Fractal Image Compression: Theory and ApplicationWhat is "Fractal Image Compression," anyway? You will have to read the book to find out everything about it, and if you read the book, you really will find out almost everything that is currently known about it. In a sentence or two: fractal image compression is a method, or class of methods, that allows images to be stored on computers in much less memory than standard ways of storing images. The "fractal" part means that the methods have something to do with fractals, complicated looking sets that arise out of simple algorithms. This book contains a collection of articles on fractal image compression. Beginners will find simple explanations, working C code, and exercises to check their progress. Mathematicians will find a rigorous and detailed development of the subject. Non-mathematicians will find a parallel intuitive discussion that explains what is behind all the "theorem-proofs." Finally, researchers - even researchers in fractal image compression - will find new and exciting results, both theoretical and applied. Here is a brief synopsis of each chapter: Chapter 1 contains a simple introduction aimed at the lay reader. It uses almost no math but explains all the main concepts of a fractal encoding/decoding scheme, so that the interested reader can write his or her own code. Chapter 2 has a rigorous mathematical description of iterated function systems and their gen eralizations for image encoding. An informal presentation of the material is made in parallel in the chapter using sans serif font. |
Contents
| 1 | |
Mathematical Background | 25 |
Fractal Image Compression with Quadtrees | 55 |
Archetype Classification in an Iterated Transformation | 79 |
7 | 110 |
Fractal Encoding with HV Partitions | 119 |
A Discrete Framework for Fractal Signal Modeling | 137 |
7 | 150 |
Orthogonal Basis IFS | 199 |
A Convergence Model | 215 |
LeastSquares Block Coding by Fractal Functions | 229 |
Inference Algorithms for WFA and Image Compression | 243 |
A Sample Code | 259 |
B Exercises | 293 |
Comparison of Results | 311 |
Fast Attractor Image Encoding by Adaptive Codebook Clustering | 177 |
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Common terms and phrases
affine transformation approximation archetypes attractor average B₁ basis vectors Chapter classification cluster centers codebook blocks coefficients Collage Theorem complete metric space compression ratio compute Contractive Mapping convergence copy machine decimated decoding method define denote dimension domain block domain pool domain vectors domain-range domains and ranges encoding Equation eventually contractive example factor fidelity Figure fixed point fractal coding fractal dimension fractal image compression given hsize image compression iterated function systems Lenna linear lines matrix max_part method metric minimize number of domains offset operator optimal original blocks original image orthogonal orthonormal basis output parameters PIFS code pixel values postprocessing PSNR quadrant quadtree partition quantization range block range vectors recursive resolution scaling scheme Section self-similarity Sierpinski triangle signal Smax space square subset subspace subsquare vsize wavelet x_exponent ysize/2