Biomedical Engineering Reference
In-Depth Information
erroneously localized position in space one. For rigid-body transformations,
this latter transformed position is
T
(
p
)
T
(TLE
p
).
The true TRE will, in general, be different from the measured value, TRE
m
,
because of the error in localization, which we will call target localization error
(TLE) in analogy with fiducial localization error. In a given measurement,
either TRE or TRE
m
may be larger in magnitude, but we should expect the
true error TRE to be smaller in the RMS sense than the measured error TRE
m
.
This expectation is based on the assumption that the localizations of the target
are uncorrelated with the registration error, a reasonable assumption because
the target feature is not used in the registration process. If we make the further
common assumption that there is no bias in the errors (i.e., the mean of each
Cartesian component is zero), then the RMS errors are related in this simple
way,
2
2
2
RMS TRE
(
)
RMS TRE
m
(
)
RMS TLE
p
(
)
RMS TLE
q
(
)
.
(6.4)
If the target localization error can be estimated, then Equation 6.4 should be
used in estimating RMS (TRE); otherwise RMS (TRE
m
) serves as an upper bound.
A similar situation holds when TRE is determined by comparison with
another registration system used as a gold standard. Since the errors of the
two systems are likely to be uncorrelated, the relationship between actual
TRE and the measured value TRE
m
is similar,
2
RMS TRE
(
)
RMS TRE
m
(
)
RMS TRE
g
(
)
,
(6.5)
where TRE
g
is the target registration error for the gold standard.
6.5
Independent Validation
System developers have used point-based methods to validate their own reg-
istration systems,
30,39
but there has been only one large-scale effort to carry
out independent validations of many methods. An international effort to val-
idate retrospective registrations of the head by using a set of patient images
with a point-based method as a gold standard was undertaken in 1995 by 12
institutions in the U.S., Belgium, England, France, and The Netherlands. In
this project, coordinated by researchers in the U.S. at Vanderbilt University, a
set of CT, MR, and PET images of patients was acquired at Vanderbilt and made
available via the Internet to researchers at the other institutions. The patients
were part of a separate, independent study in which skull-implanted mark-
ers were being used for image-guided surgery—the same markers as those
used in the marker-based validation documented by Maurer et al.
15
A subset
40
