*Sheng-Wen Shih, Yi-Ping Hung and Wei-Song Lin*

Camera Calibration, Error Analysis, Kinematic Calibration, Calibration of Active Vision Systems.

In camera calibration, due to the correlations between certain camera parameters, e.g, the correlation between the image center and the camera orientation, an estimate of a set of camera parameters which minimizes a given criterion does not guarantee that the physical camera parameter estimates are themselves accurate. This problem has not drawn much attention from our computer vision society because most computer vision applications require only accurate 3D measurements and do not care much about the values of the physical parameters as long as their composite effect is satisfactory. However, in calibrating an active vision system where the cameras are motorized such that their parameters can be adapted to the environment, accuracy of the physical parameters is very critical because we need accuracy to establish the relation between the motor positions and the camera parameters (both intrinsic and extrinsic). The contribution of this work is mainly in error analysis of camera calibration , especially in the accuracy of the physical camera parameters themselves, for four different types of calibration problems. The first type is estimation of all the camera parameters simultaneously. The second type is estimation of all the other camera parameters given the image center. The third type is estimation of the extrinsic parameters given the intrinsic parameters. The last one is estimation of the intrinsic parameters given the extrinsic parameters. For each type of calibration problem, we derive (i) the covariance matrices of the estimated camera parameters and (ii) the sensitivity matrices of the estimated parameters with respect to the error of the given parameters. Factors that affect calibration accuracy are found to be the focal length, the area and resolution of the image sensor, the average object distance, the relative object depth, the 2D observation noise and the number of calibration points. Our theoretical analysis has been verified by computer simulations. With our error analysis, the most suitable camera calibration technique and calibration configuration for providing accurate camera parameters can be determined. Also, the accuracy of the estimated physical parameters can be predicted by using our analysis results.