The Science of Fractal Images
The Science of Fractal Images

Author: Heinz-Otto Peitgen

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 328

ISBN-13: 146123784X

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This book is based on notes for the course Fractals:lntroduction, Basics and Perspectives given by MichaelF. Barnsley, RobertL. Devaney, Heinz-Otto Peit gen, Dietmar Saupe and Richard F. Voss. The course was chaired by Heinz-Otto Peitgen and was part of the SIGGRAPH '87 (Anaheim, California) course pro gram. Though the five chapters of this book have emerged from those courses we have tried to make this book a coherent and uniformly styled presentation as much as possible. It is the first book which discusses fractals solely from the point of view of computer graphics. Though fundamental concepts and algo rithms are not introduced and discussed in mathematical rigor we have made a serious attempt to justify and motivate wherever it appeared to be desirable. Ba sic algorithms are typically presented in pseudo-code or a description so close to code that a reader who is familiar with elementary computer graphics should find no problem to get started. Mandelbrot's fractal geometry provides both a description and a mathemat ical model for many of the seemingly complex forms and patterns in nature and the sciences. Fractals have blossomed enormously in the past few years and have helped reconnect pure mathematics research with both natural sciences and computing. Computer graphics has played an essential role both in its de velopment and rapidly growing popularity. Conversely, fractal geometry now plays an important role in the rendering, modelling and animation of natural phenomena and fantastic shapes in computer graphics.

Fractal Imaging
Fractal Imaging

Author: Ning Lu

Publisher: Springer Science & Business

Published: 1997

Total Pages: 458

ISBN-13: 9780124580107

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Basic rules govern our universe, and an understanding of these rules makes a wide array of subjects crystal-clear. Fractal is such a rule: it completely describes the geometry of a leaf in 24 numbers. This book tells how to apply this fractal rule to photographic images.

Fractal Geometry in Digital Imaging
Fractal Geometry in Digital Imaging

Author: Martin J. Turner

Publisher: Academic Press

Published: 1998-06-23

Total Pages: 352

ISBN-13: 9780127039701

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This book is concerned with the theory and application of fractal geometry in digital imaging. Throughout the book, a series of new approaches to defining fractals are illustrated, such as the analysis of the fractal power spectrum and the use of fractional differentials. Several new algorithms and applications are also discussed and applied to real life images. Fractal Geometry in Digital imaging will appeal to postgraduates, researchers and practitioners in image processing, mathematics and computing, information technology and engineering.

Examining Fractal Image Processing and Analysis
Examining Fractal Image Processing and Analysis

Author: Nayak, Soumya Ranjan

Publisher: IGI Global

Published: 2019-10-18

Total Pages: 323

ISBN-13: 1799800687

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Digital image processing is a field that is constantly improving. Gaining high-level understanding from digital images is a key requirement for computing. One aspect of study that is assisting with this advancement is fractal theory. This new science has gained momentum and popularity as it has become a key topic of research in the area of image analysis. Examining Fractal Image Processing and Analysis is an essential reference source that discusses fractal theory applications and analysis, including box-counting analysis, multi-fractal analysis, 3D fractal analysis, and chaos theory, as well as recent trends in other soft computing techniques. Featuring research on topics such as image compression, pattern matching, and artificial neural networks, this book is ideally designed for system engineers, computer engineers, professionals, academicians, researchers, and students seeking coverage on problem-oriented processing techniques and imaging technologies.

Fractals in Multimedia
Fractals in Multimedia

Author: Michael F. Barnsley

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 271

ISBN-13: 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.

Intelligent Fractal-Based Image Analysis
Intelligent Fractal-Based Image Analysis

Author: Soumya Ranjan Nayak

Publisher: Elsevier

Published: 2024-05-27

Total Pages: 320

ISBN-13: 0443184690

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Fractals are infinite, complex patterns used in modeling physical and dynamic systems. Fractal theory research has increased across different fields of applications including engineering science, health science, and social science. Recent literature shows the vital role fractals play in digital image analysis, specifically in biomedical image processing. Fractal graphics is an interdisciplinary field that deals with how computers can be used to gain high-level understanding from digital images. Integrating artificial intelligence with fractal characteristics has resulted in new interdisciplinary research in the fields of pattern recognition and image processing analysis. Intelligent Fractal-Based Image Analysis: Application in Pattern Recognition and Machine Vision provides insights into the current strengths and weaknesses of different applications as well as research findings on fractal graphics in engineering and science applications. The book aims to improve the exchange of ideas and coherence between various core computing methods and highlight the relevance of related application areas for advanced as well as novice-user application. The book presents an in-depth look at core concepts, methodological aspects, and advanced feature opportunities, focusing on major real time applications in engineering science and health science. The book will appeal to researchers, data scientists, industry professionals, and graduate students in the fields of fractal graphics and its related applications. - Investigates advanced fractal theories spanning neural networks, fuzzy logic, machine learning, deep learning, and hybrid intelligent systems in solving pattern recognition problems - Explores the application of fractal theories to a wide range of medical image processing modalities - Presents case studies that illustrate the application and integration of fractal theories into intelligent computing in the resolution of important pattern recognition and machine vision problems

The Beauty of Fractals
The Beauty of Fractals

Author: Heinz-Otto Peitgen

Publisher: Springer Science & Business Media

Published: 1986-07

Total Pages: 226

ISBN-13: 9783540158516

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Now approaching its tenth year, this hugely successful book presents an unusual attempt to publicise the field of Complex Dynamics. The text was originally conceived as a supplemented catalogue to the exhibition "Frontiers of Chaos", seen in Europe and the United States, and describes the context and meaning of these fascinating images. A total of 184 illustrations - including 88 full-colour pictures of Julia sets - are suggestive of a coffee-table book. However, the invited contributions which round off the book lend the text the required formality. Benoit Mandelbrot gives a very personal account, in his idiosyncratic self-centred style, of his discovery of the fractals named after him and Adrien Douady explains the solved and unsolved problems relating to this amusingly complex set.

Fractal and Wavelet Image Compression Techniques
Fractal and Wavelet Image Compression Techniques

Author: Stephen T. Welstead

Publisher: SPIE Press

Published: 1999

Total Pages: 264

ISBN-13: 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.

Fractals
Fractals

Author: Dinesh Kumar

Publisher: CRC Press

Published: 2017-02-03

Total Pages: 134

ISBN-13: 1351678388

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The book provides an insight into the advantages and limitations of the use of fractals in biomedical data. It begins with a brief introduction to the concept of fractals and other associated measures and describes applications for biomedical signals and images. Properties of biological data in relations to fractals and entropy, and the association with health and ageing are also covered. The book provides a detailed description of new techniques on physiological signals and images based on the fractal and chaos theory. The aim of this book is to serve as a comprehensive guide for researchers and readers interested in biomedical signal and image processing and feature extraction for disease risk analyses and rehabilitation applications. While it provides the mathematical rigor for those readers interested in such details, it also describes the topic intuitively such that it is suitable for audience who are interested in applying the methods to healthcare and clinical applications. The book is the outcome of years of research by the authors and is comprehensive and includes other reported outcomes.