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TitleDiscrete Tomography [electronic resource] : Foundations, Algorithms, and Applications / edited by Gabor T. Herman, Attila Kuba
ImprintBoston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 1999
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Descript XXII, 479 p. online resource


The visualization, construction, and reconstruction of multidimensional images are of intense interest in science and engineering today, and discrete tomographyโ{128}{148}which deals with the special case in which the object to be reconstructed has a small number of possible valuesโ{128}{148}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.


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 Angiography -- 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

Medicine Radiology Computer science -- Mathematics Computer graphics Image processing Medicine & Public Health Imaging / Radiology Image Processing and Computer Vision Signal Image and Speech Processing Math Applications in Computer Science Discrete Mathematics in Computer Science Computer Imaging Vision Pattern Recognition and Graphics


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