# Fractal Image Compression

## Theory and Application

• Yuval Fisher

1. Front Matter
Pages i-xviii
2. Y. Fisher
Pages 1-23
3. Y. Fisher
Pages 25-53
4. Y. Fisher
Pages 55-77
5. R. D. Boss, E. W. Jacobs
Pages 79-90
6. Z. Baharav, D. Malah, E. Karnin
Pages 91-117
7. Y. Fisher, S. Menlove
Pages 119-136
8. L. Lundheim
Pages 137-151
9. G. E. Øien, S. Lepsøy
Pages 153-175
10. S. Lepsøy, G. E. Øien
Pages 177-197
11. G. Vines
Pages 199-214
12. B. Bielefeld, Y. Fisher
Pages 215-228
13. F. Dudbridge
Pages 229-241
14. K. Culik II, J. Kari
Pages 243-258
15. Y. Fisher
Pages 259-291
16. Y. Fisher
Pages 293-296
17. Y. Fisher
Pages 297-310
18. Y. Fisher
Pages 311-315
19. Back Matter
Pages 317-341

### Introduction

What 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.

### Keywords

Finite JPEG Mathematica algorithms approximation complexity e-Book equation function image processing optimization proof theorem wavelet

### Editors and affiliations

• Yuval Fisher
• 1
1. 1.Institute for Nonlinear ScienceUniversity of California, San DiegoLa JollaUSA

### Bibliographic information

• Book Title Fractal Image Compression
• Book Subtitle Theory and Application
• Authors Yuval Fisher
• DOI https://doi.org/10.1007/978-1-4612-2472-3
• Copyright Information Springer-Verlag New York 1995
• Publisher Name Springer, New York, NY
• eBook Packages
• Hardcover ISBN 978-0-387-94211-7
• Softcover ISBN 978-1-4612-7552-7
• eBook ISBN 978-1-4612-2472-3
• Edition Number 1
• Number of Pages XVIII, 342
• Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site

## Reviews

"This book will be of great value to anyone interested in fractal image compression... It is certainly the best description of Fractal Image Compression to date, and should be the reference in this field for several years to come." J.H. Hubbard, Professor of Mathematics, Cornell University