THE TRANSFORM AND DATA COMPRESSION HANDBOOK

Transcription

1 THE TRANSFORM AND DATA COMPRESSION HANDBOOK Edited by K.R. RAO University of Texas at Arlington AND RC. YIP McMaster University CRC Press Boca Raton London New York Washington, D.C.

2 Contents 1 Karhunen-Loeve Transform Introduction Data Decorrelation Calculation of the KLT Performance of Transforms Information Theory Quantization Truncation Error Block Size Examples Calculation of KLT Quantization and Encoding Generalization Markov-1 Solution Medical Imaging Color Images Summary 30 References 34 2 The Discrete Fourier Transform Introduction The DFT Matrix An Example DFT Frequency Analysis Selected Properties of the DFT Symmetry Properties Real- Valued DFT-Based Transforms The Fast Fourier Transform The DFT in Coding Applications The DFT and Filter Banks Cosine-Modulated Filter Banks Complex DFT-Based Filter Banks 66 xv

3 xvi THE TRANSFORM AND DATA COMPRESSION HANDBOOK 2.10 Conclusion FFTWeb sites 72 References 74 Comparametric Transforms for Transmitting Eye Tap Video with Picture Transfer Protocol (PTP) Introduction: Wearable Cybernetics Historical Overview of WearComp Eye Tap Video The Edgertonian Image Sequence Edgertonian versus Nyquist Thinking Frames versus Rows, Columns, and Pixels Picture Transfer Protocol (PTP) Best Case Imaging and Fear of Functionality Comparametric Image Sequence Analysis Camera, Eye, or Head Motion: Common Assumptions and Terminology VideoOrbits Framework: Comparameter Estimation and Optical Flow Feature-Based Methods Featureless Methods Based on Generalized Cross-Correlation Featureless Methods Based on Spatio-Temporal Derivatives Multiscale Projective Flow Comparameter Estimation Four Point Method for Relating Approximate Model to Exact Model Overview of the New Projective Flow Algorithm Multiscale Repetitive Implementation Exploiting Commutativity for Parameter Estimation Performance/Applications A Paradigm Reversal in Resolution Enhancement Increasing Resolution in the "Pixel Sense" Summary Acknowledgements Ill References 112 Discrete Cosine and Sine Transforms Introduction The Family of DCTs and DSTs Definitions of DCTs and DSTs Mathematical Properties Relations to the KLT A Unified Fast Computation of DCTs and DSTs Definitions of Even-Odd Matrices DCT-II/DST-II and DCT-III/DST-III Computation DCT-I and DST-I Computation 129

4 CONTENTS xvii DCT-IV/DST-IV Computation Implementation of the Unified Fast Computation of DCTs and DSTs The 2-D DCT/DST Universal Computational Structure The Fast Direct 2-D DCT/DST Computation Implementation of the Direct 2-D DCT/DST Computation DCT and Data Compression DCT-Based Image Compression/Decompression Data Structures for Compression/Decompression Setting the Quantization Table Standard Huffman Coding/Decoding Tables Compression of One Sub-Image Block Decompression of One Sub-Image Block Image Compression/Decompression Compression of Color Images Results of Image Compression Summary 191 References 192 Lapped Transforms for Image Compression Introduction Notation BriefHistory Block Transforms Factorization of Discrete Transforms Discrete MIMO Linear Systems Block Transform as a MIMO System Lapped Transforms Orthogonal Lapped Transforms Nonorthogonal Lapped Transforms LTs as MIMO Systems Factorization of Lapped Transforms Hierarchical Connection of LTs: An Introduction Time-Frequency Diagram Tree-Structured Hierarchical Lapped Transforms Variable-Length LTs Practical Symmetric LTs The Lapped Orthogonal Transform: LOT The Lapped Bi-Orthogonal Transform: LBT The Generalized LOT: GenLOT The General Factorization: GLBT The Fast Lapped Transform: FLT Modulated LTs Finite-Length Signals Overall Transform 241

5 xviii THE TRANSFORM AND DATA COMPRESSION HANDBOOK Recovering Distorted Samples Symmetric Extensions Design Issues for Compression Transform-Based Image Compression Systems JPEG Embedded Zerotree Coding Other Coders Performance Analysis JPEG Embedded Zerotree Coding Conclusions 258 References 260 Wavelet-Based Image Compression Introduction Dyadic Wavelet Transform Two-Channel Perfect-Reconstruction Filter Bank Dyadic Wavelet Transform, Multiresolution Representation Wavelet Smoothness Wavelet-Based Image Compression Lossy Compression EZW Algorithm SPIHT Algorithm WDR Algorithm ASWDR Algorithm Lossless Compression Color Images Other Compression Algorithms Ringing Artifacts and Postprocessing Algorithms 306 References 306 Fractal-Based Image and Video Compression Introduction Basic Properties of Fractals and Image Compression Contractive Affine Transforms, Iterated Function Systems, and Image Generation Image Compression Directly Based on the IFS Theory Image Compression Based on IFS Library Image Compression Based on Partitioned IFS Image Partitions Distortion Measure A Class of Discrete Image Transformations Encoding and Decoding Procedures Experimental Results Image Coding Using Quadtree Partitioned IFS (QPIFS) 326

6 CONTENTS xix RMS Tolerance Selection A Compact Storage Scheme Experimental Results Image Coding by Exploiting Scalability of Fractals Image Spatial Sub-Sampling Decoding to a Larger Image Experimental Results Video Sequence Compression using Quadtree PIFS Definitions of Types of Range Blocks Encoding and Decoding Processes Storage Requirements Experimental Results Discussion Other Fractal-Based Image Compression Techniques Segmentation-Based Coding Using Fractal Dimension Yardstick Coding Conclusions 343 References Compression of Wavelet Transform Coefficients Introduction Embedded Coefficient Coding Statistical Context Modeling of Embedded Bit Stream.. ' Context Dilution Problem Context Formation Context Quantization Optimization of Context Quantization Dynamic Programming for Minimum Conditional Entropy Fast Algorithms for High-Order Context Modeling Context Formation via Convolution Shared Modeling Context for Signs and Textures Experimental Results Lossy Case Lossless Case Summary 374 References 375 Index 379