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We study the problem of reconstructing a convex body using only a finitenumber of measurements of outer normal vectors. More precisely, we suppose thatthe normal vectors are measured at independent random locations uniformlydistributed along the boundary of our convex set. Given a desired Hausdorfferror eta, we provide an upper bounds on the number of probes that one has toperform in order to obtain an eta-approximation of this convex set with highprobability. Our result rely on the stability theory related to Minkowski'stheorem.

On the reconstruction of convex sets from random normal measurements