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Mastering the Discrete Fourier Transform in One Two or Several Dimensions

Mastering the Discrete Fourier Transform in One  Two or Several Dimensions Author Isaac Amidror
ISBN-10 9781447151678
Release 2013-07-19
Pages 375
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The discrete Fourier transform (DFT) is an extremely useful tool that finds application in many different disciplines. However, its use requires caution. The aim of this book is to explain the DFT and its various artifacts and pitfalls and to show how to avoid these (whenever possible), or at least how to recognize them in order to avoid misinterpretations. This concentrated treatment of the DFT artifacts and pitfalls in a single volume is, indeed, new, and it makes this book a valuable source of information for the widest possible range of DFT users. Special attention is given to the one and two dimensional cases due to their particular importance, but the discussion covers the general multidimensional case, too. The book favours a pictorial, intuitive approach which is supported by mathematics, and the discussion is accompanied by a large number of figures and illustrative examples, some of which are visually attractive and even spectacular. Mastering the Discrete Fourier Transform in One, Two or Several Dimensions is intended for scientists, engineers, students and any readers who wish to widen their knowledge of the DFT and its practical use. This book will also be very useful for ‘naive’ users from various scientific or technical disciplines who have to use the DFT for their respective applications. The prerequisite mathematical background is limited to an elementary familiarity with calculus and with the continuous and discrete Fourier theory.



Operator Related Function Theory and Time Frequency Analysis

Operator Related Function Theory and Time Frequency Analysis Author Karlheinz Gröchenig
ISBN-10 9783319085579
Release 2014-11-25
Pages 195
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This book collects the proceedings of the 2012 Abel Symposium, held at the Norwegian Academy of Science and Letters, Oslo. The Symposium, and this book, are focused on two important fields of modern mathematical analysis: operator-related function theory and time-frequency analysis; and the profound interplay between them. Among the original contributions and overview lectures gathered here are a paper presenting multifractal analysis as a bridge between geometric measure theory and signal processing; local and global geometry of Prony systems and Fourier reconstruction of piecewise-smooth functions; Bernstein's problem on weighted polynomial approximation; singular distributions and symmetry of the spectrum; and many others. Offering a selection of the latest and most exciting results obtained by world-leading researchers, the book will benefit scientists working in Harmonic and Complex Analysis, Mathematical Physics and Signal Processing.



The Theory of the Moir Phenomenon

The Theory of the Moir   Phenomenon Author Isaac Amidror
ISBN-10 1848821816
Release 2009-03-15
Pages 529
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Since the first edition of this book was published several new developments have been made in the field of the moiré theory. The most important of these concern new results that have recently been obtained on moiré effects between correlated aperiodic (or random) structures, a subject that was completely absent in the first edition, and which appears now for the first time in a second, separate volume. This also explains the change in the title of the present volume, which now includes the subtitle “Volume I: Periodic Layers”. This subtitle has been added to clearly distinguish the present volume from its new companion, which is subtitled “Volume II: Aperiodic Layers”. It should be noted, however, that the new subtitle of the present volume may be somewhat misleading, since this book also treats (in Chapters 10 and 11) moiré effects between repetitive layers, which are, in fact, geometric transformations of periodic layers, that are generally no longer periodic in themselves. The most suitable subtitle for the present volume would therefore have been “Periodic or Repetitive Layers”, but in the end we have decided on the shorter version.



Computer Vision

Computer Vision Author Richard Szeliski
ISBN-10 1848829469
Release 2010-11-05
Pages 812
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Humans perceive the three-dimensional structure of the world with apparent ease. However, despite all of the recent advances in computer vision research, the dream of having a computer interpret an image at the same level as a two-year old remains elusive. Why is computer vision such a challenging problem and what is the current state of the art? Computer Vision: Algorithms and Applications explores the variety of techniques commonly used to analyze and interpret images. It also describes challenging real-world applications where vision is being successfully used, both for specialized applications such as medical imaging, and for fun, consumer-level tasks such as image editing and stitching, which students can apply to their own personal photos and videos. More than just a source of “recipes,” this exceptionally authoritative and comprehensive textbook/reference also takes a scientific approach to basic vision problems, formulating physical models of the imaging process before inverting them to produce descriptions of a scene. These problems are also analyzed using statistical models and solved using rigorous engineering techniques Topics and features: structured to support active curricula and project-oriented courses, with tips in the Introduction for using the book in a variety of customized courses; presents exercises at the end of each chapter with a heavy emphasis on testing algorithms and containing numerous suggestions for small mid-term projects; provides additional material and more detailed mathematical topics in the Appendices, which cover linear algebra, numerical techniques, and Bayesian estimation theory; suggests additional reading at the end of each chapter, including the latest research in each sub-field, in addition to a full Bibliography at the end of the book; supplies supplementary course material for students at the associated website, http://szeliski.org/Book/. Suitable for an upper-level undergraduate or graduate-level course in computer science or engineering, this textbook focuses on basic techniques that work under real-world conditions and encourages students to push their creative boundaries. Its design and exposition also make it eminently suitable as a unique reference to the fundamental techniques and current research literature in computer vision.



