Luong, Q.-T. and Faugeras, O. D. Self-calibration of a stereo rig from unknown camera motions and point correspondencesin Calibration and orientation of cameras in computer vision, Springer-Verlag, 1996.
The problem of calibrating a stereo rig is extremely important for practical applications. Existing work is based on the use of a calibration pattern whose 3D model is a priori known. We show theoretically and with experiments on real images, how it is possible to completely calibrate a stereo rig, that is to determine each camera’s intrinsic parameters and the relative displacement between the two or three cameras, using only point matches obtained during unknown motions, without any a priori knowledge of the scenes.
The first part of the chapter is devoted to the computation of the intrinsic parameters of the cameras by a method based upon the estimation of the so-called fundamental matrix associated with camera displacement. Three different displacements are sufficient to solve the Kruppa equations which yield these parameters.
The second part of the chapter is devoted to the computation of the extrinsic parameters. We first explain how to recover the unknown motions previously used, once we have an estimate of the intrinsic parameters and the fundamental matrices. The computation is quite robust to the inaccuracy of the determination of the camera parameters. We then present the equations which allow us, from two displacements of the stereo rig, for which the camera motions are computed independently, to compute the relative displacement between the cameras. This technique allows us to compute the relative displacement between two or three cameras and complete the full calibration of the rig.