Mathematics Of Medical Imaging Pdf
Author: Max A. Viergever
Publisher: Springer Science & Business Media
ISBN: 3642833063
Size: 63.75 MB
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Medical imaging is an important and rapidly expanding area in medical science. Many of the methods employed are essentially digital, for example computerized tomography, and the subject has become increasingly influenced by develop ments in both mathematics and computer science. The mathematical problems have been the concern of a relatively small group of scientists, consisting mainly of applied mathematicians and theoretical physicists. Their efforts have led to workable algorithms for most imaging modalities. However, neither the fundamentals, nor the limitations and disadvantages of these algorithms are known to a sufficient degree to the physicists, engineers and physicians trying to implement these methods. It seems both timely and important to try to bridge this gap. This book summarizes the proceedings of a NATO Advanced Study Institute, on these topics, that was held in the mountains of Tuscany for two weeks in the late summer of 1986. At another (quite different) earlier meeting on medical imaging, the authors noted that each of the speakers had given, there, a long introduction in their general area, stated that they did not have time to discuss the details of the new work, but proceeded to show lots of clinical results, while excluding any mathematics associated with the area.
Mathematics and Computer Science in Medical Imaging
Authors: Max A. Viergever, Andrew Todd-Pokropek
Categories: Computers
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media
Medical imaging is an important and rapidly expanding area in medical science. Many of the methods employed are essentially digital, for example computerized tomography, and the subject has become increasingly influenced by develop ments in both mathematics and computer science. The mathematical problems have been the concern of a relatively small group of scientists, consisting mainly of applied mathematicians and theoretical physicists. Their efforts have led to workable algorithms for most imaging modalities. However, neither the fundamentals, nor the limitations and disadvantages of these algorithms are known to a sufficient degree to the physicists, engineers and physicians trying to implement these methods. It seems both timely and important to try to bridge this gap. This book summarizes the proceedings of a NATO Advanced Study Institute, on these topics, that was held in the mountains of Tuscany for two weeks in the late summer of 1986. At another (quite different) earlier meeting on medical imaging, the authors noted that each of the speakers had given, there, a long introduction in their general area, stated that they did not have time to discuss the details of the new work, but proceeded to show lots of clinical results, while excluding any mathematics associated
Parallel Optimization
Authors: Department of Mathematics and Computer Science Yair Censor, Yair Censor, Stavros Andrea Zenios, Department of Public and Business Administration Stavros A Zenios
Categories: Mathematics
Type: BOOK - Published: 1997 - Publisher: Oxford University Press on Demand
This book offers a unique pathway to methods of parallel optimization by introducing parallel computing ideas into both optimization theory and into some numerical algorithms for large-scale optimization problems. The three parts of the book bring together relevant theory, careful study of algorithms, and modeling of significant real world problems such as image reconstruction, radiation therapy treatment planning, financial planning, transportation and multi-commodity network flow problems, planning under uncertainty, and matrix balancing problems.
Recent Developments in Optimization Theory and Nonlinear Analysis
Authors: Yair Censor, Simeon Reich
Categories: Mathematics
Type: BOOK - Published: 1997 - Publisher: American Mathematical Soc.
This volume contains the refereed proceedings of the special session on Optimization and Nonlinear Analysis held at the Joint American Mathematical Society-Israel Mathematical Union Meeting which took place at the Hebrew University of Jerusalem in May 1995. Most of the papers in this book originated from the lectures delivered at this special session. In addition, some participants who did not present lectures and invited speakers who were unable to attend contributed their work. The fields of optimization theory and nonlinear analysis continue to be very active.This book presents not only the wide spectrum and diversity of the results, but also their manifold connections to other areas, such as differential equations, functional analysis, operator theory, calculus of variations, numerical analysis, and mathematical programming. In reading this book one encounters papers that deal, for example, with convex, quasiconvex and generalized convex functions, fixed and periodic points, fractional-linear transformations, moduli of convexity, monotone operators, Morse lemmas, Navier-Stokes equations, nonexpansive maps, nonsmooth analysis, numerical stability, products of projections, steepest descent, the Leray-Schauder degree, the tumpike property, and variational inequalities.
