The complex of lines from successive points and the Horopter

The Horopter is the set of points in space which project to the same image points in the two cameras of a stereo vision system. Modern proofs are given for many of the classical results about the Horopter. Some of these rely on another classical construction, the quadratic complex of lines joining successive points. A modern derivation of this is also given. In particular the circumstances in which the image of the Horopter can degenerate is discussed in some detail. Finally, these ideas are extended to the case of optical flow where there is a single camera observing the velocities of points in space.