Algorithms for the computation of the Minkowski functionals of deterministic and random polyconvex sets

We give algorithms for the simultaneous computation of the area, boundary length and connectivity (the so-called Minkowski functionals) of binary images. It is assumed that a binary image is a discretization of a two-dimensional polyconvex set which is a union of convex components. Edge-corrected versions of these algorithms are used for the estimation of specific intrinsic volumes of a stationary random closed set from a single realization given by a binary image. Performance and exactness of the algorithms in two dimensions are discussed on numerical examples. Comparison to other known methods is provided.