Fractal Image Compression

1. Front Matter

   Pages i-xviii

   PDF

2. Introduction

   • Y. Fisher

   Pages 1-23

3. Mathematical Background

   • Y. Fisher

   Pages 25-53

4. Fractal Image Compression with Quadtrees

   • Y. Fisher

   Pages 55-77

5. Archetype Classification in an Iterated Transformation Image Compression Algorithm

   • R. D. Boss, E. W. Jacobs

   Pages 79-90

6. Hierarchical Interpretation of Fractal Image Coding and Its Applications

   • Z. Baharav, D. Malah, E. Karnin

   Pages 91-117

7. Fractal Encoding with HV Partitions

   • Y. Fisher, S. Menlove

   Pages 119-136

8. A Discrete Framework for Fractal Signal Modeling

   • L. Lundheim

   Pages 137-151

9. A Class of Fractal Image Coders with Fast Decoder Convergence

   • G. E. Øien, S. Lepsøy

   Pages 153-175

10. Fast Attractor Image Encoding by Adaptive Codebook Clustering

    • S. Lepsøy, G. E. Øien

    Pages 177-197

11. Orthogonal Basis IFS

    • G. Vines

    Pages 199-214

12. A Convergence Model

    • B. Bielefeld, Y. Fisher

    Pages 215-228

13. Least-Squares Block Coding by Fractal Functions

    • F. Dudbridge

    Pages 229-241

14. Inference Algorithms for WFA and Image Compression

    • K. Culik II, J. Kari

    Pages 243-258

15. Sample Code

    • Y. Fisher

    Pages 259-291

16. Exercises

    • Y. Fisher

    Pages 293-296

17. Projects

    • Y. Fisher

    Pages 297-310

18. Comparison of Results

    • Y. Fisher

    Pages 311-315

19. Back Matter

    Pages 317-341

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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.

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

"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

• Institute for Nonlinear Science, University of California, San Diego, La Jolla, USA

  Yuval Fisher

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