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.