Homogeneous from the point simulations is an
idealisation because of the anisotropy in SPECT's spatial resolution.
This is why investigations with real scans are necessary. In the results
from point simulation studies, the translational and rotational error
depends on the number of point pairs used, the radial distance of the
point pairs from the center of rotation, and the homology error. The
homology error itself depends on the imaging system's resolving
capacity and the contribution of operator interaction. The degree to
which operator interaction confounds the effective homology error of
the registration is not necessarily linearly dependent on the system's
spatial resolution capabilities. It is in light of the dependence of
the results from the point simulations studies on these factors that
the results from the real scan studies were examined. Although this
study is for the brain, similar dependence may be expected in
registrations involving SPECT of the trunk [BDC+93][WQC+93] where,
similar to the brain,
the transaxial cross-sections are not symmetric - they are also
elliptical. These results are different from results with PET/MR
registrations because of the anisotropy of SPECT's spatial resolution.
Although the results from this study may not be directly compared to
previous works because of significant differences in methodology, the
errors from SPECT/MR registrations should not be too much greater than
results from PET/MR registrations due the contribution of an
operator's interpretive faculties in the selection of homologous
points. It should account for reducing the effect of SPECT's deficit
in spatial resolution on the magnitude of the net homology error.
Intuitively, points of maximum and minimum curvature are no more
difficult to select even if the slopes about them are changed
slightly when points are being selected on structures with curved perimeters.
This study is different from other works in that it isolates
more factors which affected the error but were allowed to vary in
statistical measurements: the point configuration variations and the
number of point pairs between determinations. This allowed a more
direct comparison to the results from the point simulation
investigations in this study.
It has been shown that the rotational error in the coronal plane is
largest. This is because the distances of the point distributions from the
center of rotation in x and z are the smallest i.e. the brain is smaller
in left-right and inferior-superior dimensions. This implies that the
effective radii in those dimensions are smaller so that the rotational
errors are geometrically larger as well. This trend agrees well with point
simulation studies and serves to additionally validate the use of the
highly constrained point simulations to provide insight into the
quantification of registration errors. For similar reasons, the rotation
error in the transaxial plane is smallest. This is because the dimension
of the brain in the anterior-posterior and left-right dimensions is
largest, thereby effecting a larger effective radius from which homologous
points may be chosen. The translational error in the y dimension
(anterior-posterior orientation) is larger
than translational errors in the other dimensions. This was expected to
the degree obtained because of the similar degree of difference between
the resolutions. The homology error in the anterior-posterior orientation
is greater than in the left-right orientation because of the
non-homogeneous nature of the spatial resolution of the SPECT images,
arising from the variable center of rotation to detector face distance in
the elliptical scans used clinically. It may be surmised from the results and
considerations of this study that the same error distributions may not be
expected across ordinates. A cautious statement of the errors incurred in
a SPECT/MR registration with the ILM technique is given by and
in table 5.2. In general, it may
be said with a probability of 99.7 %that the translation and rotation
errors will not exceed
mm and
, respectively.
The recommendations for the specification of registration errors given above are applicable to all registration techniques. In particular, for a specific pair of imaging modalities for which the ILM technique is applied, an operator and study specific [Sor] measure of error with probability quotations provided by the determination of a Gaussian distribution may be given by the procedure used in the real scan studies. For the surface fitting [PCS+89] and principal axes [ABKC90] techniques, the measure of the distribution of error from N registrations, each with variable surface and minimised residual thresholds, against the same set of test points may be implemented. A standardised validation of all extant registration methods (modality and study specific) in terms of the parameters measured here should allow a better basis for the comparison of the robustness of a registration technique. It is only when underlying registration errors are properly quantified in a statistical manner that further work concerning the errors associated with volume of interest, VOI, analyses which are dependent on data correspondence may further be pursued.