Binocular Self-Alignment and Calibration from Planar Scenes

We consider the problem of aligning and calibrating a binocular pan-tilt device using visual information from controlled motions, while viewing a degenerate (planar) scene. By considering the invariants to controlled motions about pan and elevation axes while viewing the plane, we show how to construct the images of points at infinity in various visual directions. First, we determine an ideal point whose visual direction is orthogonal to the pan and tilt axes, and use this point to align the rig to its own natural reference frame. Second, we show how by combining stereo views we can construct further points at infinity, and determine the left-right epipoles, without computing the full epipolar geometry and/or projective structure. Third, we show how to determine the infinite homography which maps ideal points between left and right camera images, and hence solve for the two focal lengths of the cameras. The minimum requirement is three views of the plane, where the head undergoes one pan, and one elevation. Results are presented using both simulated data, and real imagery acquired from a 4 degree-of-freedom binocular rig.