Geometric tomography
著者
書誌事項
Geometric tomography
（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, v. 58）
Cambridge University Press, 2006
2nd ed
- : hbk
- : pbk
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注記
Bibliography: p. 437-469
Includes indexes
内容説明・目次
内容説明
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.
目次
- 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.
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