN13:978-0-12488516-9 1.3 Conclusions 31 ISBN10:012-0885166 1. 4 Problems 31 SBN13:978--12-372566-0 CD-ROM References 33 ISBN10:0-12-3725666 CD ROM) For information on all Academic Press publications 2 SAMPLING IN Two DIMENSiOns 3.5 gitourWcbsircatwww.books.clscvicr.com 2.1 Sampling Theorem-Rectangular Case 36 Printed in the united States of america 2.1.1R 987654321 ar Sapling 43 2. 2 Sampling Theorem--General Regular Casc 48 orking together to grow 2.1 Hexagonal Reconstruction Formula 52 libraries in developing countries 2.3 Change of Sample Rate 57 ww.clscvicr.comwww.bookaid.orgwww.sabrc.org 2.3.1 Downsampling by Integers MixM, 57 23.2 Ideal Decimation 58 ELSEVIER 〔0KAD Sabre foundation 33 Upsampling by IntegersⅠ1×L261 3 4 Ideal Interpolation 2.4 Sample 2.4.1 Gencral T)ownIsarmpling 64 of Evc frames of the author's dog he CONTENTS inning in the back yard, as captured by a DV camcorder at 30 tps. The actual displayed"trame rate here though is rather low and not recommended except to use as cover art 30 Corpora te Drive, Suite 400, Burlington, MA O1803, USA 2.5 B Street, Su te 1900, San DieyU, CalilOrnia 92101-4495, USA 84 Theobald's Road London WCIX BRR. UK 的 Copyright 2006, Flscvicr Inc All rights rescrved Preface xiii Acknowleds or mechanical, including photocopy, recording, or any information storage and retrieval systo out permission in writing from the publisher. 1 Two-DIMENSIONAL SIGNALS AND SYSTEMS 1 Permissions may be sought directly from Elscvicr's Scienee techn 1.1 Two-Dimensional Signals 2. ford,UK:phone:(+44)1865843830,fax:(-44)18G5853333,E-mail:permissions@elsevier.com.You 1. 1. 1 Scparable Signals 6 Illay also complete your t'equest Onl-line via the Elsevier homepage(hup: // com), by selecting 1.1.2 Periodic signals 7 Support Conract"rhen"C.opyrighr and Permission"and then"Obtaining Permissions. 1.1.3 2-D Discrctc-Space Systems 9 1.1.4 Two-Dimensional Convolution 11 Application submitted, oging-in-Publication Data Library of Congress 1.1.5 Stability of 2-D Systcms 13 1. 2 2-D Discrete-Space Fourier Transform 14 1. 2. 1 Inverse 2-D) Fourier 'transform 1 British [ibrary Cataloguing-in-Publication Data 1.2.2 Fourier Transform of 2-D or Spatial Convolution 19 A catalogue record for this book is available from the british libra 1.2.3 Symmetry Properties of Fourier'Iranisform 26 1.2.4 Continuous-Spatc Fourier Transform 2 SBN13:978-0-12488516-9 1.3 Conclusions 31 ISBN10:012-0885166 1. 4 Problems 31 SBN13:978--12-372566-0 CD-ROM References 33 ISBN10:0-12-3725666 CD ROM) For information on all Academic Press publications 2 SAMPLING IN Two DIMENSiOns 3.5 gitourWcbsircatwww.books.clscvicr.com 2.1 Sampling Theorem-Rectangular Case 36 Printed in the united States of america 2.1.1R 987654321 ar Sapling 43 2. 