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| Acknowledgments | |
| Introduction | p. 1 |
| Formulation of Mathematical Models for Real World Images | p. 5 |
| Description and Properties of Real World Images | p. 6 |
| Mathematical Models for Real World Images | p. 25 |
| Scanning and Digitizing | p. 33 |
| Quantization, Scan Order, and Color | p. 38 |
| Mathematical Foundations for Fractal Image Compression I | p. 47 |
| Spaces, Mappings, and Transformations | p. 48 |
| Affine Transformations in R | p. 49 |
| Construction of the Classical Cantor Set Using Two Affine Transformations on R | p. 50 |
| Affine Transformations in the Euclidean Plane | p. 51 |
| Affine Transformations in Three-Dimensional Real Space | p. 60 |
| Norms on Linear Transformations on R[superscript 2] | p. 63 |
| Topological Properties of Metric Spaces and Transformations | p. 63 |
| Contraction Mapping Theorem - Key to Fractal Image Compression | p. 70 |
| Fractal Image Compression I: IFS Fractals | p. 75 |
| Spaces of Images - the Hausdorff Space H | p. 76 |
| Contraction Mappings on the Space H | p. 78 |
| Iterated Function Systems | p. 79 |
| Iterated Function Systems of Affine Transformations in R[superscript 2] | p. 82 |
| The Photocopy Machine Algorithm for Computing the Attractor of an IFS | p. 89 |
| C Source Code for Computing the Attractor of an IFS | p. 93 |
| The Collage Theorem | p. 100 |
| Fractal Image Compression Using IFS Fractals | p. 100 |
| Measures and IFS's with Probabilities for Grayscale Images | p. 105 |
| Grayscale Photocopy Algorithm | p. 108 |
| Fractal Image Compression Using the Collage Theorem for Measures | p. 113 |
| Dudbridge's Fractal Image Compression Method | p. 115 |
| Mathematical Foundations for Fractal Image Compression II | p. 119 |
| Information Sources and Zero-Order Markov Sources | p. 120 |
| Codes | p. 122 |
| Kraft-McMillan Inequality | p. 128 |
| C Source Code for Illustrating Kraft's Theorem | p. 130 |
| Entropy | p. 134 |
| Shannon-Fano Codes | p. 138 |
| Extensions of Sources | p. 140 |
| Higher-Order Markov Sources | p. 142 |
| Huffman Codes for Compression | p. 150 |
| C Source Code Illustration of a Huffman Code | p. 155 |
| Addresses on Fractals | p. 159 |
| Arithmetic Compression and IFS Fractals | p. 162 |
| C Source Code Illustration for Arithmetic Encoding and Decoding | p. 166 |
| Fractal Image Compression II: The Fractal Transform | p. 173 |
| General Description of Fractal Image Compression Methodology | p. 174 |
| Local Iterated Function Systems | p. 176 |
| The Collage Theorem for a Local IFS | p. 179 |
| Calculation of Binary Attractors of Local IFS Using the Escape Time Algorithm | p. 181 |
| The Black and White Fractal Transform | p. 182 |
| The Grayscale Fractal Transform | p. 186 |
| A Local IFS Associated with the Fractal Transform Operator | p. 187 |
| Simple Examples of Grayscale Fractal Transforms | p. 188 |
| C Source Code Implementation | p. 198 |
| Illustrations of Fractal Transform Compression | p. 215 |
| A JPEG Image Compression | p. 219 |
| A.2. Discrete Cosine Transform (DCT) | p. 223 |
| A.3. Quantization | p. 224 |
| A.4. Runlength Encoding | p. 226 |
| A.5. Entropy Encoding | p. 227 |
| A.6. Interchange Format | p. 227 |
| A.7. C Source Code Illustrating JPEG Compression | p. 228 |
| Index | p. 241 |
| Table of Contents provided by Blackwell. All Rights Reserved. |
Fractal Image Compression
by Barnsley, Michael F.; Hurd, Lyman P.; Anson, Louisa F.Format: Hardcover
Pub. Date: 1993-01-01
Publisher(s): A K Peters Ltd
List Price: $63.75
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