  We study the problem of reconstructing a convex body using only a finite
number of measurements of outer normal vectors. More precisely, we suppose that
the normal vectors are measured at independent random locations uniformly
distributed along the boundary of our convex set. Given a desired Hausdorff
error eta, we provide an upper bounds on the number of probes that one has to
perform in order to obtain an eta-approximation of this convex set with high
probability. Our result rely on the stability theory related to Minkowski's
theorem.
