Calibration and error analysis of surgical instrument based on stereo camera

This paper proposes a method to calibrate and position surgical instruments using stereo camera, discusses the calibration error and its propagation when the instrument is positioned. A planar marker composed by X corners is attached to the instrument, and a reference frame is established on the marker. The structural parameter of instrument is calibrated on clinical site by rotating the instrument around its tip on proposed calibration template; thereafter the instruments can be distinguished and positioned by stereo camera. The method is proved by applying it in a simple instrument positioning system. The theoretical analysis and experiments reveal that calibration error depends not only on the accuracy of marker localization, but also on the marker configuration and the tip position relative to the marker reference frame. Furthermore, we analyze the calibration error propagation and find out that the instruments positioning error do not exceed the sum of calibration error and markers localization error when marker is configured properly.