Gardner R.J. and Milanfar, P. (2003) Reconstruction of Convex Bodies from Brightness Functions. Discrete & Computational Geometry, 29, 279-303.
http://dx.doi.org/10.1007/s00454-002-0759-2

has been cited by the following article:

• TITLE: Reconstruction of Three Dimensional Convex Bodies from the Curvatures of Their Shadows

  AUTHORS: Rafik Aramyan

  KEYWORDS: Integral Geometry, Convex Body, Projection Curvature, Support Function

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.5 No.2, May 25, 2015

  ABSTRACT: In this article, we study necessary and sufficient conditions for a function, defined on the space of flags to be the projection curvature radius function for a convex body. This type of inverse problems has been studied by Christoffel, Minkwoski for the case of mean and Gauss curvatures. We suggest an algorithm of reconstruction of a convex body from its projection curvature radius function by finding a representation for the support function of the body. We lead the problem to a system of differential equations of second order on the sphere and solve it applying a consistency method suggested by the author of the article.