2 Sampling Theorem--General Regular Casc 48 orking together to grow 2.1 Hexagonal Reconstruction Formula 52 libraries in developing countries 2.3 Change of Sample Rate 57 ww.clscvicr.comwww.bookaid.orgwww.sabrc.org 2.3.1 Downsampling by Integers MixM, 57 23.2 Ideal Decimation 58 ELSEVIER 〔0KAD Sabre foundation 33 Upsampling by IntegersⅠ1×L261 3 4 Ideal Interpolation 2.4 Sample 2.4.1 Gencral T)ownIsarmpling 64 v CONTENTS ONTENTS 2.5C 4.5 Fast Transform Algorithms 140 2.6 Problems 66 4.5,1 FT Algorithm 140 References 70 4.5. 2 Fast DcT Methods 141 4.6 Sectioned Convolution Meth 3 TwO-DIMENSIONAL SYSTEMS AND 4.7 Conclusions 143 4. 8 Problems 144 Z-TRANSFORMS 71 Reterences 147 3.1 Linear Spatial or 2-D Systems 72 3.2 ZTransforms 76 3 Regions of convergence 7 y 5 TWO-DIMENSIONAL FILTER DESIGN 149 3.3 1 Morc General Case 82 5.1 FIR Filter Design 1.50 3.4 Some Z-Transform Properties 83 5.1.1 FIR Window Function Design 150 3.4.1 Linear Mapping of Variables 84 5.1.2 Design by Transformation of 1-D) Filter 156 3.4.2 Perse z-Transform 85 5.1.3 Projcction-Onto-Convcx-Sets Mcthod 161 5 2-D Filter Stability 89 5.2 LIR Filter Design 165 5.1 First-Quadrant Support 91 5.2.1 2-DRecursivc filt er Design 16.5 upport 9 5.2.2 Fully Recursive Filter Design 171 3 Root mans 96 5.3 Subband/ W Filter Dcsign 174 3.5.4 Stability Criteria for NSHP Su]port Filters 98 3.6 Conclusions 100 5.3.1 Wavelet (Biorthogonal)Filter Design Method 178 5.4 Conclusions 182 3.7 Problems 101 5.5 Problems 18 References 103 References 187 4 TWo-DImENSioNAl DISCRETE TRANSFORMS 105 6 INTRODUCTORY IMAGE PROCESSING 189 4.1 Discrete Fourier Series 106 4. 1. 1 Properties of the DFS Transtor 105 6. 1 Light and Luminance 190 6.2 Still 194 3 Shifting or Delay Pl 6. 2.1 Weber's Law 195 4.2 Discrete Fourier Transform 113 6.2, 2 Contrast Sensitivity Function 196 4.2.1 DFT Properties 115 4.2.2 Relation of dft to Fourier Transform 12( 6.3 Time-Variant Human Visual Systern Properties 19% 4.2.3 Effect of Sapling in frequency 121 2.4 Interpolating the: D)FI 12 6. 4 Inage Se 4.32-D Discrete Cosine Transform 123 3.1 Review of 1-D dct 125 64,2ilm203 1-DDC Pre 128 6.5Im d video displa 4 6.5.1(amma2 4.4 Subband/Wavelet Transform(SWT 6.6 Simple Image processing Filters 206 4.1 Ideal fi 6.6.1 Bux Filter 206 4.4.21-DSWT wich Finite-Order Filter 135 6.6. 2 Gaussian Filter 207 4.4.32-DSWT with FIR Filters 137 6.6.3 Prewitt Operator 2( 6.4 Sobel (1 208 4.4.5 Rclation of SwT to Wavelets 138 6.6.5 I alcian Filter 209 v CONTENTS ONTENTS 2.5C 4.5 Fast Transform Algorithms 140 2.6 Problems 66 4.5,1 FT Algorithm 140 References 70 4.5. 2 Fast DcT Methods 141 4.6 Sectioned Convolution Meth 3 TwO-DIMENSIONAL SYSTEMS AND 4.7 Conclusions 143 4. 