Title | Fractal Image Compression [electronic resource] : Theory and Application / edited by Yuval Fisher |
---|---|
Imprint | New York, NY : Springer New York, 1995 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-2472-3 |
Descript | XVIII, 342 p. online resource |
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.8 Single 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