Local Digital Algorithms for Estimating the Integrated Mean Curvature of r-Regular Sets
Anne Marie Svane · Discrete & Computational Geometry · 2015
Suppose an r-regular set is sampled on a random lattice. A fast algorithm for estimating the integrated mean curvature is to use a weighted sum of $$2\times \cdots \times 2$$ configuration counts. We show that for a randomly translated lattice, no asymptotically unbiased estimator of this type exists in dimensions larger than two, while for stationary isotropic lattices, asymptotically unbiased estimators are plenty. The basis for this is a formula for the asymptotic behavior of hit-or-miss transforms of r-regular sets.