Geometric reasoning in Computer Vision always is performed
under uncertainty. The great potential of both, projective geometry
and statistics, can be integrated easily for propagating uncertainty
through reasoning chains, for making decisions on uncertain spatial
relations and for optimally estimating geometric entities or
transformations. This is achieved by (1) exploiting the
potential of statistical estimation and testing theory and by (2)
choosing a representation of projective entities and relations which
supports this integration.
The redundancy of the representation of geometric entities with
homogeneous vectors and matrices requires a discussion on the
equivalence of uncertain projective entities. The multi-linearity of
the geometric relations leads to simple expressions also in the
presence of uncertainty. The non-linearity of the geometric
relations finally requires to analyze the degree of approximation as
a function of the noise level and of the embedding of the vectors in
projective spaces.
The paper discusses a basic link of statistics and projective
geometry, based on a carefully chosen representation, and collects
the basic relations in 2D and 3D and for single view geometry.