Ebook: Discrete Tomography: Foundations, Algorithms, and Applications

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.

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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.

 

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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.

 

Content:
Front Matter....Pages i-xxii
Front Matter....Pages 1-1
Discrete Tomography: A Historical Overview....Pages 3-34
Sets of Uniqueness and Additivity in Integer Lattices....Pages 35-58
Tomographic Equivalence and Switching Operations....Pages 59-84
Uniqueness and Complexity in Discrete Tomography....Pages 85-113
Reconstruction of Plane Figures from Two Projections....Pages 115-135
Reconstruction of Two-Valued Functions and Matrices....Pages 137-162
Reconstruction of Connected Sets from Two Projections....Pages 163-188
Front Matter....Pages 189-189
Binary Tomography Using Gibbs Priors....Pages 191-212
Probabilistic Modeling of Discrete Images....Pages 213-235
Multiscale Bayesian Methods for Discrete Tomography....Pages 237-264
An Algebraic Solution for Discrete Tomography....Pages 265-284
Binary Steering of Nonbinary Iterative Algorithms....Pages 285-296
Reconstruction of Binary Images via the EM Algorithm....Pages 297-316
Compact Object Reconstruction....Pages 317-342
Front Matter....Pages 343-343
CT-Assisted Engineering and Manufacturing....Pages 345-361
3D Reconstruction from Sparse Radiographic Data....Pages 363-383
Heart Chamber Reconstruction from Biplane Angiography....Pages 385-403
Discrete Tomography in Electron Microscopy....Pages 405-416
Tomography on the 3D-Torus and Crystals....Pages 417-434
A Recursive Algorithm for Diffuse Planar Tomography....Pages 435-454
Back Matter....Pages 472-479
From Orthogonal Projections to Symbolic Projections....Pages 455-471

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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.

 

Content:
Front Matter....Pages i-xxii
Front Matter....Pages 1-1
Discrete Tomography: A Historical Overview....Pages 3-34
Sets of Uniqueness and Additivity in Integer Lattices....Pages 35-58
Tomographic Equivalence and Switching Operations....Pages 59-84
Uniqueness and Complexity in Discrete Tomography....Pages 85-113
Reconstruction of Plane Figures from Two Projections....Pages 115-135
Reconstruction of Two-Valued Functions and Matrices....Pages 137-162
Reconstruction of Connected Sets from Two Projections....Pages 163-188
Front Matter....Pages 189-189
Binary Tomography Using Gibbs Priors....Pages 191-212
Probabilistic Modeling of Discrete Images....Pages 213-235
Multiscale Bayesian Methods for Discrete Tomography....Pages 237-264
An Algebraic Solution for Discrete Tomography....Pages 265-284
Binary Steering of Nonbinary Iterative Algorithms....Pages 285-296
Reconstruction of Binary Images via the EM Algorithm....Pages 297-316
Compact Object Reconstruction....Pages 317-342
Front Matter....Pages 343-343
CT-Assisted Engineering and Manufacturing....Pages 345-361
3D Reconstruction from Sparse Radiographic Data....Pages 363-383
Heart Chamber Reconstruction from Biplane Angiography....Pages 385-403
Discrete Tomography in Electron Microscopy....Pages 405-416
Tomography on the 3D-Torus and Crystals....Pages 417-434
A Recursive Algorithm for Diffuse Planar Tomography....Pages 435-454
Back Matter....Pages 472-479
From Orthogonal Projections to Symbolic Projections....Pages 455-471
....