Estimating $${\hbox {FLE}}_\mathrm{image}$$ distributions of manual fiducial localization in CT images.

Purpose: 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 ( $${\hbox {FLE}}_\mathrm{patient}$$ ) is negligible when a registration probe matches the implanted screws with mechanical precision. Reliable trackers provide an unbiased estimate of the positional error ( $${\hbox {FLE}}_\mathrm{tracker}$$ ) with cheap repetitions. FLE further contains the localization error in the imaging data ( $${\hbox {FLE}}_\mathrm{image}$$ ), sampling of which in general is expensive and possibly biased. Finding the best techniques for estimating $${\hbox {FLE}}_\mathrm{image}$$ is crucial for the applicability of the TRE prediction methods. Methods: We built a ground-truth (gt)-based unbiased estimator ( $$\widehat{{\hbox {FLE}}_\mathrm{gt}}$$ ) of $${\hbox {FLE}}_\mathrm{image}$$ 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 $${\hbox {FLE}}_\mathrm{gt}$$ by the sample mean creates a practical difference-to-mean (dtm)-based estimator ( $$\widehat{{\hbox {FLE}}_\mathrm{dtm}}$$ ) 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 $${\hbox {FLE}}_\mathrm{dtm}$$ and $${\hbox {FLE}}_\mathrm{gt}$$ 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, ) statistics at $$\alpha =0.05$$ . Results: $${\hbox {FLE}}_\mathrm{dtm}$$ and $${\hbox {FLE}}_\mathrm{gt}$$ 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. Conclusions: We conclude that $$\widehat{{\hbox {FLE}}_\mathrm{dtm}}$$ is the best candidate (within our model) for estimating $${\hbox {FLE}}_\mathrm{image}$$ in homogeneous TRE prediction models. The presented approach also allows ground-truth-based numerical validation of $${\hbox {FLE}}_\mathrm{image}$$ estimators and (manual/automatic) image fiducial localization methods in phantoms with parameters similar to clinical datasets. [ABSTRACT FROM AUTHOR]