  The issue of a "mean shape" of a random set $X$ often arises, in particular
in image analysis and pattern detection. There is no canonical definition but
one possible approach is the so-called Vorob'ev expectation $\E_V(X)$, which is
closely linked to quantile sets. In this paper, we propose a consistent and
ready to use estimator of $\E_V(X)$ built from independent copies of $X$ with
spatial discretization. The control of discretization errors is handled with a
mild regularity assumption on the boundary of $X$: a not too large 'box
counting' dimension. Some examples are developed and an application to
cosmological data is presented.
