Real-Time Estimation of FLE Statistics for 3-D Tracking With Point-Based Registration

Abstract

Target registration error (TRE) has become a widely accepted error metric in point-based registration since the error metric was introduced in the 1990s. It is particularly prominent in image-guided surgery (IGS) applications where point-based registration is used in both image registration and optical tracking. In point-based registration, the TRE is a function of the fiducial marker geometry, location of the target and the fiducial localizer error (FLE). While the first two items are easily obtained, the FLE is usually estimated using an a priori technique and applied without any knowledge of real-time information. However, if the FLE can be estimated in real-time, particularly as it pertains to optical tracking, then the TRE can be estimated more robustly. In this paper, a method is presented where the FLE statistics are estimated from the latest measurement of the fiducial registration error (FRE) statistics. The solution is obtained by solving a linear system of equations of the form Ax=b for each marker at each time frame where x are the six independent FLE covariance parameters and b are the six independent estimated FRE covariance parameters. The A matrix is only a function of the tool geometry and hence the inverse of the matrix can be computed a priori and used at each instant in which the FLE estimation is required, hence minimizing the level of computation at each frame. When using a good estimate of the FRE statistics, Monte Carlo simulations demonstrate that the root mean square of the FLE can be computed within a range of 70-90 microm. Robust estimation of the TRE for an optically tracked tool, using a good estimate of the FLE, will provide two enhancements in IGS. First, better patient to image registration will be obtained by using the TRE of the optical tool as a weighting factor of point-based registration used to map the patient to image space. Second, the directionality of the TRE can be relayed back to the surgeon giving the surgeon the option of changing their strategy in order to improve the overall system accuracy and, in turn, the quality of procedure.