- Ignoring radial distortion (for the time being) and setting (measuring in pixels), we have and .
- Then, combining equations we have
- Assuming
to be known (at the center of the image) and
setting
and
, we have
and
- Eliminating
we have
- Rearranging, we have
- The unknown scale factor can be fixed by setting . Image correspondences of seven points in general position are sufficient to solve for the remaining unknowns. Let the solution be , , , , , , and
- We can estimate the correct scale factor by noting that the two rows
of the rotation matrix are supposed to be normal, i.e.,
- The scale factor
for the solution can then be determined from
- In the above procedure we didn't enforce orthogonality of the first
two rows of
. Given vectors
and
, we can
find two orthogonal vectors
and
close to the
originals as follows:
and
- can then be recovered as .
- Once we have we can estimate and from the basic equations above. This will require one more correspondence to be given.
- The above procedure may be problematic if is close to 0. In such a case the entire experimental data may have to be first translated by a fixed amount.