Hand-eye calibration with a depth camera: 2D or 3D?

Real time 3D imaging applications such as on the fly 3D inspection or 3D reconstruction can be created by rigidly coupling a depth camera with an articulated measurement arm or a robot. For such applications, the "hand-eye transformation" between the depth camera and the measurement arm needs to be known. For depth cameras, the hand-eye transformation can either be estimated using 2D images or the 3D measurements captured by the depth camera. This paper investigates the comparison between 2D image based and 3D measurement based hand-eye-calibration. First, two hand-eye calibration approaches are introduced which differ in the way the camera pose is estimated (either with 2D or with 3D data). The main problem in view of the evaluation is, that the ground truth hand-eye transformation is not available and thus a direct evaluation of the accuracy is not possible. Therefore, we introduce quantitative 2D and 3D error measures that allow for an implicit evaluation of the accuracy of the calibration without explicitly knowing the real ground truth transformation. In view of 3D precision, the 3D calibration approach provides more accurate results on average but requires more manual preparation and much more computation time than the 2D approach.