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Fractal and Wavelet Image Compression Techniques

Fractal and Wavelet Image Compression Techniques
Author: Stephen T. Welstead
Publisher: SPIE Press
Total Pages: 264
Release: 1999
Genre: Technology & Engineering
ISBN: 9780819435033

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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.


Image Compression Using Fractals and Wavelets

Image Compression Using Fractals and Wavelets
Author:
Publisher:
Total Pages: 65
Release: 1993
Genre:
ISBN:

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There are several approaches to image compression. The current most popular methods relies on eliminating high frequency components of the signal by storing only the low frequency Fourier coefficients. Other methods use a 'building block' approach, breaking up images into a small number of canonical pieces and storing only a reference to which piece goes where. Our research has focused on a new scheme based on fractals. Our approach to image compression is to tessellate the image with a tiling which varies with the local image complexity, and to check for self similarity amongst the tiles. Self similarities are coded as systems of affine transformations which can be stored far more compactly than the original images on small platforms. An original objective of our Phase II research project was to develop a hardware implementation of our Fractal based algorithm and to investigate various techniques for encoding. During the course of initial investigations it became apparent that the bulk of our efforts should be directed toward speeding up the software algorithms, especially in the decoding and adapting our fractal encoding methods to color images. This is because the most significant commercial applications of image compression require fast decoding.


A Wavelet Fractal Method for Content Based Image and Video Compression

A Wavelet Fractal Method for Content Based Image and Video Compression
Author: Robert J. Bonneau
Publisher:
Total Pages: 148
Release: 1997
Genre:
ISBN:

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Traditional methods of image and video coding rely on linear transformations that focus primarily on high compression. With the increasing demand for digital imagery and video there is now a need for functionality of the compressed information. This dissertation develops a new framework for compression that uses a fractal wavelet method to break the imagery into shape, texture, color, and motion. With this new organization, image information is readily accessible to the user in compressed form. Based on this compression method, we then develop an object-oriented video format. Image analysts tend to break imagery into the categories of shape, texture, color, and motion. Thus, we begin our approach to image compression by finding mathematical methods that preserve shape and texture in an efficient manner. This new non-traditional method begins by using fractals. A fractal is an object which when observed at its smallest level of detail resembles the overall object itself. Some natural examples include ferns, snowflakes, clouds, and mountains. Recently, engineers have applied fixed point theory to describe a method of fractal image compression . Unfortunately fixed point theory only provides a partial description of fractal compression, since it says little about the spatial frequency structure behind the process.


Fractal Image Compression

Fractal Image Compression
Author: Yuval Fisher
Publisher: Springer Science & Business Media
Total Pages: 347
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461224721

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One half of the book is authored by Yuval Fisher himself, while articles from another 12 experts in the field present material from different points of view. The focus here is solely on fractal image encoding, with the aim of providing a working code that is usable in applications, while containing the complete details of how to encode and decode images. An indispensable "how to" guide, combining the very latest results in the field. Of interest to a very wide audience, ranging from experts in image processing to high school students.


Wavelet Image and Video Compression

Wavelet Image and Video Compression
Author: Pankaj N. Topiwala
Publisher: Springer Science & Business Media
Total Pages: 434
Release: 2006-04-18
Genre: Science
ISBN: 0306470438

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An exciting new development has taken place in the digital era that has captured the imagination and talent of researchers around the globe - wavelet image compression. This technology has deep roots in theories of vision, and promises performance improvements over all other compression methods, such as those based on Fourier transforms, vectors quantizers, fractals, neural nets, and many others. It is this revolutionary new technology that is presented in Wavelet Image and Video Compression, in a form that is accessible to the largest audience possible. Wavelet Image and Video Compression is divided into four parts. Part I, Background Material, introduces the basic mathematical structures that underly image compression algorithms with the intention of providing an easy introduction to the mathematical concepts that are prerequisites for the remainder of the book. It explains such topics as change of bases, scalar and vector quantization, bit allocation and rate-distortion theory, entropy coding, the discrete-cosine transform, wavelet filters and other related topics. Part II, Still Image Coding, presents a spectrum of wavelet still image coding techniques. Part III, Special Topics in Still Image Coding, provides a variety of example coding schemes with a special flavor in either approach or application domain. Part IV, Video Coding, examines wavelet and pyramidal coding techniques for video data. Wavelet Image and Video Compression serves as an excellent reference and may be used as a text for advanced courses covering the subject.


