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Tomography of constructible functions

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Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 948))

Abstract

An explicit inversion formula for general integral transforms is given in the framework of constructible functions. It applies in particular to the real Radon transform in any dimension or the real X-rays transform in even dimension. For example, it allows us to reconstruct a body in a three dimensional vector space from the knowledge of the number of connected components and the number of holes of all its intersection by two dimensional affine slices.

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Author information

Authors and Affiliations

  1. Institut de Mathématiques, UMR 9994, Université Paris VI, Case 247 4, place Jussieu, 75252, Paris Cedex 05, France

    P. Schapira

Authors
  1. P. Schapira
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Editor information

Gérard Cohen Marc Giusti Teo Mora

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© 1995 Springer-Verlag Berlin Heidelberg

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Schapira, P. (1995). Tomography of constructible functions. In: Cohen, G., Giusti, M., Mora, T. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1995. Lecture Notes in Computer Science, vol 948. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60114-7_33

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  • DOI: https://doi.org/10.1007/3-540-60114-7_33

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60114-2

  • Online ISBN: 978-3-540-49440-9

  • eBook Packages: Springer Book Archive

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