Advances in Electronics and Electron Physics (eBook)

Front Cover 1
Image Mathematics and Image Processing 4
Copyright Page 5
Contents 6
Contributors 9
Preface 10
Chapter 1. Residual Vector Quantizers with Jointly Optimized Code Books 14
I. Introduction 15
II. Review of Single-Stage Quantizers 19
III. Residual Quantizers 24
IV. Scalar Residual Quantizers 27
V. Vector Residual Quantizers 39
VI. Reflection Symmetric RQ 43
VII. Experimental Results 50
VIII. Conclusions 64
Appendix: Tables of Rate-Distortion Data 65
References 71
Chapter 2. Foundation and Applications of Lattice Transforms in Image Processing 74
I. Introduction 74
II. Theoretical Foundation of Lattice Transforms in Image Processing 79
III. Applications 103
References 140
Chapter 3. Invariant Pattern Representations and Lie Groups Theory 144
I. Introduction 144
II. The LTG/NP Approach to Visual Perception 150
III. Invariant Integral Transforms and Lie Transformation Groups 155
IV. Transformations of Integral Transforms 170
V. Notes on Invariant Representations of 3D Objects 179
VI. Discussion 190
Appendix A 194
Appendix B 201
References 205
Chapter 4. Finite Topology and Image Analysis 210
I. Introduction 210
II. Abstract Cell Complexes 214
III. Images on Cell Complexes 221
IV. Resolution of Connectivity Contradictions 225
V. Boundaries in Complexes 229
VI. Simple Image Analysis Problems 233
VII. The Cell List Data Structure 237
VIII. Subgraph and Subcomplex Isomorphism 237
IX. Variability of Prototypes and Use of Decision Trees 251
X. Applications 258
XI. Conclusions 270
Acknowledgements 271
References 271
Chapter 5. The Intertwining of Abstract Algebra and Structured Estimation Theory 274
Foreword 275
I. Introduction 275
II. Covariance Models 277
III. Jordan Algebras 286
IV. Explicit MLE Solution 294
V. AR Processes Parameter Estimation 301
VI. Exact Loglikelihood for AR Process Parameter Estimation 309
VII. Summary and Conclusions 322
Acknowledgments 323
Appendix A 323
Appendix B 325
Appendix C 326
References 328
Chapter 6. Echographic Image Processing 330
I. Introduction 330
II. Physics of Ultrasound 331
III. Acoustic Tissue Models 334
IV. Estimation of Acoustic Parameters 336
V. Generation of Tissue Texture 338
VI. Texture Analysis 342
VII. Image Processing 351
Acknowledgements 358
References 358
Index 364