  Grey-scale local algorithms have been suggested as a fast way of estimating
surface area from grey-scale digital images. Their asymptotic mean has already
been described. In this paper, the asymptotic behaviour of the variance is
studied in isotropic and sufficiently smooth settings, resulting in a general
asymptotic bound. For compact convex sets with nowhere vanishing Gaussian
curvature, the asymptotics can be described more explicitly. As in the case of
volume estimators, the variance is decomposed into a lattice sum and an
oscillating term of at most the same magnitude.
