  Local algorithms are common tools for estimating intrinsic volumes from
black-and-white digital images. However, these algorithms are typically biased
in the design based setting, even when the resolution tends to infinity.
Moreover, images recorded in practice are most often blurred grey-scale images
rather than black-and-white. In this paper, an extended definition of local
algorithms, applying directly to grey-scale images without thresholding, is
suggested. We investigate the asymptotics of these new algorithms when the
resolution tends to infinity and apply this to construct estimators for surface
area and integrated mean curvature that are asymptotically unbiased in certain
natural settings.
