Fractal and Wavelet Image Compression Techniques / Edition 1

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Interest in image compression for Internet and other multimedia applications has spurred research into compression techniques that will increase storage capabilities and transmission speed. This tutorial provides a practical guide to fractal and wavelet approaches--two techniques with exciting potential. It is intended for scientists, engineers, researchers, and students. It provides both introductory information and implementation details. Three Windows-compatible software systems are included so that readers can explore the new technologies in depth. Complete C/C++ source code is provided, enabling readers to go beyond the accompanying software. The mathematical presentation is accessible to advanced undergraduate or beginning graduate students in technical fields.

"...a practical guide eeto image compression...using numerous computer examples...includes Windows software... access to C/C++ source code will be available to readers."

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Editorial Reviews

A tutorial text on the techniques behind fractal and wavelet approaches to image compression. Welstead (mathematics, U. of Alabama- Huntsville) assumes no previous knowledge of image compression, fractal geometry, or wavelet concepts, and figures that the mathematics should be apprehensible to advanced undergraduates and beginning graduates in technical fields. He includes three software packages for Windows, along with the complete C/C++ source code for those who want to color outside the lines. Annotation c. Book News, Inc., Portland, OR (
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Product Details

  • ISBN-13: 9780819435033
  • Publisher: SPIE Press
  • Publication date: 11/1/1999
  • Series: Tutorial Texts in Optical Engineering Series
  • Edition description: New Edition
  • Edition number: 1
  • Pages: 254
  • Product dimensions: 7.04 (w) x 10.02 (h) x 0.62 (d)