Scaling, Fractals and Wavelets

Scaling, Fractals and Wavelets
Author: Patrice Abry
Publisher: John Wiley & Sons
Total Pages: 382
Release: 2013-03-01
Genre: Mathematics
ISBN: 1118622901

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Scaling is a mathematical transformation that enlarges or diminishes objects. The technique is used in a variety of areas, including finance and image processing. This book is organized around the notions of scaling phenomena and scale invariance. The various stochastic models commonly used to describe scaling — self-similarity, long-range dependence and multi-fractals — are introduced. These models are compared and related to one another. Next, fractional integration, a mathematical tool closely related to the notion of scale invariance, is discussed, and stochastic processes with prescribed scaling properties (self-similar processes, locally self-similar processes, fractionally filtered processes, iterated function systems) are defined. A number of applications where the scaling paradigm proved fruitful are detailed: image processing, financial and stock market fluctuations, geophysics, scale relativity, and fractal time-space.


A Hybrid Fractal-wavelet Transform Image Data Compression Algorithm

A Hybrid Fractal-wavelet Transform Image Data Compression Algorithm
Author: University of Warwick. Dept. of Computer Science
Publisher:
Total Pages: 39
Release: 1995
Genre: Fractals
ISBN:

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Abstract: "This report describes two seemingly distinct areas of work, wavelet analysis and fractal image compression. A review of these two areas is presented, a new algorithm outlined, and some results presented. Finally, some speculations concerning the future direction of this research is included."


Signal Processing with Fractals

Signal Processing with Fractals
Author: Gregory W. Wornell
Publisher: Prentice Hall
Total Pages: 200
Release: 1996
Genre: Mathematics
ISBN:

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Fractal geometry and recent developments in wavelet theory are having an important impact on the field of signal processing. Efficient representations for fractal signals based on wavelets are opening up new applications for signal processing, and providing better solutions to problems in existing applications. Signal Processing with Fractals provides a valuable introduction to this new and exciting area, and develops a powerful conceptual foundation for understanding the topic. Practical techniques for synthesizing, analyzing, and processing fractal signals for a wide range of applications are developed in detail, and novel applications in communications are explored.


Fractals in Multimedia

Fractals in Multimedia
Author: Michael F. Barnsley
Publisher: Springer Science & Business Media
Total Pages: 271
Release: 2012-12-06
Genre: Computers
ISBN: 1468492446

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This IMA Volume in Mathematics and its Applications FRACTALS IN MULTIMEDIA is a result of a very successful three-day minisymposium on the same title. The event was an integral part of the IMA annual program on Mathemat ics in Multimedia, 2000-2001. We would like to thank Michael F. Barnsley (Department of Mathematics and Statistics, University of Melbourne), Di etmar Saupe (Institut fUr Informatik, UniversiUit Leipzig), and Edward R. Vrscay (Department of Applied Mathematics, University of Waterloo) for their excellent work as organizers of the meeting and for editing the proceedings. We take this opportunity to thank the National Science Foundation for their support of the IMA. Series Editors Douglas N. Arnold, Director of the IMA Fadil Santosa, Deputy Director of the IMA v PREFACE This volume grew out of a meeting on Fractals in Multimedia held at the IMA in January 2001. The meeting was an exciting and intense one, focused on fractal image compression, analysis, and synthesis, iterated function systems and fractals in education. The central concerns of the meeting were to establish within these areas where we are now and to develop a vision for the future.


Wavelets and Fractals in Earth System Sciences

Wavelets and Fractals in Earth System Sciences
Author: E. Chandrasekhar
Publisher: Taylor & Francis
Total Pages: 306
Release: 2013-11-20
Genre: Science
ISBN: 146655360X

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The subject of wavelet analysis and fractal analysis is fast developing and has drawn a great deal of attention in varied disciplines of science and engineering. Over the past couple of decades, wavelets, multiresolution, and multifractal analyses have been formalized into a thorough mathematical framework and have found a variety of applications w