Fractal Geometry In Digital Imaging

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.

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.

Medical imaging technologies play a significant role in visualization and interpretation methods in medical diagnosis and practice using decision making, pattern classification, diagnosis, and learning. Progressions in the field of medical imaging lead to interdisciplinary discovery in microscopic image processing and computer-assisted diagnosis systems, and aids physicians in the diagnosis and early detection of diseases. Histopathological Image Analysis in Medical Decision Making provides emerging research exploring the theoretical and practical applications of image technologies and feature extraction procedures within the medical field. Featuring coverage on a broad range of topics such as image classification, digital image analysis, and prediction methods, this book is ideally designed for medical professionals, system engineers, medical students, researchers, and medical practitioners seeking current research on problem-oriented processing techniques in imaging technologies.

Fractal analysis has rapidly become an important field in materials science and engineering with broad applications to theoretical analysis and quantitative description of microstructures of materials. Fractal methods have thus far shown great potential in engineering applications in quantitative microscopic analysis of materials using commercial microscopes. This book attempts to introduce the fundamentals and the basis methods of fractal description of microstructures in combination with digital imaging and computer technologies. Basic concepts are given in the form of mathematical expressions. Detailed algorithms in practical applications are also provided. Fractal measurement, error analysis and fractal description of cluster growth, thin films and surfaces are emphasized in this book. Image-Based Fractal Description of Microstructures provides a comprehensive approach to materials characterization by fractal from theory to application.

Fractal geometry has become popular in the last 15 years, its applications can be found in technology, science, or even arts. Fractal methods and formalism are seen today as a general, abstract, but nevertheless practical instrument for the description of nature in a wide sense. But it was Computer Graphics which made possible the increasing popularity of fractals several years ago, and long after their mathematical formulation. The two disciplines are tightly linked. The book contains the scientificcontributions presented in an international workshop in the "Computer Graphics Center" in Darmstadt, Germany. The target of the workshop was to present the wide spectrum of interrelationships and interactions between Fractal Geometry and Computer Graphics. The topics vary from fundamentals and new theoretical results to various applications and systems development. All contributions are original, unpublished papers.The presentations have been discussed in two working groups; the discussion results, together with actual trends and topics of future research, are reported in the last section. The topics of the book are divides into four sections: Fundamentals, Computer Graphics and Optical Simulation, Simulation of Natural Phenomena, Image Processing and Image Analysis.

This authoritative text (the second part of a complete MSc course) provides mathematical methods required to describe images, image formation and different imaging systems, coupled with the principle techniques used for processing digital images. It is based on a course for postgraduates reading physics, electronic engineering, telecommunications engineering, information technology and computer science. This book relates the methods of processing and interpreting digital images to the ‘physics’ of imaging systems. Case studies reinforce the methods discussed, with examples of current research themes. Provides mathematical methods required to describe images, image formation and different imaging systems Outlines the principle techniques used for processing digital images Relates the methods of processing and interpreting digital images to the ‘physics’ of imaging systems

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.

The first thorough treatment of the Assouad dimension in fractal geometry, with applications to many fields within pure mathematics.