From a computational point of view, it is desirable to have similar algorithms for the other intrinsic volumes of M. However, already in R^3 the surface area and the total mean curvature of these cube-approximations can significantly differ from the values of M.
To overcome this problem, we introduce modified intrinsic volumes of M_t which are based on persistent homology. The main goal of this talk is to outline these new ideas and to sketch applications in the special case of bodies in R^3.
This is joint work with Herbert Edelsbrunner.