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Author: Harrison H. Barrett Publisher: John Wiley & Sons ISBN: 1118772776 Category : Science Languages : en Pages : 1857
Book Description
Winner of the 2006 Joseph W. Goodman Book Writing Award! A comprehensive treatment of the principles, mathematics, and statistics of image science In today's visually oriented society, images play an important role in conveying messages. From seismic imaging to satellite images to medical images, our modern society would be lost without images to enhance our understanding of our health, our culture, and our world. Foundations of Image Science presents a comprehensive treatment of the principles, mathematics, and statistics needed to understand and evaluate imaging systems. The book is the first to provide a thorough treatment of the continuous-to-discrete, or CD, model of digital imaging. Foundations of Image Science emphasizes the need for meaningful, objective assessment of image quality and presents the necessary tools for this purpose. Approaching the subject within a well-defined theoretical and physical context, this landmark text presents the mathematical underpinnings of image science at a level that is accessible to graduate students and practitioners working with imaging systems, as well as well-motivated undergraduate students. Destined to become a standard text in the field, Foundations of Image Science covers: Mathematical Foundations: Examines the essential mathematical foundations of image science Image Formation–Models and Mechanisms: Presents a comprehensive and unified treatment of the mathematical and statistical principles of imaging, with an emphasis on digital imaging systems and the use of SVD methods Image Quality: Provides a systematic exposition of the methodology for objective or task-based assessment of image quality Applications: Presents detailed case studies of specific direct and indirect imaging systems and provides examples of how to apply the various mathematical tools covered in the book Appendices: Covers the prerequisite material necessary for understanding the material in the main text, including matrix algebra, complex variables, and the basics of probability theory
Author: Harrison H. Barrett Publisher: John Wiley & Sons ISBN: 1118772776 Category : Science Languages : en Pages : 1857
Book Description
Winner of the 2006 Joseph W. Goodman Book Writing Award! A comprehensive treatment of the principles, mathematics, and statistics of image science In today's visually oriented society, images play an important role in conveying messages. From seismic imaging to satellite images to medical images, our modern society would be lost without images to enhance our understanding of our health, our culture, and our world. Foundations of Image Science presents a comprehensive treatment of the principles, mathematics, and statistics needed to understand and evaluate imaging systems. The book is the first to provide a thorough treatment of the continuous-to-discrete, or CD, model of digital imaging. Foundations of Image Science emphasizes the need for meaningful, objective assessment of image quality and presents the necessary tools for this purpose. Approaching the subject within a well-defined theoretical and physical context, this landmark text presents the mathematical underpinnings of image science at a level that is accessible to graduate students and practitioners working with imaging systems, as well as well-motivated undergraduate students. Destined to become a standard text in the field, Foundations of Image Science covers: Mathematical Foundations: Examines the essential mathematical foundations of image science Image Formation–Models and Mechanisms: Presents a comprehensive and unified treatment of the mathematical and statistical principles of imaging, with an emphasis on digital imaging systems and the use of SVD methods Image Quality: Provides a systematic exposition of the methodology for objective or task-based assessment of image quality Applications: Presents detailed case studies of specific direct and indirect imaging systems and provides examples of how to apply the various mathematical tools covered in the book Appendices: Covers the prerequisite material necessary for understanding the material in the main text, including matrix algebra, complex variables, and the basics of probability theory
Author: Charles L. Epstein Publisher: SIAM ISBN: 9780898717792 Category : Mathematics Languages : en Pages : 794
Book Description
At the heart of every medical imaging technology is a sophisticated mathematical model of the measurement process and an algorithm to reconstruct an image from the measured data. This book provides a firm foundation in the mathematical tools used to model the measurements and derive the reconstruction algorithms used in most of these modalities. The text uses X-ray computed tomography (X-ray CT) as a 'pedagogical machine' to illustrate important ideas and its extensive discussion of background material makes the more advanced mathematical topics accessible to people with a less formal mathematical education. This new edition contains a chapter on magnetic resonance imaging (MRI), a revised section on the relationship between the continuum and discrete Fourier transforms, an improved description of the gridding method, and new sections on both Grangreat's formula and noise analysis in MR-imaging. Mathematical concepts are illuminated with over 200 illustrations and numerous exercises.
Author: Say Song Goh Publisher: World Scientific ISBN: 9812709061 Category : Computers Languages : en Pages : 275
Book Description
The explosion of data arising from rapid advances in communication, sensing and computational power has concentrated research effort on more advanced techniques for the representation, processing, analysis and interpretation of data sets. In view of these exciting developments, the program OC Mathematics and Computation in Imaging Science and Information ProcessingOCO was held at the Institute for Mathematical Sciences, National University of Singapore, from July to December 2003 and in August 2004 to promote and facilitate multidisciplinary research in the area. As part of the program, a series of tutorial lectures were conducted by international experts on a wide variety of topics in mathematical image, signal and information processing. This compiled volume contains survey articles by the tutorial speakers, all specialists in their respective areas. They collectively provide graduate students and researchers new to the field a unique and valuable introduction to a range of important topics at the frontiers of current research. Sample Chapter(s). Foreword (46 KB). Chapter 1: Subdivision on Arbitrary Meshes: Algorithms and Theory (771 KB). Contents: Subdivision on Arbitrary Meshes: Algorithms and Theory (D Zorin); High Order Numerical Methods for Time Dependent Hamilton-Jacobi Equations (C-W Shu); Theory and Computation of Variational Image Deblurring (T F Chan & J Shen); Data Hiding OCo Theory and Algorithms (P Moulin & R Koetter); Image Steganography and Steganalysis: Concepts and Practice (M Kharrazi et al.); The Apriori Algorithm OCo A Tutorial (M Hegland). Readership: Graduate students and researchers in mathematical image, signal and information processing."
