Case with two cameras
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# Perspective projection into two views

Let , , be two cameras, with respective optical centers C,C', we associate the frame of to the camera and the frame of to the camera .

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':

 (6)

we have also:
 (7)

combining (6) and (7) and doing some calculus we obtain the relation 8:

 (8)

where
 (9)

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)

where:
 (11)

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