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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.
ANHA Series 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