In an attempt to increase the accuracy of the scheme and as a final
parameter investigation, a method using a mean image template was
implemented. This scheme generates a mean image for the series by
averaging all the volumes over time after the first three stages of
trilinear interpolation-based motion correction have been carried
out. In doing so we hope to be registering all volumes to a more
generalised target which exhibits less overall variation from each
volume in the series than the original target (middle) volume
previously used. This new mean image is a robust target to which the
original time series is then registered, again using three trilinear
interpolation stages and an optional final sinc interpolation stage.
Because we are registering to a mean image, we no longer have ``gold
standard'' values for the transformations found by the correction
scheme. Therefore, to quantify the accuracy of the correction, a
median absolute residual variation (MARV) score was created by
initially de-meaning each voxel time-series and then measuring the
median value of the residual absolute values in this time-series.
That is,
This produce a volume of MARV scores for each voxel and the median
of these values (over the volume) is then taken as a summary measure.
This is effectively a measure characterising the level of inter-volume
intensity variation (presumed to be due to subject motion) after
retrospective motion correction has been applied. While this can only
work for activation-free data (so that in perfect alignment the
variance should be at minimum) it can give us a clear impression of
the accuracy of the motion correction scheme. Because SPM rejects
information outside a mask obtained from the data (end slice effects),
the corrected median images were masked according to the corrected SPM
data so that the measure reflected a consistent comparison across the
schemes. The results shown in Figure 15 correspond
to the MARV values generated after running MCFLIRT and SPM on the
null-activation data set for both the low and severe motion designs.
Results using the RMS measure (Table 3) revealed that,
although all three schemes provide sub-voxel accuracy, AIR 3.08 using
Least Squares (which we found to give better results than the standard
AIR measure) and Windowed Sinc interpolation was almost an order of
magnitude worse than basic 3 stage tri-linear MCFLIRT. Accordingly we
decided not to compare it further. However, we note that AIR was
primarily designed to solve several different registration problems
that arise in tomographic data sets [18] rather than
optimised for FMRI motion correction.
Table 3:
RMS deviation values for synthetic null data
Uncorrected
AIR
SPM
MCFLIRT
Sum of squared intensity errors
936.5866
406.8876
1.6405
1.5171
RMS error (mm)
2.3360
1.7570
0.1064
0.1102
Figure 15:
Median Absolute Residual Variation (MARV) values for corrected data processed by different motion correction schemes: Uncorrected, MCFLIRT w. CR, MCFLIRT w. NC, MCFLIRT w. CR & mean, MCFLIRT w. NC & mean, SPM99 run at full quality, with sinc interpolation and interpolation error adjustment
>From these results we conclude that for some cases (generally the low
motion data), MCFLIRT with the Correlation Ratio cost function
produces significantly smaller errors than SPM99 whilst in other cases
(some of the high motion data) both methods give similar results.
This can be seen be comparing the heights (MARV values) of the SPM
bars with the CR bars (typically the best MCFLIRT cost function) where
a 30% to 40% reduction can be seen in the first, second and fourth
cases.
Slightly surprisingly we found that the use of a mean image template
gave no discernable improvement in accuracy. We conclude that for
artificial data where the motion is purely rigid, there is no
advantage to using a (possible blurred) average image over an image
from the original data. We would expect that the mean template scheme
could yield greater accuracy where the data includes some physical
motion-induced artefacts and the choice of a reference image from the
original dataset is not so obvious.
Next:Null Data Study Up:Accuracy Assessment: Motion Correction Previous:Interpolation Scheme
Peter Bannister
2002-05-03