Geometric Tomography (Encyclopedia of Mathematics and its Applications, Series Number 58) 2nd Edition by Richard J. Gardner (PDF)

Description

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 integral geometry. It also has connections to discrete tomography, geometric probing in robotics and to stereology. This comprehensive study provides a rigorous treatment of the subject. Although primarily meant for researchers and graduate students in geometry and tomography, brief introductions, suitable for advanced undergraduates, are provided to the basic concepts. More than 70 illustrations are used to clarify the text. The book also presents 66 unsolved problems. Each chapter ends with extensive notes, historical remarks, and some biographies. This edition includes numerous updates and improvements, with some 300 new references bringing the total to over 800.

User’s Reviews

Editorial Reviews: Review “A comprehensive study… For people in computer vision who are interested in geometric tomography and like such a mathematical approach, this book fulfills all their needs… Also serves as a useful reference for scientists and engineers who need to understand concepts of geometric tomography applied to various fields.” Arjan Kujiper for IAPR Newsletter Book Description A comprehensive, rigorous treatment of geometric tomography, with 66 unsolved problems, over 70 illustrations, and over 800 references. About the Author Richard Gardner has been Professor of Mathematics at Western Washington University since 1991. 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 1995. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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.

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