The test results shown in Figure 12 show the
relative accuracy of the available cost functions within the MCFLIRT
optimisation framework when applied to the problem of motion
correction on our synthetic data.
Figure 12:
Median (over time) RMS (over space) error results for the MCFLIRT scheme applied to
synthetic data exhibiting known motion of one of five designs and
audiovisual activation at increasing intensities. Cost function
notation corresponds to Table 1
Although there is no clear leader over all cost functions in terms of
accuracy, we note that the most accurate results are predominantly
yielded by the Normalized Correlation and Correlation Ratio cost
functions. This observation is reinforced when we examine the number of
data sets where a particular cost function is most accurate. This is
summarised in Table 2.
Table 2:
Accuracy counts for the five cost functions offered by MCFLIRT
Cost
# sets most accurate
# sets most accurate
Normalized Correlation
8
5
Correlation Ratio
2
7
Mutual Information
2
1
Normalized Mutual Information
0
2
Least Squares
3
0
Note that previous work [5] which had
demonstrated the superiority of entropy-based cost measures over
alternatives in terms of motion correction without introducing further
spurious activations in the data, has only compared Mutual Information
metrics against least squares (SPM) and Woods (AIR) measures.
The next stage of testing was to verify that these cost functions were
in fact more accurate when smoothed (apodized) than un-smoothed
(un-apodized). The same RMS test measure and data sets were used as in the
previous test and results are given in
Figure 13.
Figure 13:
Median (over time) RMS (over space) error results (un-smoothed minus smoothed) for the
MCFLIRT scheme applied to 5 synthetic data sets (A-E) exhibiting
known motion at increasing intensities. A positive value indicates
improved accuracy as a result of smoothing the cost function. Cost
function notation corresponds to Table 1 and the
results demonstrate the improvement in accuracy achieved by using the
smoothed cost functions.