Projective reconstruction of seven 3D points from two uncalibrated images

The recovery of the geometric structure of a 3D point set from its images is fundamental in computer vision. Among other projective reconstruction methods, the direct derivation of projective invariants from uncalibrated images is attracting. There are many forms of projective invariants. For a set of seven 3D points in general position, its geometric structure can be characterized by representing other three points as linear combinations of four reference points. Then the cross ratios of the coefficients of these representations are projective invariant. This paper presents an algorithm for computing these unknown cross ratios from known point correspondences from two images. First, a system of three quadratic equations in three unknowns is derived. After solving the three quadratic equations, a set of six independent projective invariants are derived by solving three systems of linear equations.