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, 1995
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注記
Includes bibliographical references (p. 387-407) and author and subject 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 computerised tomography, which reconstructs an image from X-rays of a human patient. It overlaps with convex geometry, and employs many tools from that area, including integral geometry. It also has connections to geometric probing in robotics and to stereology. The main text contains a rigorous treatment of the subject starting from basic concepts and moving up to the research frontier: 72 unsolved problems are stated. Each chapter ends with extensive notes, historical remarks, and some biographies. The bibliography comprises over 500 references. This comprehensive study will be invaluable to specialists in geometry and tomography; the opening chapters can also be read by advanced undergraduate students.
目次
- Background material
- Parallel X-rays of planar convex bodies
- Parallel X-rays in n dimensions
- Projections and projection functions
- Projection bodies and volume inequalities
- Point X-rays
- Chord functions and equichordal problems
- Sections, section functions and point X-rays
- Intersection bodies and volume inequalities
- Estimates from projection and section functions.
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