Deblurring Images

Deblurring Images Author Per Christian Hansen
ISBN-10 0898718872
Release 2006-01-01
Pages 130
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Describes the deblurring algorithms and techniques collectively known as spectral filtering methods, in which the singular value decomposition, or a similar decomposition with spectral properties, is used to introduce the necessary regularization or filtering in the reconstructed image. The concise MATLAB® implementations described in the book provide a template of techniques that can be used to restore blurred images from many applications.



Practical Image and Video Processing Using MATLAB

Practical Image and Video Processing Using MATLAB Author Oge Marques
ISBN-10 9781118093474
Release 2011-08-04
Pages 696
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Up-to-date, technically accurate coverage of essential topics in image and video processing This is the first book to combine image and video processing with a practical MATLAB®-oriented approach in order to demonstrate the most important image and video techniques and algorithms. Utilizing minimal math, the contents are presented in a clear, objective manner, emphasizing and encouraging experimentation. The book has been organized into two parts. Part I: Image Processing begins with an overview of the field, then introduces the fundamental concepts, notation, and terminology associated with image representation and basic image processing operations. Next, it discusses MATLAB® and its Image Processing Toolbox with the start of a series of chapters with hands-on activities and step-by-step tutorials. These chapters cover image acquisition and digitization; arithmetic, logic, and geometric operations; point-based, histogram-based, and neighborhood-based image enhancement techniques; the Fourier Transform and relevant frequency-domain image filtering techniques; image restoration; mathematical morphology; edge detection techniques; image segmentation; image compression and coding; and feature extraction and representation. Part II: Video Processing presents the main concepts and terminology associated with analog video signals and systems, as well as digital video formats and standards. It then describes the technically involved problem of standards conversion, discusses motion estimation and compensation techniques, shows how video sequences can be filtered, and concludes with an example of a solution to object detection and tracking in video sequences using MATLAB®. Extra features of this book include: More than 30 MATLAB® tutorials, which consist of step-by-step guides to exploring image and video processing techniques using MATLAB® Chapters supported by figures, examples, illustrative problems, and exercises Useful websites and an extensive list of bibliographical references This accessible text is ideal for upper-level undergraduate and graduate students in digital image and video processing courses, as well as for engineers, researchers, software developers, practitioners, and anyone who wishes to learn about these increasingly popular topics on their own. Supplemental resources for readers and instructors can be found at http://www.ogemarques.com



The Sparse Fourier Transform

The Sparse Fourier Transform Author Haitham Hassanieh
ISBN-10 9781947487062
Release 2018-02-27
Pages 279
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The Fourier transform is one of the most fundamental tools for computing the frequency representation of signals. It plays a central role in signal processing, communications, audio and video compression, medical imaging, genomics, astronomy, as well as many other areas. Because of its widespread use, fast algorithms for computing the Fourier transform can benefit a large number of applications. The fastest algorithm for computing the Fourier transform is the Fast Fourier Transform (FFT), which runs in near-linear time making it an indispensable tool for many applications. However, today, the runtime of the FFT algorithm is no longer fast enough especially for big data problems where each dataset can be few terabytes. Hence, faster algorithms that run in sublinear time, i.e., do not even sample all the data points, have become necessary. This book addresses the above problem by developing the Sparse Fourier Transform algorithms and building practical systems that use these algorithms to solve key problems in six different applications: wireless networks; mobile systems; computer graphics; medical imaging; biochemistry; and digital circuits. This is a revised version of the thesis that won the 2016 ACM Doctoral Dissertation Award.



The Essential Guide to Image Processing

The Essential Guide to Image Processing Author Alan C. Bovik
ISBN-10 0080922511
Release 2009-07-08
Pages 672
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A complete introduction to the basic and intermediate concepts of image processing from the leading people in the field Up-to-date content, including statistical modeling of natural, anistropic diffusion, image quality and the latest developments in JPEG 2000 This comprehensive and state-of-the art approach to image processing gives engineers and students a thorough introduction, and includes full coverage of key applications: image watermarking, fingerprint recognition, face recognition and iris recognition and medical imaging. "This book combines basic image processing techniques with some of the most advanced procedures. Introductory chapters dedicated to general principles are presented alongside detailed application-orientated ones. As a result it is suitably adapted for different classes of readers, ranging from Master to PhD students and beyond." – Prof. Jean-Philippe Thiran, EPFL, Lausanne, Switzerland "Al Bovik’s compendium proceeds systematically from fundamentals to today’s research frontiers. Professor Bovik, himself a highly respected leader in the field, has invited an all-star team of contributors. Students, researchers, and practitioners of image processing alike should benefit from the Essential Guide." – Prof. Bernd Girod, Stanford University, USA "This book is informative, easy to read with plenty of examples, and allows great flexibility in tailoring a course on image processing or analysis." – Prof. Pamela Cosman, University of California, San Diego, USA A complete and modern introduction to the basic and intermediate concepts of image processing – edited and written by the leading people in the field An essential reference for all types of engineers working on image processing applications Up-to-date content, including statistical modelling of natural, anisotropic diffusion, image quality and the latest developments in JPEG 2000



