Geometric tomography

From Wikipedia, the free encyclopedia
Jump to: navigation, search

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[edit]

A key theorem in this area states that any convex body in  E^n can be determined by parallel, coplanar X-rays in a set of four directions whose slopes have a transcendental cross ratio.

See also[edit]

References[edit]

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

External links[edit]