- Given the two cameras 1 and 2, we have the camera equations:
and
- The optical center projects as
- Writing
where
is
non-singular we have that
is the optical center.
- The epipole
in the second image is the projection of the
optical center of the first image:
- The projection of point on infinity along the optical ray
on to the second image is given by:
- The epipolar line
is given by the
cross product
.
- If
is the
antisymmetric matrix representing cross product with
,
then we have that the epipolar line is given by
- Any point
on this epipolar line satisfies
-
is called the fundamental matrix. It is of rank 2 and
can be computed from 8 point correspondences.
- Clearly
(degenerate epipolar line) and
. The epipoles are
obtained as the null spaces of
.
Subhashis Banerjee
2008-01-21