Geometric tomography
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
References
- ^ 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
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