Biomedical Engineering Reference
In-Depth Information
their meanings is crucial to understanding and evaluating claims of registra-
tion accuracy.
6.2.1.1
Target Registration Error
A common geometrical measure, which we will call target registration error (TRE),
is the displacement between two corresponding points after registration, i.e.,
after one of the points has been subjected to the registering transformation. The
word “target” in the name of this error measure is meant to suggest that the error
is being measured at an anatomical position that is the target of some interven-
tion or diagnosis. Such errors would be expected to be more meaningful than
errors measured at points with no intrinsic clinical significance. We let
p
repre-
sent a point in the first image of a pair to be registered, and
a point in the second
image. A registration method applied to this pair leads to a transformation
q
T
that, without loss of generality, registers the first image to the second. The differ-
ence between the two vectors representing the transformed point and the corre-
sponding point gives the target registration error. Thus,
TRE
T
(
p
)
q
.
(6.1)
If the direction of the error is important, the vector quantity must be
reported; normally, however, only the magnitude TRE of the error is reported.
6.2.1.2
Fiducial Registration Error
An example of an error measure that lacks the intrinsic clinical meaning asso-
ciated with TRE is fiducial registration error (FRE). This error is sometimes
reported for systems that achieve registration by aligning pairs of points
associated with specially selected “fiducial” features that are visible in both
spaces. Both this error and TRE are illustrated in Figure 6.1. Fiducial features
are selected not because of their clinical significance, but because of their
locatability. They may be part of some easily visible anatomical features or
they may be the centroids of specially designed fiducial markers that have
been affixed to the anatomy before imaging. In either case the word “fidu-
cial” is meant to suggest reliability. The reliability of anatomical points is
enhanced by restricting their choice to clearly visible features; the reliability
of the marker derives from its design, which typically insures that it is bright
enough and large enough to render a consistent centroid in each image. The
reliability of a point used in any point-based registration system is directly
related to the consistency with which the identical geometrical location
within the fiducial feature can be identified in each image space. An error
in this localization step, which is commonly called the fiducial localization
error
(FLE) as illustrated in Figure 6.2, will propagate throughout the regis-
tration process, but if the magnitude of FLE is small, it can be expected that a
transformation that aligns fiducial points will align less visible target points
