Invariants of 6 Points from 3 Uncalibrated Images

Abstract

There are three projective invariants of a set of six points in general position in space. It is well known that these invariants cannot be recovered from one image, however an invariant relationship does exist between space invariants and image invariants. This invariant relationship will first be derived for a single image. Then this invariant relationship is used to derive the space invariants, when multiple images are available. This paper establishes that the minimum number of images for computing these invariants is three, and invariants from three images can have as many as three solutions. Algorithms are presented for computing these invariants in closed form. The accuracy and stability with respect to image noise, selection of the triplets of images and distance between viewing positions are studied both through real and simulated images. Application of these invariants is also presented, this extends the results of projective reconstruction of Faugeras [6] and Hartley et al. [10] and the method of epipolar geometry determination of Sturm [18] for two uncalibrated images to the case of three uncalibrated images.