From Gestalt Theory to Image Analysis

From Gestalt Theory to Image Analysis Author Agnès Desolneux
ISBN-10 9780387726359
Release 2007-12-18
Pages 276
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This book introduces a new theory in Computer Vision yielding elementary techniques to analyze digital images. These techniques are a mathematical formalization of the Gestalt theory. From the mathematical viewpoint the closest field to it is stochastic geometry, involving basic probability and statistics, in the context of image analysis. The book is mathematically self-contained, needing only basic understanding of probability and calculus. The text includes more than 130 illustrations, and numerous examples based on specific images on which the theory is tested. Detailed exercises at the end of each chapter help the reader develop a firm understanding of the concepts imparted.



Computational Photography

Computational Photography Author Ramesh Raskar
ISBN-10 1568813139
Release 2016-05-15
Pages 350
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Computational Photography combines plentiful computing, digital sensors, modern optics, actuators, probes, and smart lights to escape the limitations of traditional film cameras and enables novel imaging applications. This book provides a practical guide to topics in image capture and manipulation methods for generating compelling pictures for graphics, special effects, scene comprehension, and art. The computational techniques discussed cover topics in exploiting new ideas in manipulating optics, illumination, and sensors at time of capture. In addition, the authors describe sophisticated reconstruction procedures from direct and indirect pixel measurements that go well beyond the traditional digital darkroom experience.



Theoretical Foundations of Digital Imaging Using MATLAB

Theoretical Foundations of Digital Imaging Using MATLAB  Author Leonid P. Yaroslavsky
ISBN-10 9781466592193
Release 2012-11-26
Pages 511
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With the ubiquitous use of digital imaging, a new profession has emerged: imaging engineering. Designed for newcomers to imaging science and engineering, Theoretical Foundations of Digital Imaging Using MATLAB® treats the theory of digital imaging as a specific branch of science. It covers the subject in its entirety, from image formation to image perfecting. Based on the author’s 50 years of working and teaching in the field, the text first addresses the problem of converting images into digital signals that can be stored, transmitted, and processed on digital computers. It then explains how to adequately represent image transformations on computers. After presenting several examples of computational imaging, including numerical reconstruction of holograms and virtual image formation through computer-generated display holograms, the author introduces methods for image perfect resampling and building continuous image models. He also examines the fundamental problem of the optimal estimation of image parameters, such as how to localize targets in images. The book concludes with a comprehensive discussion of linear and nonlinear filtering methods for image perfecting and enhancement. Helping you master digital imaging, this book presents a unified theoretical basis for understanding and designing methods of imaging and image processing. To facilitate a deeper understanding of the major results, it offers a number of exercises supported by MATLAB programs, with the code available at www.crcpress.com.



Advanced Digital Imaging Laboratory Using MATLAB

Advanced Digital Imaging Laboratory Using MATLAB  Author Leonid P. Yaroslavsky
ISBN-10 0750310510
Release 2014-07-10
Pages 114
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Whether you are studying or already using digital imaging techniques, developing proficiency in the subject is not possible without mastering practical skills. In this book, Prof. Yaroslavsky delivers a complete applied course in digital imaging aimed at advanced students and practitioners. Covering all areas of digital imaging, the text provides an outline of outlying principles of each topic while offering more than 80 MATLAB(R) based exercises. Subjects addressed embrace image digitization (discretization, quantization, compression), digital image formation and computational imaging, image resampling and building continuous image models, image and noise statistical characterization and diagnostics, statistical image models and pattern formation, image correlators for localization of objects, methods of image perfecting (denoising, deblurring), and methods of image enhancement. Key features include: Supports studying of all aspects of digital imaging from image signal digitization to image parameter estimation, recovery, restoration and enhancement. MATLAB(r) source codes for exercises are provided, which readers can modify for their particular needs and tastes, to design new exercises and, in addition, to use them for solving particular image-processing tasks. Test signals and images provided in the book, as well as methodology of the experiments, will be useful for readers in their further studies and practical work. Exercises are supported by outlines of the corresponding theory. The book offers a unique combination of exercises, supportive software and data set that can be used not only for studying the subject, but in further practical work.



