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Open Access 01-06-2016 | Original Article
Estimating \({\hbox {FLE}}_\mathrm{image}\) distributions of manual fiducial localization in CT images
Published in: International Journal of Computer Assisted Radiology and Surgery | Issue 6/2016
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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, 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.
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.