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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.

Keywords

Inversion Formula Dimensional Vector Space Constructible Function Flag Manifold Real Analytic Manifold 
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References

  1. 1.
    R. Bott and L.W. Tu, Differential forms in algebraic topology. Graduate Text in Math. Springer-Verlag, 82 (1982)Google Scholar
  2. 2.
    L. Erström, Topological Radon transforms and the local Euler obstruction. Duke Math. Journal, 76, p. 1–21 (1994)Google Scholar
  3. 3.
    M. Kashiwara and P. Schapira, Sheaves on manifolds. Grundlehren Math. Wiss. Springer-Verlag, 292 (1990)Google Scholar
  4. 4.
    C. McCrory and A. Parusinski Complex monodromy and the topology of real algebraic sets Rep. 94-28 School of Math. The Univ. of Sydney (1994)Google Scholar
  5. 5.
    J.-J. Risler, Placement of curved polygons AAECC-9, Lectures Notes in Comput. Sci. 539, p. 368–383 Springer Verlag (1991)Google Scholar
  6. 6.
    P. Schapira, Cycles Lagrangiens, fonctions constructibles et applications. Séminaire EDP, Publ. Ecole Polytechnique (1988/89)Google Scholar
  7. 7.
    P. Schapira, Operations on constructible functions. J. Pure Appl. Algebra 72, p. 83–93 (1991)Google Scholar
  8. 8.
    P. Schapira, Constructible functions, Lagrangian cycles and computational geometry. The Gelfand Seminar 1990–92, L. Corwin, I. Gelfand, J. Lepowsky eds. Birkhaüser Boston (1993)Google Scholar
  9. 9.
    O.Y. Viro, Some integral calculus based on Euler characteristic. In: Lecture Notes in Math 1346, Springer Verlag (1988)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • P. Schapira
    • 1
  1. 1.Institut de Mathématiques, UMR 9994Université Paris VIParis Cedex 05France

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