Geometric hand-eye calibration for an endoscopic neurosurgery system

We present an algorithm in the conformal geometric algebra framework which computes the transformation (rotation and translation) relating the coordinate system of an endoscopic camera, with the coordinate system of the markers placed on it. Such markers are placed in order to track the camera´s position in real time by using an optical tracking system. The problem is an adaptation of the so-called hand-eye calibration, well known in robotics; however we name it the endoscope-tracking system calibration. By this way, we can relate the preoperative data (3D model and planing of the surgery), with the data acquired in real time during the surgery by means of the optical tracking system and the endoscope. Results obtained with our approach are compared with other approach which computes separately (in a two-step algorithm) the rotation and translation, and they are promising.