Advances in Electronics and Electron Physics
Inhaltsverzeichnis
1;Front Cover;1 2;Image Mathematics and Image Processing;4 3;Copyright Page;5 4;Contents;6 5;Contributors;9 6;Preface;10 7;Chapter 1. Residual Vector Quantizers with Jointly Optimized Code Books;14 7.1;I. Introduction;15 7.2;II. Review of Single-Stage Quantizers;19 7.3;III. Residual Quantizers;24 7.4;IV. Scalar Residual Quantizers;27 7.5;V. Vector Residual Quantizers;39 7.6;VI. Reflection Symmetric RQ;43 7.7;VII. Experimental Results;50 7.8;VIII. Conclusions;64 7.9;Appendix: Tables of Rate-Distortion Data;65 7.10;References;71 8;Chapter 2. Foundation and Applications of Lattice Transforms in Image Processing;74 8.1;I. Introduction;74 8.2;II. Theoretical Foundation of Lattice Transforms in Image Processing;79 8.3;III. Applications;103 8.4;References;140 9;Chapter 3. Invariant Pattern Representations and Lie Groups Theory;144 9.1;I. Introduction;144 9.2;II. The LTG/NP Approach to Visual Perception;150 9.3;III. Invariant Integral Transforms and Lie Transformation Groups;155 9.4;IV. Transformations of Integral Transforms;170 9.5;V. Notes on Invariant Representations of 3D Objects;179 9.6;VI. Discussion;190 9.7;Appendix A;194 9.8;Appendix B;201 9.9;References;205 10;Chapter 4. Finite Topology and Image Analysis;210 10.1;I. Introduction;210 10.2;II. Abstract Cell Complexes;214 10.3;III. Images on Cell Complexes;221 10.4;IV. Resolution of Connectivity Contradictions;225 10.5;V. Boundaries in Complexes;229 10.6;VI. Simple Image Analysis Problems;233 10.7;VII. The Cell List Data Structure;237 10.8;VIII. Subgraph and Subcomplex Isomorphism;237 10.9;IX. Variability of Prototypes and Use of Decision Trees;251 10.10;X. Applications;258 10.11;XI. Conclusions;270 10.12;Acknowledgements;271 10.13;References;271 11;Chapter 5. The Intertwining of Abstract Algebra and Structured Estimation Theory;274 11.1;Foreword;275 11.2;I. Introduction;275 11.3;II. Covariance Models;277 11.4;III. Jordan Algebras;286 11.5;IV. Explicit MLE Solution;294 11.6;V. AR Processes Parameter Estimation;301 11
.7;VI. Exact Loglikelihood for AR Process Parameter Estimation;309 11.8;VII. Summary and Conclusions;322 11.9;Acknowledgments;323 11.10;Appendix A;323 11.11;Appendix B;325 11.12;Appendix C;326 11.13;References;328 12;Chapter 6. Echographic Image Processing;330 12.1;I. Introduction;330 12.2;II. Physics of Ultrasound;331 12.3;III. Acoustic Tissue Models;334 12.4;IV. Estimation of Acoustic Parameters;336 12.5;V. Generation of Tissue Texture;338 12.6;VI. Texture Analysis;342 12.7;VII. Image Processing;351 12.8;Acknowledgements;358 12.9;References;358 13;Index;364
