Geodesic
Reconstruction problems of convex bodies from surface area measures and lightness functions
Canadian journal of mathematics, Tome 75 (2023) no. 5, pp. 1685-1710

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DOI

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.
DOI : 10.4153/S0008414X22000505
Mots-clés : Reconstruction problem, Minkowski problem, reconstruction, surface area measure, lightness function, spherical harmonic 
Leng, Gangsong; Liu, Chang; Xi, Dongmeng. Reconstruction problems of convex bodies from surface area measures and lightness functions. Canadian journal of mathematics, Tome 75 (2023) no. 5, pp. 1685-1710. doi: 10.4153/S0008414X22000505
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     title = {Reconstruction problems of convex bodies from surface area measures and lightness functions},
     journal = {Canadian journal of mathematics},
     pages = {1685--1710},
     year = {2023},
     volume = {75},
     number = {5},
     doi = {10.4153/S0008414X22000505},
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