Synopses & Reviews
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.
Review
"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
Table of Contents
Preface
Contributors
Part I. Foundations
Discrete Tomography: A Historical Overview \ Attila Kuba, Gabor T. Herman
Sets of Uniqueness and Additivity in Integer Lattices \ Peter C. Fishburn, Lawrence A. Shepp
Tomopgraphic Equivalence and Switching Operations \ T. Yung Kong, Gabor T. Herman
Uniqueness and Complexity in Discrete Tomography \ Richard J. Gardner, Peter Gritzmann
Reconstruction of Plane Figures from Two Projections \ Akira Kaneko, Lei Huang
Reconstruction of Two-Valued Functions and Matrices \ Attila Kuba
Reconstruction of Connected Sets from Two Projections \ Alberto Del Lungo, Maurice Nivat
Part II. Algorithms
Binary Tomography Using Gibbs Priors \ Samuel Matej, Avi Vardi, Gabor T. Herman, Eilat Vardi
Probabilistic Modeling of Discrete Images \ Michael T. Chan, Gabor T. Herman, Emanuel Levitan
Multiscale Bayesian Methods for Discrete Tomography \ Thomas Frese, Charles A. Bouman, Ken Sauer
An Algebraic Solution for Discrete Tomography \ Andrew E. Yagle
Binary Steering of Nonbinary Iterative Algorithms \ Yair Censor, Samuel Matej
Reconstruction of Binary Images via the EM Algorithm \ Yehuda Vardi, Cun-Hui Zhang
Part III. Applications
CT-Assisted Engineering and Manufacturing \ Jolyon A. Browne, Mathew Koshy
3D Reconstruction from Sparse Radiographic Data \ James Sachs, Jr., Ken Sauer
Heart Chamber Reconstruction from Biplane Angiography \ Dietrich G.W. Onnasch, Guido P.M. Prause
Discrete Tomography in Electron Microscopy \ J.M. Carazo, C.O. Sorzano, E. Rietzel, R. Schröder, R. Marabini
Tomopgraphy on the 3D-Torus and Crystals \ Pablo M. Salzberg, Raul Figueroa
A Recursive Algorithm for Diffuse Planar Tomography \ Sarah K. Patch
From Orthogonal Projections to Symbolic Projections \ Shi-Kuo Chang
Index