3 edition of **Geometric Tomography (Encyclopedia of Mathematics and its Applications)** found in the catalog.

- 44 Want to read
- 6 Currently reading

Published
**June 19, 2006**
by Cambridge University Press
.

Written in English

- Geometry,
- Mathematics,
- Science/Mathematics,
- Geometry - Differential,
- Mathematics / Geometry / General,
- Geometry - General,
- Geometric tomography

The Physical Object | |
---|---|

Format | Hardcover |

Number of Pages | 514 |

ID Numbers | |

Open Library | OL7767391M |

ISBN 10 | 0521866804 |

ISBN 10 | 9780521866804 |

Geometric tomography consists of reconstructing a 3-dimensional object from 2-dimensional information such as projections or sections. In this paper, we are interested in the reconstruction of a 3D object from its intersections with a set of planes, called : Omid Amini, Jean-Daniel Boissonnat, Pooran Memari. X-ray computed tomography (CT) has experienced tremendous growth in recent years, in terms of both basic technology and new clinical applications. This book provides an overview of the evolution of CT, the mathematical and physical aspects of the technology, and the fundamentals of image reconstruction using algorithms. It examines image display from traditional methods through the most recent 5/5(3).

The book offers a comprehensive and user-oriented description of the theoretical and technical system fundamentals of computed tomography (CT) for a wide readership, from conventional single-slice acquisitions to volume acquisition with multi-slice and cone-beam spiral CT. these bodies. Geometric tomography has important applications to many areas of mathematics and science, in general. The book “Geometric Tomography” [4] by Gardner gives an excellent account of various problems and techniques that arise in geometric tomography. Of paramount importance are questions about unique.

Geometric Tomography is a geometric relative of Computerized Tomography, where the usual density functions are replaced by geometric objects. The main goal is to find conditions which guarantee a faithful reconstruction, possibly unique, within a given geometric class of subsets of $\mathbb{R}^n$. Presence of ambiguities is often related to the so-called switching-components, or analogous. Geometric tomography deals with the retrieval of information about a Geometric object from data concerning its projections (shadows) on planes or cross-sections by planes. It is a Geometric relative of computerized tomography, which reconstructs an image from X-rays of a human patient. The subject overlaps with convex geometry and employs many tools from that area, including some formulas from.

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This book is a good complement to Schneider's "Convex Bodies: The Brunn-Minkowski Theory". While not as comprehensive as the latter book in convex geometry, it is very well written and clear. "Geometric Tomography" is a necessary book for any researcher in convex geometry.5/5(2).

Geometric tomography is the area of mathematics dealing with the retrieval of information about a geometric object from data about its sections by lines or planes, or orthogonal projections onto lines or planes, or both.

The use of the term "geometric object" is deliberately vague. A special case would be the study of sections or projections of a convex body or polytope, but it is sometimes.

Geometric tomography deals with the retrieval of information about a geometric object from data concerning its projections (shadows) on planes or cross-sections by planes.

It is a geometric relative of computerized tomography, which reconstructs an image from X-rays of a human patient. Geometric Tomography (Encyclopedia of Mathematics and its Applications Book 58) - Kindle edition by Gardner, Richard J.

Download it once and read it on your Kindle device, PC, phones or tablets. Use features Geometric Tomography book bookmarks, note taking and highlighting while reading Geometric Tomography (Encyclopedia of Mathematics and its Applications Book 58).5/5(1). Geometric tomography deals with the retrieval of information about a geometric object from data concerning its projections (shadows) on planes or cross-sections by planes.

In part, it is a geometric relative of computerized tomography, which reconstructs an image from X-rays of a human patient.

Geometric tomography overlaps with convex geometry and employs many tools from that area, including some formulas from integral geometry. This comprehensive study provides a. Richard Gardner has been Professor of Mathematics at Western Washington University since He is the author of 70 papers and founded geometric tomography as a subject in its own right with the publication of the first edition of this book in %().

Geometric tomography deals with the retrieval of information about a geometric object from data concerning its projections (shadows) on planes or cross-sections by planes. It is a geometric relative of computerized tomography, which reconstructs an image from X-rays of a human : Richard J.

Gardner. A comprehensive, rigorous treatment of geometric tomography, with 66 unsolved problems, over 70 illustrations, and over : $ term geometric tomography. In the author’s book [21], the fol-lowing definition is offered: “Geometric tomographyis the area of math-ematics dealing with the retrieval of information about a geometric object from data about its sec-tions, or projections, or both.” The use of File Size: 1MB.

Geometric Tomography: Richard J. Gardner: Books - Skip to main content. Try Prime Hello, Sign in Account & Lists Sign in Account & Lists Orders Try Prime Cart. Books Go Search Best Sellers Gift Ideas New Releases Deals Store 5/5(1).

This text, taken from the back cover of the book gives a true description of the book. It is a comprehensive study, covering the field of geometric tomography from principles to recent state-of-the-art, including problems that are still open.

The main topics are discussed in the text of the 9 chapters. Tomography is imaging by sections or sectioning through the use of any kind of penetrating method is used in radiology, archaeology, biology, atmospheric science, geophysics, oceanography, plasma physics, materials science, astrophysics, quantum information, and other areas of word tomography is derived from Ancient Greek τόμος tomos, "slice, section" and γράφω.

Find many great new & used options and get the best deals for Encyclopedia of Mathematics and Its Applications: Geometric Tomography 58 by Richard J. Gardner (, Hardcover, Revised) at the best online prices at eBay. Free shipping for many products.

Geometric Tomography, second edition Geometric tomography deals with the retrieval of information about a geometric object from data concerning its projections (shadows) on planes or cross-sections by planes.

It is a geometric relative of computerized tomography, which recon-structs an image from X-rays of a human patient. The subject overlaps. This book contains the refereed proceedings of the AMS-SIAM Summer Seminar on Tomography, Impedance Imaging, and Integral Geometry, held at Mount Holyoke College in June A number of common themes are found among the papers.

Group theory is fundamental both to tomographic sampling theorems and to pure Radon transforms. The second edition of my book "Geometric Tomography" was published by Cambridge University Press (New York) in Juneand is available in both hardback and paperback.

It is designed to be somewhat accessible even to advanced undergraduate students, and contains 79 computer-generated pictures, 66 open problems, and references. Geometric Tomography. Book Review. The Factorization Method for Inverse Problems.

Book Review. The Mathematics of Medical Imaging: A Beginner's Guide. Book Review. Tomography and Inverse Transport Theory. Book Review. Mathematical Foundations of Imaging, Tomography and.

Background material; 1. Parallel X-rays of planar convex bodies; 2. Parallel X-rays in n dimensions; 3. Projections and projection functions; 4. A novel on-line method based on the symmetry property of the sum of projections (SOP) is proposed to obtain the geometric parameters in cone-beam computed tomography (CBCT).

Build the foundation necessary for the practice of CT scanning with Computed Tomography: Physical Principles, Clinical Applications, and Quality Control, 4th Edition. Written to meet the varied requirements of radiography students and practitioners, this two-color text provides comprehensive coverage of the physical principles of CT and its clinical s: 2.

12 geometric tomography with topological guarantees according to a theorem by W olter [ Wol92 ], this deformation is contin uous and is hence a continuous deformation retract from .This book focuses on basics and clinical interpretation of corneal tomography in clinical practice (pentacam system).

Tomography is a revolution in corneal imaging. Topography is now used to describe the data generated by placido-based devices from the anterior corneal surface, while “Tomography” is a term given to the data generated from the whole cornea by either slit-scanning technology.