Self-calibration and Euclidean reconstruction using motions of a stereo rig

This paper describes a method to upgrade projective reconstruction to affine and to metric reconstructions using rigid general motions of a stereo rig. We make clear the algebraic relationships between projective reconstruction, the plane at infinity (affine reconstruction), camera calibration, and metric reconstruction. We show that all the computations can be carried out using standard linear resolution methods and that these methods compare favorably with nonlinear optimization, methods in the presence of Gaussian noise. We carry out a theoretical error analysis which quantify the relative importance of the accuracies of projective-to-affine conversion and affine-to-Euclidean conversion. Experiments with with real data are consistent with the theoretical error analysis and with a sensitivity analysis performed with simulated data.