A simple and analytical procedure for calibrating extrinsic camera parameters

This paper presents a simple and analytical procedure for calibrating extrinsic camera parameters. First, a calibration equation that separates rotational and translational parameters is given. The calibrating equation involves only rotational parameters and requires no absolute position information. A four-point calibration procedure is proposed that involves three points on a line and one point out of the line, and leads to four possible calibration solutions, obtained analytically. Additional steps required to eliminate false solutions are also discussed. Once the true rotational parameters are identified, the translational parameters are obtained analytically and uniquely with additional absolute position information. The required absolute position information appears in a simple and explicit form. For extrinsic calibration among multiple cameras, such as stereo cameras, it is easy to show that the absolution position information is not needed.