It s a Nonlinear World

It s a Nonlinear World Author Richard H. Enns
ISBN-10 9780387753409
Release 2010-10-14
Pages 384
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Drawing examples from mathematics, physics, chemistry, biology, engineering, economics, medicine, politics, and sports, this book illustrates how nonlinear dynamics plays a vital role in our world. Examples cover a wide range from the spread and possible control of communicable diseases, to the lack of predictability in long-range weather forecasting, to competition between political groups and nations. After an introductory chapter that explores what it means to be nonlinear, the book covers the mathematical concepts such as limit cycles, fractals, chaos, bifurcations, and solitons, that will be applied throughout the book. Numerous computer simulations and exercises allow students to explore topics in greater depth using the Maple computer algebra system. The mathematical level of the text assumes prior exposure to ordinary differential equations and familiarity with the wave and diffusion equations. No prior knowledge of Maple is assumed. The book may be used at the undergraduate or graduate level to prepare science and engineering students for problems in the "real world", or for self-study by practicing scientists and engineers.



Geometry of Curves and Surfaces with MAPLE

Geometry of Curves and Surfaces with MAPLE Author Vladimir Rovenski
ISBN-10 9781461221289
Release 2013-12-01
Pages 310
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This concise text on geometry with computer modeling presents some elementary methods for analytical modeling and visualization of curves and surfaces. The author systematically examines such powerful tools as 2-D and 3-D animation of geometric images, transformations, shadows, and colors, and then further studies more complex problems in differential geometry. Well-illustrated with more than 350 figures---reproducible using Maple programs in the book---the work is devoted to three main areas: curves, surfaces, and polyhedra. Pedagogical benefits can be found in the large number of Maple programs, some of which are analogous to C++ programs, including those for splines and fractals. To avoid tedious typing, readers will be able to download many of the programs from the Birkhauser web site. Aimed at a broad audience of students, instructors of mathematics, computer scientists, and engineers who have knowledge of analytical geometry, i.e., method of coordinates, this text will be an excellent classroom resource or self-study reference. With over 100 stimulating exercises, problems and solutions, {\it Geometry of Curves and Surfaces with Maple} will integrate traditional differential and non- Euclidean geometries with more current computer algebra systems in a practical and user-friendly format.



Fundamentals of Multimedia

Fundamentals of Multimedia Author Ze-Nian Li
ISBN-10 9783319052908
Release 2014-04-09
Pages 727
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This textbook introduces the “Fundamentals of Multimedia”, addressing real issues commonly faced in the workplace. The essential concepts are explained in a practical way to enable students to apply their existing skills to address problems in multimedia. Fully revised and updated, this new edition now includes coverage of such topics as 3D TV, social networks, high-efficiency video compression and conferencing, wireless and mobile networks, and their attendant technologies. Features: presents an overview of the key concepts in multimedia, including color science; reviews lossless and lossy compression methods for image, video and audio data; examines the demands placed by multimedia communications on wired and wireless networks; discusses the impact of social media and cloud computing on information sharing and on multimedia content search and retrieval; includes study exercises at the end of each chapter; provides supplementary resources for both students and instructors at an associated website.



Image and Video Based Artistic Stylisation

Image and Video Based Artistic Stylisation Author Paul Rosin
ISBN-10 9781447145196
Release 2012-10-29
Pages 397
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Non-photorealistic rendering (NPR) is a combination of computer graphics and computer vision that produces renderings in various artistic, expressive or stylized ways such as painting and drawing. This book focuses on image and video based NPR, where the input is a 2D photograph or a video rather than a 3D model. 2D NPR techniques have application in areas as diverse as consumer and professional digital photography and visual effects for TV and film production. The book covers the full range of the state of the art of NPR with every chapter authored by internationally renowned experts in the field, covering both classical and contemporary techniques. It will enable both graduate students in computer graphics, computer vision or image processing and professional developers alike to quickly become familiar with contemporary techniques, enabling them to apply 2D NPR algorithms in their own projects.



Discrete Fourier Analysis

Discrete Fourier Analysis Author M. W. Wong
ISBN-10 9783034801164
Release 2011-05-30
Pages 177
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This textbook presents basic notions and techniques of Fourier analysis in discrete settings. Written in a concise style, it is interlaced with remarks, discussions and motivations from signal analysis. The first part is dedicated to topics related to the Fourier transform, including discrete time-frequency analysis and discrete wavelet analysis. Basic knowledge of linear algebra and calculus is the only prerequisite. The second part is built on Hilbert spaces and Fourier series and culminates in a section on pseudo-differential operators, providing a lucid introduction to this advanced topic in analysis. Some measure theory language is used, although most of this part is accessible to students familiar with an undergraduate course in real analysis. Discrete Fourier Analysis is aimed at advanced undergraduate and graduate students in mathematics and applied mathematics. Enhanced with exercises, it will be an excellent resource for the classroom as well as for self-study.