Paper  Abstract 
A structure from motion inequality 
We set the general framework and state an inequality,
which answers the question how many cameras and points
are needed to invert the structure from motion map F.
The paper includes the above mathematical definition of
the structure from motion problem which is general enough to cover situations,
where points are moving while the camera takes pictures. The
point manifold N could be a space of jets of functions P_{i}(t).
Inverting the structure from motion map means recovering the
paths of the points and the camera locations from the camera pictures.
We illustrate the inequality for various camera types.

On Ullmans theorem in computer vision 
We provide explicit locally unique reconstruction of the
structure from motion map F in the case of three orthographic
cameras and three points both in 2 and 3 dimensions.
While Ullmans theorem shows that the structure from motion map
F is 2:1 for 3 cameras and 4 points, the reconstruction is 64:1
for 3 cameras and 3 points but in the later case, the map F has
an image which has the same dimension. In Ullmans case, the image of
F is a codimension 3 manifold. We also demonstrate that the map F
is not surjective. Its boundary is the image of the set det(F)=0.

Space and camera path reconstruction for omnidirectional vision 
For oriented omnidirectional cameras, the structure from motion map can be reduced
to linear problems.
We give a complete answer for the question when a unique reconstructions is
possible without ambiguities. For example, for 3 points and 3 cameras
in the plane, a unique reconstruction of points and cameras is possible
if the 3 cameras are not collinear, the 3 points are not collinear and
the 6 points are not contained in the union of two lines. This is sharp and relaxing
any of these conditions leads to counter examples. Proving these facts involves
elementary geometry like Desargues theorem.
We do the reconstruction for arbitrarily many
cameras and arbitrarily many points using least square solutions and show
that it is robust. The goal will be to take a movie with many frames,
observe many points and do a reconstruction both of the camera path
and the scene. We have programs to do the reconstruction with synthetic
data for arbitrary many points and cameras. 