Fractal image compression /
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| Author / Creator: | Barnsley, M. F. (Michael Fielding), 1946- |
|---|---|
| Imprint: | Wellesley, Mass. : AK Peters, c1993. |
| Description: | 244 p. : ill. ; 24 cm. |
| Language: | English |
| Subject: | Image processing -- Digital techniques -- Mathematics. Fractals Fractals. Image compression. Image processing -- Digital techniques -- Mathematics. |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/1449180 |
Table of Contents:
- 1. Introduction
- 2. Formulation of Mathematical Models for Real World Images. 2.2. Description and Properties of Real World Images. 2.3. Mathematical Models for Real World Images. 2.4. Scanning and Digitizing. 2.5. Quantization, Scan Order, and Color
- 3. Mathematical Foundations for Fractal Image Compression I. 3.2. Spaces, Mappings, and Transformations. 3.3. Affine Transformations in R. 3.4. Construction of the Classical Cantor Set Using Two Affine Transformations on R. 3.5. Affine Transformations in the Euclidean Plane. 3.6. Affine Transformations in Three-Dimensional Real Space. 3.7. Norms on Linear Transformations on R[superscript 2]. 3.8. Topological Properties of Metric Spaces and Transformations. 3.9. Contraction Mapping Theorem - Key to Fractal Image Compression
- 4. Fractal Image Compression I: IFS Fractals. 4.2. Spaces of Images - the Hausdorff Space H. 4.3. Contraction Mappings on the Space H. 4.4. Iterated Function Systems. 4.5. Iterated Function Systems of Affine Transformations in R[superscript 2]. 4.6. The Photocopy Machine Algorithm for Computing the Attractor of an IFS. 4.7. C Source Code for Computing the Attractor of an IFS. 4.8. The Collage Theorem. 4.9. Fractal Image Compression Using IFS Fractals. 4.10. Measures and IFS's with Probabilities for Grayscale Images. 4.11. Grayscale Photocopy Algorithm. 4.12. Fractal Image Compression Using the Collage Theorem for Measures. 4.13. Dudbridge's Fractal Image Compression Method
- 5. Mathematical Foundations for Fractal Image Compression II. 5.2. Information Sources and Zero-Order Markov Sources. 5.3. Codes. 5.4. Kraft-McMillan Inequality. 5.5. C Source Code for Illustrating Kraft's Theorem. 5.6. Entropy. 5.7. Shannon-Fano Codes. 5.8. Extensions of Sources. 5.9. Higher-Order Markov Sources. 5.10. Huffman Codes for Compression. 5.11. C Source Code Illustration of a Huffman Code. 5.12. Addresses on Fractals. 5.13. Arithmetic Compression and IFS Fractals. 5.14. C Source Code Illustration for Arithmetic Encoding and Decoding
- 6. Fractal Image Compression II: The Fractal Transform. 6.2. General Description of Fractal Image Compression Methodology. 6.3. Local Iterated Function Systems. 6.4. The Collage Theorem for a Local IFS. 6.5. Calculation of Binary Attractors of Local IFS Using the Escape Time Algorithm. 6.6. The Black and White Fractal Transform. 6.7. The Grayscale Fractal Transform. 6.8. A Local IFS Associated with the Fractal Transform Operator. 6.9. Simple Examples of Grayscale Fractal Transforms. 6.10. C Source Code Implementation. 6.11. Illustrations of Fractal Transform Compression. A JPEG Image Compression
- A.2. Discrete Cosine Transform (DCT)
- A.3. Quantization
- A.4. Runlength Encoding
- A.5. Entropy Encoding
- A.6. Interchange Format
- A.7. C Source Code Illustrating JPEG Compression.
