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Discrete Tomography
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Discrete Tomography

Discrete Tomography

Foundations, Algorithms, and Applications

Gabor T. Herman, Attila Kuba

479 pages, parution le 06/10/2004


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 and 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.


  • Foundations
    • Discrete Tomography : A Historical Overview
    • Sets of Uniqueness and Additivity in Integer Lattices
    • Tomographic 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
    • Compact Object Reconstruction
  • Applications
    • CT-Assisted Engineering and Manufacturing
    • 3D Reconstruction from Sparse Radiographic Data
    • Heart Chamber Reconstruction from Biplane
    • Discrete Tomography in Electron Microscopy
    • Tomography on the 3D-Torus and Crystals
    • A Recursive Algorithm for Diffuse Planar Tomography
    • From Orthogonal Projections to Symbolic Projections
Voir tout

Caractéristiques techniques

Éditeur(s) Birkhäuser
Auteur(s) Gabor T. Herman, Attila Kuba
Parution 06/10/2004
Nb. de pages 479
Format 16 x 24
Couverture Relié
Poids 835g
Intérieur Noir et Blanc
EAN13 9780817641016

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