The paper presents a new technique for optimal estimation for
statistically uncertain geometric entites. It is an extension of the
classical eigenvector solution technique but takes the full
covariance information into account to arrive at a ML-estimate. The
proposed solution is significantly more transparent than the solution
for estimation under heteroscedasticity proposed by Leedan, Matei and
Meer. We give a new representation of algebraic projective geometry
easing statistical reasoning. We show how the setup can be used in
object reconstruction, especially when estimating points and edges of
polyhedra. We explicitely give an example for estimating 3D-points
and 3D-lines from image points and image lines. The direct solutions
do practically require no approximate values.