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Cost Functions

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
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...fig{figure=5.0_costs_errbars.eps,width=\figwidth}
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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 $ 2^{nd}$ 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.
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Overall, the smoothed cost functions outperform their un-smoothed versions.
next up previous
Next: Interpolation Scheme Up: Accuracy Assessment: Motion Correction Previous: Simulated Data
Peter Bannister 2002-05-03