Affine Structure-from-Motion: Two Frames (6)

Suppose we just know where the k’th point is in image 1.

Then, we can use the first two equations to write xk and yk as linear in zk.  The final two equations lead to two linear equations in the missing values and zk.  If we eliminate zk we get one linear equation in the missing values.  This means the unknown point lies on a known line.  That is, we recover the epipolar constraint.  Furthermore, these lines are all parallel.