Optimization of camera parameter calibration based on a new criterion with effective visual angle

The 3D information obtained from camera, actually 2D image, is given as visual angles, and, so, we should evaluate the accuracy of calibration based on the visual angles. When we evaluate the accuracy, the visual angle, which direction should we take as the reference? True values of the coordinates of the principal points have been ordinarily used as the reference of the visual angle. But, the kind of evaluation criterion makes us overestimate visual angle errors although it is simple, and conforms to a fail-safe principle. And, it also causes us an ill effect that we should change fiducial-chart setup to suit an optimal condition that is given to each camera according to principal distances. We propose a novel criterion for the visual angle evaluation: the calibrated coordinates of principal points are taken as the references of the visual angle. It yields useful results: it markedly decreases visual angle estimation errors, and it also makes the optimal setup condition not vary with the principal distance. Further more, we present a useful formula enabling us to estimate calibration error for every camera in advance.