Constraint on five points in two images

It is well-known that epipolar geometry relating two uncalibrated images is determined by at least seven correspondences. If there are more than seven of them, their positions cannot be arbitrary if they are to be projections of any world points by any two cameras. Less than seven matches have been thought not to be constrained in any way. We show that there is a constraint even on five matches, i.e., that there exist forbidden configurations of five points in two images. The constraint is obtained by requiring orientation consistence points on the wrong side of rays are not allowed. For allowed configurations, we show that epipoles must lie in domains with piecewise-conic boundaries, and how to compute them. We present a concise algorithm deciding whether a configuration is allowed or forbidden.