Author: Otmar Scherzer Publisher: Springer Science & Business Media ISBN: 0387929193 Category : Mathematics Languages : en Pages : 1626
Book Description
The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.
Author: Timothy G. Feeman Publisher: Springer Science & Business Media ISBN: 0387927115 Category : Computers Languages : en Pages : 150
Book Description
Medical imaging is a major part of twenty-first century health care. This introduction explores the mathematical aspects of imaging in medicine to explain approximation methods in addition to computer implementation of inversion algorithms.
Author: S. G. Hoggar Publisher: Cambridge University Press ISBN: 9781139451352 Category : Computers Languages : en Pages : 896
Book Description
Compression, restoration and recognition are three of the key components of digital imaging. The mathematics needed to understand and carry out all these components are explained here in a style that is at once rigorous and practical with many worked examples, exercises with solutions, pseudocode, and sample calculations on images. The introduction lists fast tracks to special topics such as Principal Component Analysis, and ways into and through the book, which abounds with illustrations. The first part describes plane geometry and pattern-generating symmetries, along with some on 3D rotation and reflection matrices. Subsequent chapters cover vectors, matrices and probability. These are applied to simulation, Bayesian methods, Shannon's information theory, compression, filtering and tomography. The book will be suited for advanced courses or for self-study. It will appeal to all those working in biomedical imaging and diagnosis, computer graphics, machine vision, remote sensing, image processing and information theory and its applications.
Author: Habib Ammari Publisher: Springer ISBN: 3319025856 Category : Mathematics Languages : en Pages : 366
Book Description
This book covers recent mathematical, numerical, and statistical approaches for multistatic imaging of targets with waves at single or multiple frequencies. The waves can be acoustic, elastic or electromagnetic. They are generated by point sources on a transmitter array and measured on a receiver array. An important problem in multistatic imaging is to quantify and understand the trade-offs between data size, computational complexity, signal-to-noise ratio, and resolution. Another fundamental problem is to have a shape representation well suited to solving target imaging problems from multistatic data. In this book the trade-off between resolution and stability when the data are noisy is addressed. Efficient imaging algorithms are provided and their resolution and stability with respect to noise in the measurements analyzed. It also shows that high-order polarization tensors provide an accurate representation of the target. Moreover, a dictionary-matching technique based on new invariants for the generalized polarization tensors is introduced. Matlab codes for the main algorithms described in this book are provided. Numerical illustrations using these codes in order to highlight the performance and show the limitations of numerical approaches for multistatic imaging are presented.
Author: Jack Lancaster Publisher: CRC Press ISBN: 1498751644 Category : Medical Languages : en Pages : 361
Book Description
Authored by a leading educator, this book teaches the fundamental mathematics and physics concepts associated with medical imaging systems. Going beyond mere description of imaging modalities, this book delves into the mechanisms of image formation and image quality common to all imaging systems: contrast mechanisms, noise, and spatial and temporal resolution, making it an important reference for medical physicists and biomedical engineering students. This is an extensively revised new edition of The Physics of Medical X-Ray Imaging by Bruce Hasegawa (Medical Physics Publishing, 1991), and includes a wide range of modalities such as X-ray CT, MRI and SPECT.
Author: Gilles Aubert Publisher: Springer Science & Business Media ISBN: 0387217665 Category : Mathematics Languages : en Pages : 303
Book Description
Partial differential equations and variational methods were introduced into image processing about 15 years ago, and intensive research has been carried out since then. The main goal of this work is to present the variety of image analysis applications and the precise mathematics involved. It is intended for two audiences. The first is the mathematical community, to show the contribution of mathematics to this domain and to highlight some unresolved theoretical questions. The second is the computer vision community, to present a clear, self-contained, and global overview of the mathematics involved in image processing problems. The book is divided into five main parts. Chapter 1 is a detailed overview. Chapter 2 describes and illustrates most of the mathematical notions found throughout the work. Chapters 3 and 4 examine how PDEs and variational methods can be successfully applied in image restoration and segmentation processes. Chapter 5, which is more applied, describes some challenging computer vision problems, such as sequence analysis or classification. This book will be useful to researchers and graduate students in mathematics and computer vision.
Author: Harrison H. Barrett
Author: Harrison H. Barrett
Author: Charles L. Epstein
Author: Say Song Goh
Author: Otmar Scherzer
Author: Timothy G. Feeman
Author: S. G. Hoggar
Author: Frank Natterer
Author: Habib Ammari
Author: Jack Lancaster
Author: Gilles Aubert