At our institute we developed application software which can use with different camera models to compute the camera calibration. Furthermore, the parameter estimation can be performed simultaneously for different poses of the same camera. All involved measurement errors can be considered statistically (not only pixel errors, but also the fabrication tolerances of the calibration body). Different procedures have been implemented and compared with each other.

For discussion of accuracies residual pictures can be calculated. These pictures show the differences between acquired pass points and the calculated pass points based on the estimated parameters.

Typical residual image (magnification of errors: 50 times)
If the camera is mounted on the hand of a robot, a further calibration problem has to be solved: The camera location relative to the robot wrist. This information is important, to avoid recalibration of the external camera parameters each time the robot hand has moved. The estimation of this relative transform is called hand-eye-calibration. In order to determine this transformation, the robot with the camera in its hand is moved to several locations and at each location a camera calibration will be performed. From each calibration the camera location relative to the calibration body can be obtained and from the robot kinematics the hand location relativ to the robot basis can be derived. In the following picture the involved transformations are depicted.

Involved Transformations
If several relative transforms between pairs of two robot poses are known, they can be combined to determine equations which have only the relative transform between the camera and the robot hand as unknown included. This equation system can be solved uniquely, if at least the relative transforms from three robot configurations in some proper arrangement are available. Together with some non-linear constraints, the parametrisation of the relative transform delivers a non linear equation system, which can be used to compute the hand-eye-transformation by means of a parameter estimation algorithm.

We have developed software for the hand-eye-calibration which can consider measurement errors at different levels of detail. If the transform of the hand relative to the basis is not known exactly, our approach can be used to improve the estimation of the hand location; the improvement is based on the visually measured locations of the camera relativ to the calibration body.

The statistical consideration of the measurement errors revealed, that it is not allowed to seperate the camera calibration from the hand-eye-calibration, because that will not take into account correlations between the internal camera parameters with the hand-eye-transformation.