Biomedical Engineering Reference
In-Depth Information
relative to C in the B-C registration. These two displacements, while they con-
tribute to each of the two single-registration TREs, will tend to cancel in the
circuit, erroneously reducing their contribution to the TRE of the circuit.
Thus, dividing the TRE of the circuit by can be expected to underestimate
TRE for a single registration. To compute RMS values, many sets of
n
reg-
istrations would need to be made, but these correlated errors will not be
reduced in the mean. The problem does not occur for the point-based, rigid-
body problem when data are gathered for Equation 6.3 because no image
contributes to more than one registration.
n
6.4
Accounting for Error in the Standard
Comparison with a standard introduces the error of the standard into the
validation. The target feature, for example, even when it is based on a marker
designed to be accurately localizable, will not provide a perfect estimate of
TRE. The effect of its localization error can be seen in Figure 6.3. Here the
white and gray circles with dashed borders represent positions in space two.
T
(
p
) is the transformed position arising from
p
in space one. The black circle
with solid border represents the erroneously localized position
q
TLE
q
in
space two as determined by the localization process, and the white circle
with solid border represents the transformed position in space two of the
FIGURE 6.3
Schematic of registration error measurement based on a target feature. Because of target
localization error (TLE), the measured target registration error (TRE
m
) differs from the true
target registration error (TRE).
p
and
q
represent the true positions of the marker in the two
spaces;
T
is the registering transformation.
