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1 results

  • Reconstruction problems of convex bodies from surface area measures and lightness functions

  • Part of
  • Gangsong Leng, Chang Liu, Dongmeng Xi
  • Journal:
    Canadian Journal of Mathematics / Volume 75 / Issue 5 / October 2023
    Published online by Cambridge University Press:
    03 October 2022, pp. 1685-1710
    Print publication:
    October 2023
    • Article
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  • First, we build a computational procedure to reconstruct the convex body from a pre-given surface area measure. Nontrivially, we prove the convergence of this procedure. Then, the sufficient and necessary conditions of a Sobolev binary function to be a lightness function of a convex body are investigated. Finally, we present a computational procedure to compute the curvature function from a pre-given lightness function, and then we reconstruct the convex body from this curvature function by using the first procedure. The convergence is also proved. The main computations in both procedures are simply about the spherical harmonics.