## Fractal image compression: theory and applicationThis book presents the theory and application of new methods of image compression based on self-transformations of an image. These methods lead to a representation of an image as a fractal, an object with detail at all scales. Very practical and completely up-to-date, this book will serve as a useful reference for those working in image processing and encoding and as a great introduction for those unfamiliar with fractals. The book begins with an elementary introduction to the concept of fractal image compression and contains a rigorous description of all the relevant mathemtics of the subjects. |

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### Contents

Introduction | 1 |

Mathematical Background | 25 |

Fractal Image Compression with Quadtrees | 55 |

Copyright | |

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### Common terms and phrases

affine transformation approximation attractor average basis vectors Chapter classes classification cluster centers codebook blocks coefficients Collage Theorem complete metric space compression ratio compute Contractive Mapping convergence copy machine corresponding decoding method define denote discussed domain block domain pool domain vectors domain_y domain-range domains and ranges edges Equation eventually contractive example fidelity fixed point Fixed-Point flag fractal code fractal dimension fractal image compression given grey-scale image compression inference algorithm initial image input image iterated function systems Lenna lines Lipschitz matrix max_part method minimize node number of bits number of domains operator optimal original blocks original image orthogonal orthonormal basis output parameters piecewise PIFS code pixel values postprocessing printf PSNR quadrant quadtree partition quantization range block range vectors recursive resolution samples scheme Section self-similar shows Sierpinski triangle signal smax square sub-image subset subspace subsquare wavelet y_exponent