Front-End Vision and Multi-Scale Image Analysis
Authors: Bart M. Haar Romeny
Categories: Computers
Type: BOOK - Published: 2008-10-24 - Publisher: Springer Science & Business Media
Many approaches have been proposed to solve the problem of finding the optic flow field of an image sequence. Three major classes of optic flow computation techniques can discriminated (see for a good overview Beauchemin and Barron IBeauchemin19951): gradient based (or differential) methods; phase based (or frequency domain) methods; correlation based (or area) methods; feature point (or sparse data) tracking methods; In this chapter we compute the optic flow as a dense optic flow field with a multi scale differential method. The method, originally proposed by Florack and Nielsen [Florack1998a] is known as the Multiscale Optic Flow Constrain Equation (MOFCE). This is a scale space version of the well known computer vision implementation of the optic flow constraint equation, as originally proposed by Horn and Schunck [Horn1981]. This scale space variation, as usual, consists of the introduction of the aperture of the observation in the process. The application to stereo has been described by Maas et al. [Maas 1995a, Maas 1996a]. Of course, difficulties arise when structure emerges or disappears, such as with occlusion, cloud formation etc. Then knowledge is needed about the processes and objects involved. In this chapter we focus on the scale space approach to the local
Image Processing Technologies
Authors: Kiyoharu Aizawa, Katsuhiko Sakaue, Yasuhito Suenaga
Categories: Computers
Type: BOOK - Published: 2004-03-01 - Publisher: CRC Press
Showcasing the most influential developments, experiments, and architectures impacting the digital, surveillance, automotive, industrial, and medical sciences, this text/reference tracks the evolution and advancement of CVIP technologies - examining methods and algorithms for image analysis, optimization, segmentation, and restoration.
Instrumentierung der Bioimpedanzmessung
Authors: Steffen Kaufmann
Categories: Technology & Engineering
Type: BOOK - Published: 2015-05-05 - Publisher: Springer-Verlag
Steffen Kaufmann entwickelt ein Verfahren zur verbesserten Instrumentierung der Transferimpedanzmessung mit Fokus auf die Anwendung in der Elektroimpedanztomographie (EIT). Die Optimierung wird durch eine Erhöhung des Signal-Rauschabstandes erreicht, gleichzeitig ermöglicht das Verfahren spektroskopische Mehrfrequenz-Messungen, mit einer Auflösung nach Betrag und Phase. Der Autor entwickelt und evaluiert ein Bioimpedanzmesssystem (BMS), das zu einem Mehrfrequenz-EIT-System erweitert und für unterschiedliche Messungen an Widerstands- und Tankphantomen sowie zur Visualisierung der Atmung eingesetzt wird. Den Abschluss bildet die Konzeption eines parallelen Mehrfrequenz-Aktivelektroden-EIT-Systems.
Current Catalog
Authors: National Library of Medicine (U.S.)
Categories: Medicine
Type: BOOK - Published: - Publisher:
First multi-year cumulation covers six years: 1965-70.
The Mathematics of Medical Imaging
Authors: Timothy G. Feeman
Categories: Mathematics
Type: BOOK - Published: 2010-03-10 - Publisher: Springer Science & Business Media
This text explores medical imaging, one of the most significant areas of recent mathematical applications, in a concise manner accessible to undergraduate students. The author emphasizes the mathematical aspects of medical imaging, including not only the theoretical background, but also the role of approximation methods and the computer implementation of the inversion algorithms. In twenty-first century health care, CAT scans, ultrasounds, and MRIs are commonplace. Significant computational advances, along with the development, design, and improvement of the machines themselves, can only occur in conjunction with a proper understanding of the mathematics. This book is inherently interdisciplinary in nature, and therefore is appropriate for students of engineering, physics, and computer science, in addition to mathematics.
Mathematics Of Medical Imaging Pdf
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