Estimating FLEimage distributions of manual fiducial localization in CT images.

Abstract

PurposeThe 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.MethodsWe 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, 2012) 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.ConclusionsWe 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.