Robust hand-eye calibration for computer aided medical endoscopy

Endoscopic camera for surgical navigation and 3D visualization requires precise and stable estimates of the calibration parameters. The estimation of the hand-eye transform between the camera frame and the opto-tracked body of the endoscope is an important issue of the calibration. This paper presents a new stable method for the hand-eye calibration problem. The most popular method estimates the transform directly in the special euclidean group SE(3) by computing separately the rotation and the translation. The second famous approach formulates the problem in the dual quaternion space and estimates jointly the rotation and the translation. In a first glance, the simultaneous estimation seems to be always advantageous. However, and according to the experiments, this is not the case for the rotation estimation that is affected by the noise in translation. Our approach takes advantage of the both methods and uses the dual quaternion to estimate separately the rotation and the translation. We show experimentally that our algorithm is more stable with minimal number and small amplitude of motions.