Fractal and Wavelet Image Compression Techniques / Edition 1

Fractal and Wavelet Image Compression Techniques / Edition 1

by Stephen T. Welstead
     
 

ISBN-10: 0819435031

ISBN-13: 9780819435033

Pub. Date: 11/01/1999

Publisher: SPIE Press

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

Overview

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.

Product Details

ISBN-13:
9780819435033
Publisher:
SPIE Press
Publication date:
11/01/1999
Series:
Tutorial Texts in Optical Engineering Series
Edition description:
New Edition
Pages:
254
Product dimensions:
7.04(w) x 10.02(h) x 0.62(d)

Table of Contents

Preface
1.Introduction1
1.1Images2
1.2The image compression problem3
1.3Information, entropy, and data modeling4
1.4Scalar and vector quantization5
1.5Transform methods7
1.6Color images8
1.7The focus of this book9
Part 1Fractal Image Compression
2.Iterated Function Systems1
2.1Iterated function systems as the motivation for fractal image compression
2.2Metric spaces2
2.2.1Basic concepts2
2.2.2Compact sets and Hausdorff space4
2.2.3Contraction mappings6
2.3Iterated function systems8
2.3.1Introduction8
2.3.2The Collage Theorem9
2.3.3What the Collage Theorem says9
2.3.4Affine transformations11
2.4Implementation of an iterated function system12
2.4.1Points and transformations12
2.4.2Affine coefficients14
2.4.3Computing the fractat attractor image from the IFS15
2.4.3.1Deterministic algorithm15
2.4.3.2Random algorithm18
2.5Examples24
2.5.1Sierpinski triangle24
2.5.1.1Fractal dimension25
2.5.2Constructing an IFS from a real image27
2.5.3A few more EFS examples28
3.Fractal Encoding of Grayscale Images1
3.1A metric space for grayscale images1
3.2Partitioned iterated function systems (PIFS)2
3.2.1Affine transformations on grayscale images2
3.2.2Contraction mappings on grayscale images3
3.2.3Contraction mapping theorem for grayscale images3
3.2.4Collage Theorem for grayscale images5
3.3Fractal image encoding6
3.3.1Domain cells8
3.3.2Quadtree partitioning of range cells9
3.3.2.1A scheme for keeping track of quadtree partitioning11
3.3.3Mapping domains to ranges12
3.3.4Encoding times14
3.4Image decoding15
3.4.1Measuring the error16
3.5Storing the encoded image18
3.5.1Range file format18
3.5.2Binary range file format19
3.5.2.1Efficient quadtree storage20
3.5.2.2Bit structure for storing range information21
3.5.2.3Transmission robustness22
3.6Resolution independence23
3.7Operator representation of fractal image encoding24
3.7.1"Get-block" and "put-block" operators24
3.7.2Operator formulation25
3.7.3Solution of the operator equation26
3.7.4Error analysis27
4.Speeding Up Fractal Encoding1
4.1Feature extraction1
4.1.1Feature definitions1
4.1.2Encoding algorithm using feature extraction3
4.1.3Sample results using feature extraction6
4.2Domain classification11
4.2.1Self-organizing neural networks12
4.2.2Fractal image encoding using self-organizing domain classification
4.2.3Sample results using self-organizing domain classifier16
4.3Other approaches for speeding up fractal encoding20
Part IIWavelet Image Compression
5.Simple Wavelets1
5.1Introduction1
5.2Averaging and detail2
5.3Scaling functions and wavelet functions4
5.4Multiresolution analysis9
5.5Normalization12
5.6Wavelet transform13
5.7Inverse wavelet transform17
5.8Wavelet transform in two dimensions19
5.8.1What a wavelet transform looks like21
5.8.2Simple wavelet compression scheme24
6.Daubechies Wavelets1
6.1Weighted averages and differences1
6.1.1Lowpass and highpass filtering1
6.1.2Matrix representation2
6.2Properties and conditions on the coefficients3
6.3Wavelet transform4
6.4Scaling functions and wavelet functions5
6.5Daubechies wavelets6
6.6Simple image compression with Daubechies wavelets8
6.7Summary11
7.Wavelet Image Compression Techniques1
7.1Introduction1
7.2Wavelet zerotrees3
7.2.1An implementation of wavelet zerotree coding5
7.2.1.1Terminology: Which way is up?6
7.2.1.2Handling the insignificant coefficients8
7.2.1.3The zerotree encoding algorithm12
7.2.1.4Bit planes13
7.2.2Decoding a zerotree encoded image14
7.2.3Where is the compression?21
7.2.4Encoding speed22
7.3Hybrid fractal-wavelet coding23
7.3.1Operator approach to hybrid fractal-wavelet coding24
7.3.2Other hybrid approaches26
8.Comparison of Fractal and Wavelet Image Compression1
8.1Rate distortion1
8.2Encodincy speed4
8.3Larger imaores5
8.4Conclusions8
References
Appendix AUsing the Accompanying Software1
A.1IFS System1
A.1.1Points window1
A.1.2Transformation window3
A.1.3IFS window5
A.2IMG System: Fractal Image Compression8
A.2.1Encode window9
A.2.1.1Encode setup10
A.2.1.2Running image encoding12
A.2.2Self-organizing encoding window13
A.2.2.1Setting up the self-organizing network14
A.2.2.2Running self-organized image encoding15
A.2.3Decode window15
A.2.4Subtraction window17
A.2.5Plot window17
A.3WAV System: Wavelet Image Compression20
A.3.1Wavelet compression window20
A.3.2Wavelet zerotree encoding22
A.3.3Wavelet zerotree decoding23
A.3.4Image subtraction with the WAV System24
A.3.5Wavelet plotting window24
A.3.3.1Setting Up the Graph Parameters25
Appendix BUtility Windows Library (UWL)1
B.1Windows Programming1
B.1.1Multiple Document Interface (MDI)2
B.1.2Dialogs3
B.1.2.1Modal vs. modeless dialogs3
B.1.2.2Windows Common Dialogs4
B.2Utility Windows Library (UWL)5
B.2.1The t-window class6
B.2.2MDI frame window8
B.2.3MDI windows11
B.2.4Graph window13
B.2.5WinMain in a UWL application15
B.2.6UWL dialogs20
B.2.7Building UWL21
B.3Windows Programming References23
Appendix COrganization of the Accompanying Software Source Code1
C.1IFS System1
C.1.1IFS classes1
C.1.2IFS code files3
C.1.3UTM Library4
C.2IMG System5
C.2.1IMG classes5
C.2.2IMG code files6
C.3WAV System8
C.3.1WAV classes8
C.3.2WAV code files9

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