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Tomography

Tomography is the study of the reconstruction of two- and three-dimensional objects from one-dimensional slices. The Radon transform is an important tool in tomography.

Rather surprisingly, there exist certain sets of four directions in Euclidean n-space such that X-rays of a convex body in these directions distinguish it from all other convex bodies.

See also

Aleksandrov's Uniqueness Theorem, Brunn-Minkowski Inequality, Busemann-Petty Problem, Dvoretzky's Theorem, Hammer's X-Ray Problems, Radon Transform, Stereology

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References

Gardner, R. J. "Geometric Tomography." Not. Amer. Math. Soc. 42, 422-429, 1995.Gardner, R. J. Geometric Tomography. New York: Cambridge University Press, 1995.Herman, G. T. and Kuba, A. (Eds.). Discrete Tomography: Foundations, Algorithms, and Applications. Boston, MA: Birkhäuser, 1999.Kak, A. C. and Slaney, M. Principles of Computerized Tomographic Imaging. IEEE Press, 1988.Weisstein, E. W. "Books about Tomography." http://www.ericweisstein.com/encyclopedias/books/Tomography.html.

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Tomography

Cite this as:

Weisstein, Eric W. "Tomography." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Tomography.html

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