Improved statistical TRE model when using a reference frame.

Target registration error (TRE) refers to the uncertainty in localizing a point of interest after a point-based registration is performed. Common in medical image registration, the metric is typically represented as a root-mean-square statistic. In the late 1990s, a statistical model was developed based on the rigid body definition of the fiducial markers and the localization error associated in measuring the fiducials. The statistical model assumed that the fiducial localizer error was isotropic, but recently the model was reworked to handle anisotropic fiducial localizer error (FLE). In image guided surgery, the statistical model is used to predict the surgical tool tip tracking accuracy associated with optical spatial measurement systems for which anisotropic FLE models are required. However, optical tracking systems often track the surgical tools relative to a patient based reference tool. Here the formulation for modeling the TRE of a surgical probe relative to a reference frame is developed mathematically and evaluated using a Monte Carlo simulation. The effectiveness of the statistical model is directly related to the FLE model, the fiducial marker design and the distance from centroid to target.