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Geometric Tomography

Geometric Tomography

2nd Edition

$247.00 (C)

Part of Encyclopedia of Mathematics and its Applications

  • Date Published: June 2006
  • availability: Available
  • format: Hardback
  • isbn: 9780521866804

$ 247.00 (C)
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About the Authors
  • 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.

    • Over 70 illustrations
    • Comprehensive bibliography has over 800 references
    • Well-written and clear; the opening chapters are accessible to advanced undergraduates
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    Reviews & endorsements

    "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

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    Product details

    • Edition: 2nd Edition
    • Date Published: June 2006
    • format: Hardback
    • isbn: 9780521866804
    • length: 516 pages
    • dimensions: 234 x 156 x 33 mm
    • weight: 0.97kg
    • availability: Available
  • Table of Contents

    Preface to the second edition
    Preface
    0. Background material
    1. Parallel X-rays of planar convex bodies
    2. Parallel X-rays in n dimensions
    3. Projections and projection functions
    4. Projection bodies and volume inequalities
    5. Point X-rays
    6. Chord functions and equichordal problems
    7. Sections, section functions, and point X-rays
    8. Intersection bodies and volume inequalities
    9. Estimates from projection and section functions
    Appendix A. Mixed volumes and dual mixed volumes
    Appendix B. Inequalities
    Appendix C. Integral transforms
    References
    Notation
    Author index
    Subject index.

  • Author

    Richard J. Gardner, Western Washington University
    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.

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