Improved Modelling of Tool Tracking Errors by Modelling Dependent Marker Errors

Accurate understanding of equipment tracking error is essential for decision making in image guided surgery. For tools tracked using markers attached to a rigid body, existing error estimation methods use the assumption that the individual marker errors are independent random variables. This assumption is not valid for all tracking systems. This paper presents a method to estimate a more accurate tracking error function, consisting of a systematic and random component. The proposed method does not require detailed knowledge of the tracking system physics. Results from a pointer calibration are used to demonstrate that the proposed method provides a better match to observed results than the existing state of the art. A simulation of the pointer calibration process is then used to show that existing methods can underestimate the pointer calibration error by a factor of two. A further simulation of laparoscopic camera tracking is used to show that existing methods cannot model important variations in system performance due to the angular arrangement of the tracking markers. By arranging the markers such that the systematic errors are nearly identical for all markers, the rotational component of the tracking error can be reduced, resulting in a significant reduction in target tracking errors.