Discrete Tomography

1. Front Matter

   Pages i-xxii

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2. Foundations

   1. Front Matter

      Pages 1-1

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   2. Discrete Tomography: A Historical Overview

      • Attila Kuba, Gabor T. Herman

      Pages 3-34

   3. Sets of Uniqueness and Additivity in Integer Lattices

      • Peter C. Fishburn, Lawrence A. Shepp

      Pages 35-58

   4. Tomographic Equivalence and Switching Operations

      • T. Yung Kong, Gabor T. Herman

      Pages 59-84

   5. Uniqueness and Complexity in Discrete Tomography

      • Richard J. Gardner, Peter Gritzmann

      Pages 85-113

   6. Reconstruction of Plane Figures from Two Projections

      • Akira Kaneko, Lei Huang

      Pages 115-135

   7. Reconstruction of Two-Valued Functions and Matrices

      • Attila Kuba

      Pages 137-162

   8. Reconstruction of Connected Sets from Two Projections

      • Alberto Del Lungo, Maurice Nivat

      Pages 163-188

3. Algorithms

   1. Front Matter

      Pages 189-189

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   2. Binary Tomography Using Gibbs Priors

      • Samuel Matej, Avi Vardi, Gabor T. Herman, Eilat Vardi

      Pages 191-212

   3. Probabilistic Modeling of Discrete Images

      • Michael T. Chan, Gabor T. Herman, Emanuel Levitan

      Pages 213-235

   4. Multiscale Bayesian Methods for Discrete Tomography

      • Thomas Frese, Charles A. Bouman, Ken Sauer

      Pages 237-264

   5. An Algebraic Solution for Discrete Tomography

      • Andrew E. Yagle

      Pages 265-284

   6. Binary Steering of Nonbinary Iterative Algorithms

      • Yair Censor, Samuel Matej

      Pages 285-296

   7. Reconstruction of Binary Images via the EM Algorithm

      • Yehuda Vardi, Cun-Hui Zhang

      Pages 297-316

   8. Compact Object Reconstruction

      • Ali Mohammad-Djafari, Charles Soussen

      Pages 317-342

4. Applications

   1. Front Matter

      Pages 343-343

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   2. CT-Assisted Engineering and Manufacturing

      • Jolyon A. Browne, Mathew Koshy

      Pages 345-361

   3. 3D Reconstruction from Sparse Radiographic Data

      • James Sachs Jr., Ken Sauer

      Pages 363-383

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.

• 3-D torus
• bayesian methods
• binary tomography
• computer imaging
• diffuse planar tomography
• discrete images
• electron microscopy
• image processing
• image projections
• multidimensional image processing
• multidimensional images
• nonbinary iterative algorithms
• orthogonal projections
• radiographic data
• symbolic projections

"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

• Department of Radiology, University of Pennsylvania, Philadelphia, USA

  Gabor T. Herman

• Department of Applied Informatics, József Attila University, Szeged, Hungary

  Attila Kuba

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