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In this paper we show how to calibrate a camera, mounted on a robot, with respect to the intrinsic camera parameters when the so-called hand-eye transformation between the robot hand and the camera is unknown. The calibration is based directly on the spatial and temporal derivatives in an image sequence and do not need any matching and tracking of features or a reference object. The calibration is to be performed on an active robot vision system where the motion of the robot hand can be controlled. A minimum of 3 non-coplanar translations of the robot hand are needed for the calculation. In conjunction with the intrinsic camera calibration the orientation of the camera, with respect to the robot hand, is calculated. The position of the camera can then also be obtained. At each stage only the image derivatives and the known motion of the robot hand are used. For the full, intrinsic and extrinsic, calibration a total of 5 distinct motions are used. The algorithm has been tested in extensive experiments with respect to e.g. noise sensitivity.