Motion of an uncalibrated stereo rig: Self-Calibration and metric reconstruction

We address in this paper the problem of self-calibration and metric reconstruction (up to a scale factor) from one unknown motion of an uncalibrated stereo rig. The epipolar constraint is first formulated for two uncalibrated images. The problem then becomes one of estimating unknowns such that the discrepancy from the epipolar constraint, in terms of sum of squared distances between points and their corresponding epipolar lines, is minimized. Although the full self-calibration is theoretically possible, we assume in this paper that the coordinates of the principal point of each camera are known. Then, the initialization of the unknowns can be done based on our previous work on self-calibration of a single moving camera, which requires to solve a set of so-called Kruppa equations. Redundancy of the information contained in a sequence of stereo images makes this method more robust than using a sequence of monocular images. Real data has been used to test the proposed method, and the results obtained are quite good. We also show experimentally that it is very difficult to estimate precisely the coordinates of the principal points of cameras. A variation of as high as several dozen pixels in the principal point coordinates does not affect significantly the 3-D reconstruction.