To describe the relationship between *R*,
,
*A*_{1}, and *A*_{2} more
exactly, and to connect the above equations with those found in
[6], we offer the following algebraic derivation.

Recall that a point
produces an image
through the equation
.
Without loss of generality, we can assume that
is given
with respect to the first camera's coordinate frame to yield the following
two imaging equations:

where and are scale factors, is the identity matrix and is the null vector. By letting ( is ), we achieve the following relation:

Geometrically, this equation says that the vector on the left is a linear combination of the two vectors on the right. Therefore, they are all coplanar, and the vector is perpendicular to that plane:

which is identical to (6).

Similarly, the vector
is perpendicular to the vectors in (8):

This is a surprising result because it gives us a new and equivalent expression for

(10) |

which shows that