Front Cover; Image Mathematics and Image Processing; Copyright Page; Contents; Contributors; Preface; Chapter 1. Residual Vector Quantizers with Jointly Optimized Code Books; I. Introduction; II. Review of Single-Stage Quantizers; III. Residual Quantizers; IV. Scalar Residual Quantizers; V. Vector Residual Quantizers; VI. Reflection Symmetric RQ; VII. Experimental Results; VIII. Conclusions; Appendix: Tables of Rate-Distortion Data; References; Chapter 2. Foundation and Applications of Lattice Transforms in Image Processing; I. Introduction

II. Theoretical Foundation of Lattice Transforms in Image ProcessingIII. Applications; References; Chapter 3. Invariant Pattern Representations and Lie Groups Theory; I. Introduction; II. The LTG/NP Approach to Visual Perception; III. Invariant Integral Transforms and Lie Transformation Groups; IV. Transformations of Integral Transforms; V. Notes on Invariant Representations of 3D Objects; VI. Discussion; Appendix A; Appendix B; References; Chapter 4. Finite Topology and Image Analysis; I. Introduction; II. Abstract Cell Complexes; III. Images on Cell Complexes

IV. Resolution of Connectivity ContradictionsV. Boundaries in Complexes; VI. Simple Image Analysis Problems; VII. The Cell List Data Structure; VIII. Subgraph and Subcomplex Isomorphism; IX. Variability of Prototypes and Use of Decision Trees; X. Applications; XI. Conclusions; Acknowledgements; References; Chapter 5. The Intertwining of Abstract Algebra and Structured Estimation Theory; Foreword; I. Introduction; II. Covariance Models; III. Jordan Algebras; IV. Explicit MLE Solution; V. AR Processes Parameter Estimation; VI. Exact Loglikelihood for AR Process Parameter Estimation

VII. Summary and ConclusionsAcknowledgments; Appendix A; Appendix B; Appendix C; References; Chapter 6. Echographic Image Processing; I. Introduction; II. Physics of Ultrasound; III. Acoustic Tissue Models; IV. Estimation of Acoustic Parameters; V. Generation of Tissue Texture; VI. Texture Analysis; VII. Image Processing; Acknowledgements; References; Index