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

摘要

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.