Instead of choosing
, KVD choose
(i.e. the direction of viewing in the
first frame). Since
, the
projection of in the first image is degenerate reducing
it to a single point. Thus, only two basis vectors are chosen in
the first image

In the second image, the third axis vector is no longer degenerate,
given by
.
is actually an epipolar line. If we use and
to predict the position where each point would appear in image 2,
as if they lay on plane
, we get

the disparity between the predicted position and the observed position

is solely due to the component

Geometrically, according to the notations of the figure, the projections
of a fourth point and an arbitrary fifth point form two similar
trapezoids
and
.
From similarity of trapezoids we have

By assuming that and are cooresponding points, we obtain the affine structure invariant .