Progressive Hand-Eye Calibration for Laparoscopic Surgery Navigation

In this paper, we presented a progressive strategy based on an invariant point to accomplish hand-eye calibration for laparoscopic surgery navigation. An invariant dot was imaged by a stereo laparoscopy, the 2D image coordinate of the invariant dot was calculated by the blob detection algorithm, and mapped into the 3D coordinate system by the triangulation. In the meanwhile, reflective passive markers (RPM) fixed on the distal end of a stereo laparoscope was located by an optical tracking system. The Levenberg-Marquardt (LM) algorithm was used to iteratively estimate the hand-eye transformation based on the dot image coordinates and RPM’s poses. One pair of dot image coordinate and RPM’s pose were acquired in each iteration procedure, and were added into their accumulated data buffer as the input of LM optimization. The calibration error was calculated as well for each iteration. To evaluate accuracy of the proposed method, laboratory experiments were conducted by computing two errors, including forward error and backward error. The results show that the minimal forward error of 1.32 mm and backward error of 0.86 pixels were obtained at the 8^th iteration. In conclusion, the high calibration accuracy can be achieved with a few progressive iterations by our method. Additionally, the proposed approach provided a way for operators to monitor the procedure so that the calibration process can be stopped when the procedure feedbacks an acceptable accuracy.