8 Problems 144 Z-TRANSFORMS 71 Reterences 147 3.1 Linear Spatial or 2-D Systems 72 3.2 ZTransforms 76 3 Regions of convergence 7 y 5 TWO-DIMENSIONAL FILTER DESIGN 149 3.3 1 Morc General Case 82 5.1 FIR Filter Design 1.50 3.4 Some Z-Transform Properties 83 5.1.1 FIR Window Function Design 150 3.4.1 Linear Mapping of Variables 84 5.1.2 Design by Transformation of 1-D) Filter 156 3.4.2 Perse z-Transform 85 5.1.3 Projcction-Onto-Convcx-Sets Mcthod 161 5 2-D Filter Stability 89 5.2 LIR Filter Design 165 5.1 First-Quadrant Support 91 5.2.1 2-DRecursivc filt er Design 16.5 upport 9 5.2.2 Fully Recursive Filter Design 171 3 Root mans 96 5.3 Subband/ W Filter Dcsign 174 3.5.4 Stability Criteria for NSHP Su]port Filters 98 3.6 Conclusions 100 5.3.1 Wavelet (Biorthogonal)Filter Design Method 178 5.4 Conclusions 182 3.7 Problems 101 5.5 Problems 18 References 103 References 187 4 TWo-DImENSioNAl DISCRETE TRANSFORMS 105 6 INTRODUCTORY IMAGE PROCESSING 189 4.1 Discrete Fourier Series 106 4. 1. 1 Properties of the DFS Transtor 105 6. 1 Light and Luminance 190 6.2 Still 194 3 Shifting or Delay Pl 6. 2.1 Weber's Law 195 4.2 Discrete Fourier Transform 113 6.2, 2 Contrast Sensitivity Function 196 4.2.1 DFT Properties 115 4.2.2 Relation of dft to Fourier Transform 12( 6.3 Time-Variant Human Visual Systern Properties 19% 4.2.3 Effect of Sapling in frequency 121 2.4 Interpolating the: D)FI 12 6. 4 Inage Se 4.32-D Discrete Cosine Transform 123 3.1 Review of 1-D dct 125 64,2ilm203 1-DDC Pre 128 6.5Im d video displa 4 6.5.1(amma2 4.4 Subband/Wavelet Transform(SWT 6.6 Simple Image processing Filters 206 4.1 Ideal fi 6.6.1 Bux Filter 206 4.4.21-DSWT wich Finite-Order Filter 135 6.6. 2 Gaussian Filter 207 4.4.32-DSWT with FIR Filters 137 6.6.3 Prewitt Operator 2( 6.4 Sobel (1 208 4.4.5 Rclation of SwT to Wavelets 138 6.6.5 I alcian Filter 209 CONTENTS CONTENTS 6.7C 8.3.3 Vector quantization 280 LBG Algorithm[7 282 213 8.4 Entropy Caring 284 4.2 Arithmetic Codit 8.4.3 ECSQ and E(VQ 287 7 IMAGE ESTIMATION AND RESTORA 12-D Random fields 216 8.6 SWT Coder 292 -D) Random field 218 7.1.2 Autoregressive Random Signal Modcls 2 8.6.2 Nondyadic SWT Decompositions 300 7. 2 Estimation for random Ficlds 224 8.6.3 Fully Errbekkled SwT Coders 300 bservation domain 22 6.4 Embedded Zero-'lrce Wavelet(EZW)Coder 301 3 2-D Recursive Estimation 229 8.6.5 Set Partitioning in Hierarchical Trees(SPIHT)Cider 304 1 1-D Kalman Filter 229 8.6.6 Embedded zero Black Coder(EZBC) 306 3.2 2-D Kalman Filtering 233 8.7JPEG2000308 3.3 Reduccd Update Kalman Filter 235 8.8 Color Image Coding 309 3. 4 Approximate RUKF 236 8.8.1 Scalable Coder Results Comp 7.3.5 Steady -State RUKF 231 8.y Robustness Considerations 317Fison 311 7.3.6 LSI Estimation and Restoration Examples with RUKF 237 8. 10 Conclusions 312 4 Inhonageneaus Gaussian Estimation 241 1 Prublems 312 7.4.1 Inhomogeneous Estimation with RUKF 24 References 31.5 7.6 Bayesian and MAP Estimation 248 omain 244 in the Subband/Wavelet D 7.6. 