Estimating FLEimage distributions of manual fiducial localization in CT images

The fiducial localization error distribution (FLE) and fiducial configuration govern the application accuracy of point-based registration and drive target registration error (TRE) prediction models. The error of physically localizing patient fiducials ([Formula: see text]) is negligible when a registration probe matches the implanted screws with mechanical precision. Reliable trackers provide an unbiased estimate of the positional error ([Formula: see text]) with cheap repetitions. FLE further contains the localization error in the imaging data ([Formula: see text]), sampling of which in general is expensive and possibly biased. Finding the best techniques for estimating [Formula: see text] is crucial for the applicability of the TRE prediction methods.

We built a ground-truth (gt)-based unbiased estimator ([Formula: see text]) of [Formula: see text] from the samples collected in a virtual CT dataset in which the true locations of image fiducials are known by definition. Replacing true locations in [Formula: see text] by the sample mean creates a practical difference-to-mean (dtm)-based estimator ([Formula: see text]) that is applicable on any dataset. To check the practical validity of the dtm estimator, ten persons manually localized nine fiducials ten times in the virtual CT and the resulting [Formula: see text] and [Formula: see text] distributions were tested for statistical equality with a kernel-based two-sample test using the maximum mean discrepancy (MMD) (Gretton in J Mach Learn Res 13:723-773, 2012) statistics at [Formula: see text].

[Formula: see text] and [Formula: see text] were found (for most of the cases) not to be statistically significantly different; conditioning them on persons and/or screws however yielded statistically significant differences much more often.

We conclude that [Formula: see text] is the best candidate (within our model) for estimating [Formula: see text] in homogeneous TRE prediction models. The presented approach also allows ground-truth-based numerical validation of [Formula: see text] estimators and (manual/automatic) image fiducial localization methods in phantoms with parameters similar to clinical datasets.