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Discrete Tomography : Foundations, Algorithms, and Applications - Gabor T. Herman

Discrete Tomography

Foundations, Algorithms, and Applications

By: Gabor T. Herman (Editor), Attila Kuba (Editor)

Hardcover Published: 1st November 1999
ISBN: 9780817641016
Number Of Pages: 479

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Goals of the Book Overthelast thirty yearsthere has been arevolutionindiagnostic radiology as a result oftheemergenceofcomputerized tomography (CT), which is the process of obtaining the density distribution within the human body from multiple x-ray projections. Since an enormous variety of possible density values may occur in the body, a large number of projections are necessary to ensure the accurate reconstruction oftheir distribution. There are other situations in which we desire to reconstruct an object from its projections, but in which we know that the object to be recon- structed has only a small number of possible values. For example, a large fraction of objects scanned in industrial CT (for the purpose of nonde- structive testing or reverse engineering) are made of a single material and so the ideal reconstruction should contain only two values: zero for air and the value associated with the material composing the object. Similar as- sumptions may even be made for some specific medical applications; for example, in angiography ofthe heart chambers the value is either zero (in- dicating the absence of dye) or the value associated with the dye in the chamber. Another example arises in the electron microscopy of biological macromolecules, where we may assume that the object to be reconstructed is composed of ice, protein, and RNA. One can also apply electron mi- croscopy to determine the presenceor absence ofatoms in crystallinestruc- tures, which is again a two-valued situation.

"This book is the first book on discrete tomography. The editors have collected very aptly papers representing all possible directions in discrete tomography. For anyone entering the area of discrete tomography [the book] is a must as it is comprehensive and covers all major aspects of this field." --International Journal of Tomography & Statistics

Preface
Contributors
Foundations Discrete Tomography: A Historical Overview
Herman Sets of Uniqueness and Additivity in Integer Lattices
Tomopgraphic Equivalence and Switching Operations
Uniqueness and Complexity in Discrete Tomography
Reconstruction of Plane Figures from Two Projections
Reconstruction of Two-Valued Functions and Matrices
Reconstruction of Connected Sets from Two Projections
Algorithms Binary Tomography Using Gibbs Priors
Probabilistic Modeling of Discrete Images
Multiscale Bayesian Methods for Discrete Tomography
An Algebraic Solution for Discrete Tomography
Binary Steering of Nonbinary Iterative Algorithms
Reconstruction of Binary Images via the EM Algorithm
Applications CT-Assisted Engineering and Manufacturing
Browne, Mathew Koshy3D Reconstruction from Sparse Radiographic Data
Heart Chamber Reconstruction from Biplane Angiography
Prause Discrete Tomography in Electron Microscopy
Tomopgraphy on the 3D-Torus and Crystals
A Recursive Algorithm for Diffuse Planar Tomography
Patch From Orthogonal Projections to Symbolic Projections
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780817641016
ISBN-10: 0817641017
Series: Applied and Numerical Harmonic Analysis
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 479
Published: 1st November 1999
Publisher: BIRKHAUSER BOSTON INC
Country of Publication: US
Dimensions (cm): 24.77 x 16.51  x 2.54
Weight (kg): 0.84