Let S be a set of six points in space, let \psi be any hyperboloid of one sheet containing S, and let I be a sequence of images of S taken by an uncalibrated camera moving over \psi. Then reconstruction from I is subject to a three way ambiguity which is unbroken as long as the optical centre of the camera remains on \psi.

Let p be an image of S taken from a point on \psi. The images "near" p define a tangent space which splits into a direct sum W_p \oplus N_p \oplus F_p, where W_p corresponds to images near p for which the ambiguity is maintained, N_p corresponds to images for which the ambiguity is broken and F_p corresponds to images which are physically impossible.