1 Introduction. - 1. 1 What Is Fractal Image Compression?. - 1. 2 Self-Similarity in Images. - 1. 3 A Special Copying Machine. - 1. 4 Encoding Images. - 1. 5 Ways to Partition Images. - 1. 6 Implementation. - 1. 7 Conclusion. - 2 Mathematical Background. - 2. 1 Fractals. - 2. 2 Iterated Function Systems. - 2. 3 Recurrent Iterated Function Systems. - 2. 4 Image Models. - 2. 5 Affine Transformations. - 2. 6 Partitioned Iterated Function Systems. - 2. 7 Encoding Images. - 2. 8 Other Models. - 3 Fractal Image Compression with Quadtrees. - 3. 1 Encoding. - 3. 2 Decoding. - 3. 3 Sample Results. - 3. 4 Remarks. - 3. 5 Conclusion. - 4 Archetype Classification in an Iterated Transformation Image Compression Algorithm. - 4. 1 Archetype Classification. - 4. 2 Results. - 4. 3 Discussion. - 5 Hierarchical Interpretation of Fractal Image Coding and Its Applications. - 5. 1 Formulation of PIFS Coding/Decoding. - 5. 2 Hierarchical Interpretation. - 5. 3 Matrix Description of the PIFS Transformation. - 5. 4 Fast Decoding. - 5. 5 Super-resolution. - 5. 6 Different Sampling Methods. - 5. 7 Conclusions. - A Proof of Theorem 5. 1 (Zoom). - B Proof of Theorem 5. 2 (PIFS Embedded Function). - C Proof of Theorem 5. 3 (Fractal Dimension of the PIFS Embedded Function). - 6 Fractal Encoding with HV Partitions. - 6. 1 The Encoding Method. - 6. 2 Efficient Storage. - 6. 3 Decoding. - 6. 4 Results. - 6. 5 More Discussion. - 6. 6 Other Work. - 7 A Discrete Framework for Fractal Signal Modeling. - 7. 1 Sampled Signals Pieces and Piecewise Self-transformability. - 7. 2 Self-transformable Objects and Fractal Coding. - 7. 3 Eventual Contractivity and Collage Theorems. - 7. 4 Affine Transforms. - 7. 5 Computation of Contractivity Factors. - 7. 6 A Least-squares Method. - 7. 7 Conclusion. - A Derivation of Equation (7. 9). - 8 A Class of Fractal Image Coders with Fast Decoder Convergence. - 8. 1 Affine Mappings on Finite-Dimensional Signals. - 8. 2 Conditions for Decoder Convergence. - 8. 3 Improving Decoder Convergence. - 8. 4 Collage Optimization Revisited. - 8. 5 A Generalized Sufficient Condition for Fast Decoding. - 8. 6 An Image Example. - 8. 7 Conclusion. - 9 Fast Attractor Image Encoding by Adaptive Codebook Clustering. - 9. 1 Notation and Problem Statement. - 9. 2 Complexity Reduction in the Encoding Step. - 9. 3 How to Choose a Block. - 9. 4 Initialization. - 9. 5 Two Methods for Computing Cluster Centers. - 9. 6 Selecting the Number of Clusters. - 9. 7 Experimental Results. - 9. 8 Possible Improvements. - 9. 9 Conclusion. - 10 Orthogonal Basis IFS. - 10. 1 Orthonormal Basis Approach. - 10. 2 Quantization. - 10. 3 Construction of Coders. - 10. 4 Comparison of Results. - 10. 5 Conclusion. - 11 A Convergence Model. - 11. 1 The r Operator. - 11. 2 Lp Convergence of the RIFS Model. - 11. 3 Almost Everywhere Convergence. - 11. 4 Decoding by Matrix Inversion. - 12 Least-Squares Block Coding by Fractal Functions. - 12. 1 Fractal Functions. - 12. 2 Least-Squares Approximation. - 12. 3 Construction of Fractal Approximation. - 12. 4 Conclusion. - 13 Inference Algorithms for WFA and Image Compression. - 13. 1 Images and Weighted Finite Automata. - 13. 2 The Inference Algorithm for WFA. - 13. 3 A Fast Decoding Algorithm for WFA. - 13. 4 A Recursive Inference Algorithm for WFA. - A Sample Code. - A. l The Enc Manual Page. - A. 2 The Dec Manual Page. - A. 3 Enc. c. - A. 4 Dec. c. - A. 5 The Encoding Program. - A. 6 The Decoding Program. - A. 7 Possible Modifications. - B Exercises. - C Projects. - C. 1 Decoding by Matrix Inversion. - C. 2 Linear Combinations of Domains. - C. 3 Postprocessing: Overlapping Weighted Ranges and Tilt. - C. 4 Encoding Optimization. - C. 5 Theoretical Modeling for Continuous Images. - C. 6 Scan-line Fractal Encoding. - C. 7 Video Encoding. - C. 8Single Encoding of Several Frames. - C. 9 Edge-based Partitioning. - C. 10 Classification Schemes. - C. l1 From Classification to Multi-dimensional Keys. - C. 12 Polygonal Partitioning305. - C. 13 Decoding by Pixel Chasing. - C. 14 Second Iterate Collaging. - C. 15 Rectangular IFS Partitioning. - C. 16 Hexagonal Partitioning. - C. 17 Parallel Processing. - C. 18 Non-contractive IFSs. - D Comparison of Results. - E Original Images. Language: English