Image analysis frequently deals with shape estimation and image
reconstruction. The ob jects of interest in these problems may be thought of as
random sets, and one is interested in finding a representative, or expected,
set. We consider a definition of set expectation using oriented distance
functions and study the properties of the associated empirical set. Conditions
are given such that the empirical average is consistent, and a method to
calculate a confidence region for the expected set is introduced. The proposed
method is applied to both real and simulated data examples.