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词条 Geometric tomography
释义

  1. Theory

  2. Examples

  3. See also

  4. References

  5. External links

Geometric tomography is a mathematical field that focuses on problems of reconstructing homogeneous (often convex) objects from tomographic data (this might be X-rays, projections, sections, brightness functions, or covariograms). More precisely, according to R.J. Gardner (who introduced the term), "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."[1]

Theory

A key theorem in this area states that any convex body in can be determined by parallel, coplanar

X-rays in a set of four directions whose slopes have a transcendental cross ratio.

Examples

  • Radon transform
  • Funk transform (a.k.a. spherical Radon transform)

See also

  • Tomography
  • Tomographic reconstruction
  • Discrete tomography
  • Generalized conic

References

1. ^Gardner, R.J., Geometric Tomography, Cambridge University Press, Cambridge, UK, 2nd ed., 2006

External links

  • Website summarizing geometric tomography – Describes its history, theory, relation to computerized and discrete tomography, and includes interactive demonstrations of reconstruction algorithms.
  • Geometric tomography applet I
  • Geometric tomography applet II

2 : Tomography|Projective geometry
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