  Consider the design based situation where an $r$-regular set is sampled on a
random lattice. A fast algorithm for estimating the integrated mean curvature
based on this observation is to use a weighted sum of $2\times \dotsm \times 2$
configuration counts. We show that for a randomly translated lattice, no
asymptotically unbiased estimator of this type exists in dimension greater than
or equal to three, while for stationary isotropic lattices, asymptotically
unbiased estimators are plenty. Both results follow from a general formula that
we state and prove, describing the asymptotic behavior of hit-or-miss
transforms of $r$-regular sets.
