A new algorithmic approach to the computation of Minkowski functionals of polyconvex sets

An algorithm is proposed for the simultaneous computation of all Minkowski functionals (except for the volume) of sets from the convex ring in Rd discretized with respect to a given regular lattice. For this purpose, a polyhedral approximation is used to reconstruct their boundary structure. In the planar case d=2, the performance and precision of the algorithm is studied on various examples of particular polyconvex sets. The algorithm is implemented in Java for two different approximation systems. The results of numerical experiments are compared with those obtained by other methods known in the literature.