1 Gauss Markov Imagc Models 249 9 THREE-DIMENSIONAL AND SPATIOTLMPORAL 2 Simulated Annealing 253 7.7 Imagc: Identification and Restoration 257 PROCESSING 317 7. 7. 1 Expectation-Maxirmizatinn AlgorithTnl Approach 2.5 9.1 3-D Signals and Systems 3 18 7.7.2 LM Method in the Subband wavelet domain 262 9.1.1 Propcrtics of 3-D Fourier Transform 320 7.8 Color Image Processing 263 9. 1.2 3-D Filters 321 263 9.2 3-D Sampling and Reconstruction 3 7.10 Problems 263 9.2.1 Gcncral 3-D Sampling 323 References 266 9.3 Spatiotemporal Signal Processing 325 Sampli 93.2S 8 DIGTTAL IMAGE COMPRESSION 269 9.3.3 Intraframe Filtering 328 9.3.4 Intraframe Filter 328 8. 1 Introduction 8.2 Transformation 272 9.3.6 Interframe Wiener Filler 331 4 Spatiotemporal Markey Models 3.32 82.2SWT274 4.] Causal and Semicausal 3-D) Field s 33 DPCM 27 9.4.2 Reduced Update Spatiotemporal Kalman Filter 335 8.3 Quantization 276 9.5 Conclusions 33 8 9.6 Probl 8.3.2 Optimal MSE Quantization 278 Refer CONTENTS CONTENTS 6.7C 8.3.3 Vector quantization 280 LBG Algorithm[7 282 213 8.4 Entropy Caring 284 4.2 Arithmetic Codit 8.4.3 ECSQ and E(VQ 287 7 IMAGE ESTIMATION AND RESTORA 12-D Random fields 216 8.6 SWT Coder 292 -D) Random field 218 7.1.2 Autoregressive Random Signal Modcls 2 8.6.2 Nondyadic SWT Decompositions 300 7. 2 Estimation for random Ficlds 224 8.6.3 Fully Errbekkled SwT Coders 300 bservation domain 22 6.4 Embedded Zero-'lrce Wavelet(EZW)Coder 301 3 2-D Recursive Estimation 229 8.6.5 Set Partitioning in Hierarchical Trees(SPIHT)Cider 304 1 1-D Kalman Filter 229 8.6.6 Embedded zero Black Coder(EZBC) 306 3.2 2-D Kalman Filtering 233 8.7JPEG2000308 3.3 Reduccd Update Kalman Filter 235 8.8 Color Image Coding 309 3. 4 Approximate RUKF 236 8.8.1 Scalable Coder Results Comp 7.3.5 Steady -State RUKF 231 8.y Robustness Considerations 317Fison 311 7.3.6 LSI Estimation and Restoration Examples with RUKF 237 8. 10 Conclusions 312 4 Inhonageneaus Gaussian Estimation 241 1 Prublems 312 7.4.1 Inhomogeneous Estimation with RUKF 24 References 31.5 7.6 Bayesian and MAP Estimation 248 omain 244 in the Subband/Wavelet D 7.6. 1 Gauss Markov Imagc Models 249 9 THREE-DIMENSIONAL AND SPATIOTLMPORAL 2 Simulated Annealing 253 7.7 Imagc: Identification and Restoration 257 PROCESSING 317 7. 7. 1 Expectation-Maxirmizatinn AlgorithTnl Approach 2.5 9.1 3-D Signals and Systems 3 18 7.7.2 LM Method in the Subband wavelet domain 262 9.1.1 Propcrtics of 3-D Fourier Transform 320 7.8 Color Image Processing 263 9. 1.2 3-D Filters 321 263 9.2 3-D Sampling and Reconstruction 3 7.10 Problems 263 9.2.1 Gcncral 3-D Sampling 323 References 266 9.3 Spatiotemporal Signal Processing 325 Sampli 93.2S 8 DIGTTAL IMAGE COMPRESSION 269 9.3.3 Intraframe Filtering 328 9.3.4 Intraframe Filter 328 8. 