Table of Contents

1. Introduction 1
1.1 Images 2
1.2 The image compression problem 3
1.3 Information, entropy, and data modeling 4
1.4 Scalar and vector quantization 5
1.5 Transform methods 7
1.6 Color images 8
1.7 The focus of this book 9
Part 1 Fractal Image Compression
2. Iterated Function Systems 1
2.1 Iterated function systems as the motivation for fractal image compression
2.2 Metric spaces 2
2.2.1 Basic concepts 2
2.2.2 Compact sets and Hausdorff space 4
2.2.3 Contraction mappings 6
2.3 Iterated function systems 8
2.3.1 Introduction 8
2.3.2 The Collage Theorem 9
2.3.3 What the Collage Theorem says 9
2.3.4 Affine transformations 11
2.4 Implementation of an iterated function system 12
2.4.1 Points and transformations 12
2.4.2 Affine coefficients 14
2.4.3 Computing the fractat attractor image from the IFS 15 Deterministic algorithm 15 Random algorithm 18
2.5 Examples 24
2.5.1 Sierpinski triangle 24 Fractal dimension 25
2.5.2 Constructing an IFS from a real image 27
2.5.3 A few more EFS examples 28
3. Fractal Encoding of Grayscale Images 1
3.1 A metric space for grayscale images 1
3.2 Partitioned iterated function systems (PIFS) 2
3.2.1 Affine transformations on grayscale images 2
3.2.2 Contraction mappings on grayscale images 3
3.2.3 Contraction mapping theorem for grayscale images 3
3.2.4 Collage Theorem for grayscale images 5
3.3 Fractal image encoding 6
3.3.1 Domain cells 8
3.3.2 Quadtree partitioning of range cells 9 A scheme for keeping track of quadtree partitioning 11
3.3.3 Mapping domains to ranges 12
3.3.4 Encoding times 14
3.4 Image decoding 15
3.4.1 Measuring the error 16
3.5 Storing the encoded image 18
3.5.1 Range file format 18
3.5.2 Binary range file format 19 Efficient quadtree storage 20 Bit structure for storing range information 21 Transmission robustness 22
3.6 Resolution independence 23
3.7 Operator representation of fractal image encoding 24
3.7.1 "Get-block" and "put-block" operators 24
3.7.2 Operator formulation 25
3.7.3 Solution of the operator equation 26
3.7.4 Error analysis 27
4. Speeding Up Fractal Encoding 1
4.1 Feature extraction 1
4.1.1 Feature definitions 1
4.1.2 Encoding algorithm using feature extraction 3
4.1.3 Sample results using feature extraction 6
4.2 Domain classification 11
4.2.1 Self-organizing neural networks 12
4.2.2 Fractal image encoding using self-organizing domain classification
4.2.3 Sample results using self-organizing domain classifier 16
4.3 Other approaches for speeding up fractal encoding 20
Part II Wavelet Image Compression
5. Simple Wavelets 1
5.1 Introduction 1
5.2 Averaging and detail 2
5.3 Scaling functions and wavelet functions 4
5.4 Multiresolution analysis 9
5.5 Normalization 12
5.6 Wavelet transform 13
5.7 Inverse wavelet transform 17
5.8 Wavelet transform in two dimensions 19
5.8.1 What a wavelet transform looks like 21
5.8.2 Simple wavelet compression scheme 24
6. Daubechies Wavelets 1
6.1 Weighted averages and differences 1
6.1.1 Lowpass and highpass filtering 1
6.1.2 Matrix representation 2
6.2 Properties and conditions on the coefficients 3
6.3 Wavelet transform 4
6.4 Scaling functions and wavelet functions 5
6.5 Daubechies wavelets 6
6.6 Simple image compression with Daubechies wavelets 8
6.7 Summary 11
7. Wavelet Image Compression Techniques 1
7.1 Introduction 1
7.2 Wavelet zerotrees 3
7.2.1 An implementation of wavelet zerotree coding 5 Terminology: Which way is up? 6 Handling the insignificant coefficients 8 The zerotree encoding algorithm 12 Bit planes 13
7.2.2 Decoding a zerotree encoded image 14
7.2.3 Where is the compression? 21
7.2.4 Encoding speed 22
7.3 Hybrid fractal-wavelet coding 23
7.3.1 Operator approach to hybrid fractal-wavelet coding 24
7.3.2 Other hybrid approaches 26
8. Comparison of Fractal and Wavelet Image Compression 1
8.1 Rate distortion 1
8.2 Encodincy speed 4
8.3 Larger imaores 5
8.4 Conclusions 8
Appendix A Using the Accompanying Software 1
A.1 IFS System 1
A.1.1 Points window 1
A.1.2 Transformation window 3
A.1.3 IFS window 5
A.2 IMG System: Fractal Image Compression 8
A.2.1 Encode window 9
A.2.1.1 Encode setup 10
A.2.1.2 Running image encoding 12
A.2.2 Self-organizing encoding window 13
A.2.2.1 Setting up the self-organizing network 14
A.2.2.2 Running self-organized image encoding 15
A.2.3 Decode window 15
A.2.4 Subtraction window 17
A.2.5 Plot window 17
A.3 WAV System: Wavelet Image Compression 20
A.3.1 Wavelet compression window 20
A.3.2 Wavelet zerotree encoding 22
A.3.3 Wavelet zerotree decoding 23
A.3.4 Image subtraction with the WAV System 24
A.3.5 Wavelet plotting window 24
A.3.3.1 Setting Up the Graph Parameters 25
Appendix B Utility Windows Library (UWL) 1
B.1 Windows Programming 1
B.1.1 Multiple Document Interface (MDI) 2
B.1.2 Dialogs 3
B.1.2.1 Modal vs. modeless dialogs 3
B.1.2.2 Windows Common Dialogs 4
B.2 Utility Windows Library (UWL) 5
B.2.1 The t-window class 6
B.2.2 MDI frame window 8
B.2.3 MDI windows 11
B.2.4 Graph window 13
B.2.5 WinMain in a UWL application 15
B.2.6 UWL dialogs 20
B.2.7 Building UWL 21
B.3 Windows Programming References 23
Appendix C Organization of the Accompanying Software Source Code 1
C.1 IFS System 1
C.1.1 IFS classes 1
C.1.2 IFS code files 3
C.1.3 UTM Library 4
C.2 IMG System 5
C.2.1 IMG classes 5
C.2.2 IMG code files 6
C.3 WAV System 8
C.3.1 WAV classes 8
C.3.2 WAV code files 9
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