Rigid-body point-based registration: The distribution of the target registration error when the fiducial registration errors are given

Medical guidance systems often employ several data sources using different coordinate systems. In order to map positions from one coordinate system to the other, these guidance systems usually employ rigid-body point-based registration, using pairs of fiducial points: pairs which describe the same physical positions, but in different coordinate systems. The customary test for the quality of the registration is the fiducial registration error (FRE), which is the root-mean-square of the mismatch between the fiducials in each pair (after the registration). The FRE, however, does not give an answer to the question which is usually of interest, and that is the accuracy at a “target” point which is not part of the set of fiducial points.The statistics of the target registration error (TRE) have been studied before and approximate expressions were derived, but those expressions require as input the unknown true fiducial positions. In the present paper, it is proven that by replacing these unknowable true positions with the known measured positions in the expression for mean-square TRE, a higher order approximation is achieved. In other words, it is shown that more accurate estimates are obtained by using less accurate, but available, inputs. Furthermore, in previous approximations FRE and TRE were shown to be statistically independent, whereas here, due to the higher approximation level, it is shown that a slight dependence exists. Thus, the knowledge of FRE can in fact be employed to improve predictions of the TRE statistics. These results are supported by simulations and hold even for fiducial localization error (FLE) distributions with large standard deviations.

An improved estimator for the expected value of the target registration error squared (〈TRE2〉〈TRE2〉) has been found. This higher order estimator uses only measured fiducial positions, instead of the fiducials’ true positions. Further more, the new estimator is better than the currently accepted estimator, an estimator based on the (typically) unknown true fiducial positions. The improved estimator holds even for large measurement errors, well beyond acceptable errors in clinical use.Figure optionsDownload high-quality image (200 K)Download as PowerPoint slideResearch highlights
► New estimator for the mean-squared target registration error (TRE) is found.
► Estimator uses only measured fiducial positions, instead of true fiducial positions.
► Estimator is more accurate than using the typically unknown true fiducial positions.
► Estimator shows a dependence on the fiducial registration error vectors.