Sensitivity of Calibration to Principal Point Position

A common practice when carrying out self-calibration and Euclidean reconstruction from one or more views is to start with a guess at the principal point of the camera. The general belief is that inaccuracies in the estimation of the principal point do not have a significant effect on the other calibration parameters, or on reconstruction accuracy. It is the purpose of this paper to refute that belief. Indeed, it is demonstrated that the determination of the focal length of the camera is tied up very closely with the estimate of the principal point. Small changes in the estimated (sometimes merely guessed) principal point can cause very large changes in the estimated focal length, and the accuracy of reconstruction. In fact, the relative uncertainty in the focal length is inversely proportional to the distance of the principal point to the epipolar line. This analysis is geometric and exact, rather than experimental.