Simple parameter counting shows that we have 2*nm* independent
measurements and only
11 *m* + 3 *n* unknowns, so with enough points and
images the problem ought to be soluble. However, the solution can
never be unique as we always have the freedom to change the 3D
coordinate system we use. In fact, in homogeneous coordinates the
equations become

So we always have the freedom to apply a nonsingular transformation

One simple way to obtain the solution is to work in a projective basis tied to the 3D points [3]. Five of the visible points (no four of them coplanar) can be selected for this purpose.

An alternative to this is to select the projection center of the first
camera as the coordinate origin, the projection center of the second
camera as the unit point, and complete the basis with three other
visible 3D points
*A*_{1}, *A*_{2}, *A*_{3} such that no four of the five
points are coplanar.

Let
*a*_{1}, *a*_{2}, *a*_{3} and
*a*'_{1}, *a*'_{2}, *a*'_{3} respectively be
the projections in image 1 and image 2 of the 3D points
*A*_{1}, *A*_{2},
*A*_{3}. Make a projective transformation of each image so that these
three points and the epipoles become a standard basis:

Also fix the 3D coordinates of

It follows that the two projection matrices can be written:

Since the projection matrices are now known, 3D reconstruction is
relatively straightforward. This is just a simple, tutorial example so
we will not bother to work out the details. In any case, for precise
results, a least squares fit has to be obtained starting from this
initial algebraic solution (*e.g.* by bundle adjustment).