Let M be a point of the projective space , represented in by and in by , we call m and m' their two respective projections in the frame induced by in the focal plane of the camera , and by in the focal plane of the camera .
the relation (1) can be written for the point m':
we have also:
combining (6) and (7) and doing some calculus we obtain the relation 8:
is the homography of the infinite plane. Note that if t=0 (i.e. we have no translation between the two views, but only rotation), the relation 9 will become a homographic relation (i.e. relation in the projective plane ).
Obviously, if the points are coplanar we have also a homographic relation between the points. In formula 10 we present the relation in case of co-planarity (we obtain this relation starting from formula 8 and doing some simplification using the co-planarity of the points).
|Zc'm' = Zc H m||(10)|