When the perspective effects are small, the problem of locating perspective epipolar lines becomes ill-conditioned. In such cases it is convenient to assume the parallel projection model of the affine camera which explicitly models the ambiguities.

The affine epipolar constraint can be described in terms of the
affine fundamental matrix as , i.e.,

where and are homogeneous 3-vectors representing corresponding image points in two views.

(See Shapiro, Zisserman and Brady).

To derive the above, we write as
where is a general (non-singular) matrix and
is a vector. The projection equation then
gives

Similarly, for , we have

Eliminating scene coordinates gives

where , and .

and are functions only of camera parameters and the motion transformation , while explains the motion of the reference point (centroid) and depend on the translation of the object and the camera origins and .

This equation shows that associated with lies
on a line (epipolar) on the second image with offset
and direction . The unknown depth determines how far
along this line does lie. Inverting the equation we obtain

The translation invariant versions of these equations are

We can eliminate from the above equations and obtain a single
equation in terms of *image measurables*:

where, and its perpendicular . This equation can be written as

where , and . This gives us