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Discrete Tomography: Foundations, Algorithms, and Applications (Applied and Numerical Harmonic Analysis)From Birkh�user
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Goals of the Book Overthelast thirty yearsthere has been arevolutionindiagnostic radiology as a result oftheemergenceofcomputerized tomography (CT), which is the process of obtaining the density distribution within the human body from multiple x-ray projections. Since an enormous variety of possible density values may occur in the body, a large number of projections are necessary to ensure the accurate reconstruction oftheir distribution. There are other situations in which we desire to reconstruct an object from its projections, but in which we know that the object to be recon structed has only a small number of possible values. For example, a large fraction of objects scanned in industrial CT (for the purpose of nonde structive testing or reverse engineering) are made of a single material and so the ideal reconstruction should contain only two values: zero for air and the value associated with the material composing the object. Similar as sumptions may even be made for some specific medical applications; for example, in angiography ofthe heart chambers the value is either zero (in dicating the absence of dye) or the value associated with the dye in the chamber. Another example arises in the electron microscopy of biological macromolecules, where we may assume that the object to be reconstructed is composed of ice, protein, and RNA. One can also apply electron mi croscopy to determine the presenceor absence ofatoms in crystallinestruc tures, which is again a two-valued situation.
- Sales Rank: #6364323 in Books
- Published on: 1999-11-01
- Original language: English
- Number of items: 1
- Dimensions: 9.21" h x 1.13" w x 6.14" l, 1.88 pounds
- Binding: Hardcover
- 479 pages
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
From the Back Cover
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.
Most helpful customer reviews
2 of 2 people found the following review helpful.
an engineer's view
By D E Bodette
Each chapter in the book is by different authors and so the level of detail, notation, etc. is uneven. The chapters are more than just reprints of previous materials and are self-contained. The early foundation chapters are written from a mathematician's perspective, which is wholly unsatisfying for an engineer. There is a minor emphasis on binary images throughout the book, but binary images are not treated in any depth. In general, the algorithm and application chapters are more overview than details. Examples are almost nonexistent which means this would be an extremely poor textbook even for upper-level classes. The example in chapter 11 is full of errors and a bit incomplete. Overall, the chapters are much better than any one of the conference papers they are based on, but you will still need to consult the references to really use any of the information.
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