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Birkhäuser - Birkhäuser Engineering | Advances in Discrete Tomography and Its Applications

Advances in Discrete Tomography and Its Applications

Herman, Gabor T., Kuba, Attila (Eds.)

2007, XX, 392 p. 140 illus.

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  • Covers theoretical results, algorithms, and practical applications
  • Explores various mathematical and computational problems of discrete tomography with an emphasis on new applications
  • Provides a useful guide and reference to state-of-the-art research, methods, and applications

Advances in Discrete Tomography and Its Applications is a unified presentation of new methods, algorithms, and select applications that are the foundations of multidimensional image reconstruction by discrete tomographic methods. The self-contained chapters, written by leading mathematicians, engineers, and computer scientists, present cutting-edge research and results in the field.

Three main areas are covered: foundations, algorithms, and practical applications. Following an introduction that reports the recent literature of the field, the book explores various mathematical and computational problems of discrete tomography including new applications.

Topics and Features:

* introduction to discrete point X-rays

* uniqueness and additivity in discrete tomography

* network flow algorithms for discrete tomography

* convex programming and variational methods

* applications to electron microscopy, materials science, nondestructive testing, and diagnostic medicine

Professionals, researchers, practitioners, and students in mathematics, computer imaging, biomedical imaging, computer science, and image processing will find the book to be a useful guide and reference to state-of-the-art research, methods, and applications.

 

Content Level » Professional/practitioner

Keywords » 3-D tomographic reconstruction - algorithms - computer imaging - convex programming - diagnostic medicine - discrete point X-rays - discrete tomography - electron microscopy - image processing - linear optimization - multidimensional image reconstruction - network flow algorithms - nondestructive testing

Related subjects » Birkhäuser Engineering - Birkhäuser Mathematics

Table of contents 

ANHA Series Preface Preface List of Contributors Introduction / A. Kuba and G.T. Herman Part I. Foundations of Discrete Tomography An Introduction to Discrete Point X-Rays / P. Dulio, R.J. Gardner, and C. Peri Reconstruction of Q-Convex Lattice Sets / S. Brunetti and A. Daurat Algebraic Discrete Tomography / L. Hajdu and R. Tijdeman Uniqueness and Additivity for n-Dimensional Binary Matrices with Respect to Their 1-Marginals / E. Vallejo Constructing (0, 1)-Matrices with Given Line Sums and Certain Fixed Zeros / R.A. Brualdi and G. Dahl Reconstruction of Binary Matrices under Adjacency Constraints / S. Brunetti, M.C. Costa, A. Frosini, F. Jarray, and C. Picouleau Part II. Discrete Tomography Reconstruction Algorithms Decomposition Algorithms for Reconstructing Discrete Sets with Disjoint Components / P. Balázs Network Flow Algorithms for Discrete Tomography / K.J. Batenburg A Convex Programming Algorithm for Noisy Discrete Tomography / T.D. Capricelli and P.L. Combettes Variational Reconstruction with DC-Programming / C. Schnörr, T. Schüle, and S. Weber Part III. Applications of Discrete Tomography Direct Image Reconstruction-Segmentation, as Motivated by Electron Microscopy / Hstau Y. Liao and Gabor T. Herman Discrete Tomography for Generating Grain Maps of Polycrystals / A. Alpers, L. Rodek, H.F. Poulsen, E. Knudsen, G.T. Herman Discrete Tomography Methods for Nondestructive Testing / J. Baumann, Z. Kiss, S. Krimmel, A. Kuba, A. Nagy, L. Rodek, B. Schillinger, and J. Stephan Emission Discrete Tomography / E. Barcucci, A. Frosini, A. Kuba, A. Nagy, S. Rinaldi, M. Samal, and S. Zopf Application of a Discrete Tomography Approach to Computerized Tomography / Y. Gerard and F. Feschet Index

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