Computing projective and permutation invariants of points and lines

Abstract

Until very recently it was believed that visual tasks require camera calibration. More recently it has been shown that various visual or visually-guided robotics tasks may be carried out using only a projective representation characterized by the projective invariants. This paper studies different algebraic and geometric methods of computation of projective invariants of points and/or lines using only informations obtained by a pair of uncalibrated cameras. We develop combinations of those projective invariants which are insensitive to permutations of the geometric primitives of each of the basic configurations and test our methods on real data in the case of the six points configuration.