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Discrete Tomography

Foundations, Algorithms, and Applications

  • Gabor T. Herman
  • Attila Kuba

Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Table of contents

  1. Front Matter
    Pages i-xxii
  2. Foundations

    1. Front Matter
      Pages 1-1
    2. Attila Kuba, Gabor T. Herman
      Pages 3-34
    3. Peter C. Fishburn, Lawrence A. Shepp
      Pages 35-58
    4. T. Yung Kong, Gabor T. Herman
      Pages 59-84
    5. Richard J. Gardner, Peter Gritzmann
      Pages 85-113
    6. Akira Kaneko, Lei Huang
      Pages 115-135
    7. Alberto Del Lungo, Maurice Nivat
      Pages 163-188
  3. Algorithms

    1. Front Matter
      Pages 189-189
    2. Samuel Matej, Avi Vardi, Gabor T. Herman, Eilat Vardi
      Pages 191-212
    3. Michael T. Chan, Gabor T. Herman, Emanuel Levitan
      Pages 213-235
    4. Thomas Frese, Charles A. Bouman, Ken Sauer
      Pages 237-264
    5. Andrew E. Yagle
      Pages 265-284
    6. Yair Censor, Samuel Matej
      Pages 285-296
    7. Yehuda Vardi, Cun-Hui Zhang
      Pages 297-316
    8. Ali Mohammad-Djafari, Charles Soussen
      Pages 317-342
  4. Applications

    1. Front Matter
      Pages 343-343
    2. Jolyon A. Browne, Mathew Koshy
      Pages 345-361
    3. James Sachs Jr., Ken Sauer
      Pages 363-383
    4. Dietrich G. W. Onnasch, Guido P. M. Prause
      Pages 385-403
    5. J. M. Carazo, C. O. Sorzano, E. Rietzel, R. Schröder, R. Marabini
      Pages 405-416
    6. Pablo M. Salzberg, Raul Figueroa
      Pages 417-434
  5. Back Matter
    Pages 472-479

About this book

Introduction

The visualization, construction, and reconstruction of multidimensional images are of intense interest in science and engineering today, and discrete tomography—which deals with the special case in which the object to be reconstructed has a small number of possible values—offers some significant new analytical and computational tools.

Discrete Tomography: Foundations, Algorithms, and Applications provides a critical survey of new methods, algorithms, and select applications that are the foundations of multidimensional image construction and reconstruction. The survey chapters, written by leading international authorities, are self-contained adn present the latest research and results in the field. The book covers three main areas: important theoretical results, available algorithms to utilize for reconstruction, and key applications where new results are indicative of greater utility. Following a thorough historical overview of the field, the book provides a journey through the various mathematical and computational problems of discrete tomography. This is followed by a section on numerous algorithmic techniques that can be used to achieve real reconstructions from image projections.

Topics and Features:

* historical overview and summary chapter

* uniqueness and complexity in discrete tomography

* probabilistic modeling  of discrete images

* binary tomography using Gibb priors

* discrete tomography on the 3-D torus and crystals

* binary steering

* 3-D tomographic reconstruction from sparse radiographic data

* symbolic projections

The book is an essential resource for the latest developments and tools in discrete tomography. Professionals, researchers, and practitioners in mathematics, computer imaging, scientific visualization, computer engineering, and multidimensional image processing will find the book an authoritative guide and reference to current research, methods, and applications.

 

Keywords

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

Editors and affiliations

  • Gabor T. Herman
    • 1
  • Attila Kuba
    • 2
  1. 1.Department of RadiologyUniversity of PennsylvaniaPhiladelphiaUSA
  2. 2.Department of Applied InformaticsJózsef Attila UniversitySzegedHungary

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1568-4
  • Copyright Information Springer Science+Business Media New York 1999
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-7196-3
  • Online ISBN 978-1-4612-1568-4
  • Series Print ISSN 2296-5009
  • Series Online ISSN 2296-5017
  • Buy this book on publisher's site
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