Stereo Calibration from Rigid Motions

This paper describes a method to upgrade projective reconstruction to affine and to metric reconstructions using rigid general or planar 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 when a 3-D scene is observed with a moving stereo rig. Based on an in-depth algebraic analysis we show that all the computations can be carried out using standard linear resolution methods. 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. Extensive experiments performed with calibrated and natural data confirm the theoretical error analysis and are consistent with a sensitivity analysis performed with simulated data