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'''Geometric tomography''' is a mathematical field that focuses on problems of reconstructing homogeneous (often [[convex polytope|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."<ref name="ref1">
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Gardner, R.J., Geometric Tomography, Cambridge University Press, Cambridge, UK, 2nd ed., 2006</ref>
 
==Theory==
A key theorem in this area states that any convex body in <math> E^n</math> can be determined by parallel, coplanar
X-rays in a set of four directions whose slopes have a transcendental [[cross ratio]].
 
==See also==
*[[Tomography]]
*[[Tomographic reconstruction]]
*[[Discrete tomography]]
 
==References==
{{reflist}}
 
== External links ==
*[http://cgm.cs.mcgill.ca/~godfried/research/tomography.html Geometric tomography applet I]
*[http://faculty.wwu.edu/gardner/GeometricTomography.html Geometric tomography applet II]
 
[[Category:Tomography]]
[[Category:Projective geometry]]

Revision as of 14:13, 23 February 2014

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