Many image-guidance surgical systems rely on rigid-body, point-based registration of fiducial markers attached to the
patient. Marker locations in image space and physical space are used to provide the transformation that maps a point
from one space to the other. Target registration error (TRE) is known to depend on the fiducial localization error (FLE),
and the fiducial registration error (FRE) of a set of markers, though a poor predictor of TRE, is a useful predictor of FLE.
All fiducials are typically weighted equally for registration purposes, but is also a common practice to ignore a marker at
position r by zeroing its weight when its individual error,
FRE(r), is high in an effort to reduce TRE. The idea is that
such markers are likely to have been compromised, i.e., perturbed badly between imaging and surgery. While ignoring a
compromised marker may indeed reduce TRE, the expected effect of ignoring an uncompromised marker is to increase
TRE. There is unfortunately no established method for deciding whether a given marker is likely to have been
compromised. In order to make this decision, it is necessary to know the probability distribution p(FRE(r)), which has
not been heretofore determined. With such a distribution, it may be possible to identify a compromised marker and to
adjust its weight in order to improve the expected TRE. In this paper we derive an approximate formula for p(FRE(r))
accurate to first order in FLE. We show by means of numerical simulations that the approximation is valid.