Analysis of projections of a convex body is a familiar topic in
tomography. However,
instead of considering standard projection bodies, this work investigates
a convex body introduced by Schneider [8] which is
a Minkowski average of projections.
The question addressed here is similar to that posed by Goodey and
Weil [4] with
respect to Minkowski averages of sections, as opposed to projections, that
is, can
the shape of a convex body be determined from random sections? Their main
result
shows that a body K is determined by the average of its two-dimensional
sections,
but not by the average of its one-dimensional sections. The goal of this
study is
to uncover the extent to which a convex body is determined by the average
of its
projections.