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
Introduction | 1 |
Fast Attractor Image Encoding by Adaptive Codebook Clustering | 9 |
Mathematical Background | 25 |
Copyright | |
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Common terms and phrases
affine transformation algorithm approximation archetype classification archetype sets attractor average B₁ Chapter classes cluster centers code vectors codebook blocks Collage Theorem complete metric space compression ratio compute Contractive Mapping convergence copy machine corresponding D₁ decimation decoding decoding method define denote described discussed domain block domain pool domain vectors domain-range domains and ranges elements Equation eventually contractive example fidelity fixed point Fixed-Point fractal dimension given Hausdorff metric i-th range block image compression index block input iterated function systems Lenna Lenna image linear matrix method metric space minimize number of domains operator optimal orthogonal output parameters piecewise PIFS code PIFS embedded function pixel values postprocessing PSNR PSNR dB pyramid quadrant quadtree partition quantization R₁ recursively resolution sampling Section self-similarity Sierpinski triangle signal Smax square subset subsquare super-resolution supremum w₁