Ambiguity in reconstruction from images of six points
Let S be a set of six points in space, let /spl 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 /spl 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 /spl psi/. Let p be an image of S taken from a point on /spl psi/. The images 'near' p define a tangent space which splits into a direct sum W/sub p//spl oplus/N/sub p//spl oplus/F/sub p/, where W/sub p/ corresponds to images near p for which the ambiguity is maintained, N/sub p/ corresponds to images for which the ambiguity is broken and F/sub p/ corresponds to images which are physically impossible.