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Sensitivity Measures

To identify which weighting scheme provides the best behaviour, a measure of sensitivity was desirable. Performance of a measure can be described it term of its ability to discern a good registration from a worse one. Put differently, the problem in question is revealing howsmall a degradation can be and still get detected. This enables us to compare the merits of our model-based assessement method and comparing it with an overlap-based method. It also makes it clearer to see which weighting scheme works best in terms of performance.

It is worth paying attention to the fact that slopes and errors vary systematically. This affects the size of perturbation that can be detected. To make a quantitative comparison of the different methods, we define the sensitivity, as a function of perturbation as $(\frac{1}{\overline{\sigma}})\frac{m-m_{0}}{d}$, where $m$ is the quality measured for a given value of displacement, $m_{0}$ is the measured quality at registration, $d$ is the degree of deformation and $\overline{\sigma}$ is the mean error in the estimate of $m$ over the range.

Sensitivity averaged of the range of perturbations shown in figures 10, 11, and 12 is plotted in Figure 13 for all the methods of assessment. This shows that the Specificitymeasure with shuffle radius 1.5 or 2.1 is the most sensitive of the measures studied, and that this difference is statistically significant.

Figure 13: Sensitivity of different NRR assessment methods