Biomedical Engineering Reference
In-Depth Information
is often recorded by the registration algorithm. It is also referred to as the root
mean square (RMS) error, residual error or fiducial registration error (FRE).
The mathematical solution for calculating this transformation has been
known for many years, and is known as the solution to the orthogonal Pro-
crustes problem after the unpleasant practice of Procrustes, a robber in Greek
mythology, fitting his guests with extreme prejudice to a bed of the wrong
size. The mathematics of the solution are provided in Chapter 3 together with
the full story of the fate of Procrustes.
Many commercial image registration packages and image guided-surgery
systems quote the FRE. Although this can be useful as a quick check of gross
errors in correspondence, FRE is not a direct measure of the accuracy with
which features of interest in the images are aligned. Indeed, it can be mislead-
ing, as changing the positions of the registration landmarks in order to
reduce FRE can actually increase the error in correspondence between other
structures in the images. A more meaningful measure of registration error is
the accuracy with which a point of interest (such as a surgical target) in the
two images can be aligned. This error is normally position-dependent in the
image, and is called the target registration error (TRE). In practical terms,
TRE, and how it varies over the field of view, is the most important parameter
determining image registration quality. Fitzpatrick
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has derived a formula to
predict TRE based on corresponding point identification. The formula com-
putes TRE from the distribution of fiducial points and the estimate of error in
identifying correspondence at each point, the fiducial localization error
(FLE). This formula has been verified by computer simulation and predicts
experimental results accurately (see Chapter 3).
The point landmarks may be pins or markers fixed to the patient and vis-
ible on each scan. These may be attached to the skin or screwed into bone.
The latter can provide very accurate registration but are more invasive and
cause some discomfort and a small risk of infection or damage to underlying
tissue. Skin markers, on the other hand, can easily move by several millimeters
due to the mobility of the skin, and are difficult to attach firmly. Care must be
taken to ensure that the coordinate of each marker is computed accurately and
that the coordinate computed in each modality corresponds to the same point
in physical space. Subvoxel precision is possible, for example, by using the
intersection of two tubes containing contrast material visible in each modality,
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the apex of a “V, ”
or the center of gravity of spherical or cylindrical markers
with a volume much larger than the voxel sizes.
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Markers like these can be
identified automatically in the images. Each of these systems was also de-
signed so that the corresponding point in physical space could be accurately
located. These are used widely in image-guided surgery as described in
Chapter 12.
Alternatively, corresponding internal anatomical landmarks may be identi-
fied by hand on each image. These must correspond to truly point-like ana-
tomical landmarks at the resolution of the images (such as the apical turn of
the cochlea), structures in which points can be unambiguously defined (such