1 Introduction 8.2 Transformation 272 9.3.6 Interframe Wiener Filler 331 4 Spatiotemporal Markey Models 3.32 82.2SWT274 4.] Causal and Semicausal 3-D) Field s 33 DPCM 27 9.4.2 Reduced Update Spatiotemporal Kalman Filter 335 8.3 Quantization 276 9.5 Conclusions 33 8 9.6 Probl 8.3.2 Optimal MSE Quantization 278 Refer CONTENTS CONTENTS 10 DIGITAL VIDEO PROCESSING 341 11. 4 Interframe SWt Coders 410 10.1 Interframe processing 342 11.4.1 Motiori- ComPensated SWT Hybrid Coding 412 11.4.2 3-D or Spatiotemporal Transtorm Coding 413 10.2 Motion Estimation and Motion Compensation 348 11.5 Scalable video Coders 417 10.2.1 Block Matching Method 3.50 l1.5.1 More on mctF 42( 10.2.2 Hierarchical Block Matching 353 d Block Motion Compensation 354 11.5.2 Detection of covered pixels 421 10.2.4 Pel-Recursive Motion Estimation 355 1.5.3 Bidirectional MCTF 42 10.2.5 Optical flow methods 35 11.6 Object- Based Video Coding 426 10.3 Motion-Compensated Filtering 3.58 11.7 Comments on the Sensitivity of Compresscd video 428 10,3. 1 MC-Wiener Filter 358 11.8 Conclusions 42 10.3. 2 MC-Kalman Filter 360 11.9 Problens 430 103 3 Frame-Rate Conversion 36.3 References 431 10.3.4 Deinterlacing 365 10).4 Bayesian Method for Estimating Motion 371 0.4. 1 Joint Molion Fstimnatiotl and Segmentation 373 12 VIDEO TRANSMISSION OVER NETWORKS 435 10.5 Conclusions 377 12. 1 Video on iP Networks 436 10.6 Prublems 378 Reterences 379 12.1.2 Error Resilient Coding 10.7 Appendix: Digital Video formats 380 12, 1.3 Transport-Level Error Control 442 12.1.4 Wireless nel CIF 381 12.1.5 Joint Source-Channel Coding 444 IIU 601 Digital TV aka SMPTE D1 and D5)381 12.1.6 Error Concealment 446 ATSC Formats 382 12.2 Robust SWr Video Coding( Bajic) 447 12.2.1 Dispersive Packetization 447 12.2.2 Multiple Description FEC 453 1 1 DIGITAL VIDEO COMPRESSION 385 12.3 Frror -Resilience Features of h. 264/AVc 458 12.3.1 Syntax458 11.1 Intraframe Coding 387 12.3. 2 Data Partitioning 459 11.1.1 M-JPEG Pseudo Algorithm 388 12.3.3 SLice Interleaving and Flexible Macroblock Ordering 459 11,1.2V(odec391 12.3. 4 Switching Frarmies 459 11. 1.3 Intraframe SWT Coding 392 12.3.5 Reference Frame: Selection 461 11.4 M-JPEG200039 12.3.6 Intrablock Refreshing 461 11.2 Interframe Coding 395 12.3.7 Error Concealment in H. 264/AVC 461 11.2.1 Generalizing 1-D DPCM to interframe Coding 396 12.4 Joint Source-Network Coding 463 11.2.2 MC Spatiotemporal Prediction 39 12.4.1 Digital IteTrl Adaptation(DIA)in MPEG 21 463 11.3 Interframe Coding Standards 398 12. 4.2 Fine-Grain Adaptive FEC 464 11.3.1MPEG1399 12. 5 Conclusions 469 11.3.2MPEG2-“ a generic Standard”401 12.6 Problems 469 11.3.3 The Missing MPEG 3--High-Definition Television 40.3 References 471 11.3, 4 MPEG 4-Natural and Synthetic Combined 403 11.3.5 Video processing of MPLG-Coded Bitstreams 404 11.3.6 H 263 Coder for Visual Conferencing 40S 11.3.8 Vidco Coder Mode Control 408 11.3. Nerwork Adaptation 410

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