  The projective shape of a configuration of k points or "landmarks" in RP(d)
consists of the information that is invariant under projective transformations
and hence is reconstructable from uncalibrated camera views. Mathematically,
the space of projective shapes for these k landmarks can be described as the
quotient space of k copies of RP(d) modulo the action of the projective linear
group PGL(d). Using homogeneous coordinates, such configurations can be
described as real k-times-(d+1)-dimensional matrices given up to
left-multiplication of non-singular diagonal matrices, while the group PGL(d)
acts as GL(d+1) from the right. The main purpose of this paper is to give a
detailed examination of the topology of projective shape space, and, using
matrix notation, it is shown how to derive subsets that are in a certain sense
maximal, differentiable Hausdorff manifolds which can be provided with a
Riemannian metric. A special subclass of the projective shapes consists of the
Tyler regular shapes, for which geometrically motivated pre-shapes can be
defined, thus allowing for the construction of a natural Riemannian metric.
