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Sensitivity

The size of perturbation that can be detected in the validation experiments will depend both on the change in the values of the measures as a function of misregistration and the standard error of those values. To quantify this, the sensitivity of a measure was defined as follows.

$$D(m;d) = \frac{1}{{\sigma}_m}\left(\frac{m(d)-m(0)}{d}\right),$$ (7.1)

where $m(d)$ is the value of the measure for some degree of deformation $d$, ${\sigma}_m$ is the standard error of the estimate of $m(d)$. $D(m;d)=1$ is the change in $d$ required for $m(d)$ to change by one noise standard error, which indicates the lower limit of change in misregistration $d$ which can be detected by the measure. $D$ is a function of $d$; to simplify comparison between different methods of evaluation, we also use the mean sensitivity over a range of values of $d$.

In order to compare the sensitivities of different methods of evaluation, the expected error in $D$ also needed to be estimated. Since the validation experiments provided repeated estimates of $m(d)$, one can obtain empirical estimates of the errors in $m(d)$, $m(0)$, and ${\sigma}_m$. These can be combined, using error propagation in Equation 7.1, to estimate the uncertainty in the estimate of sensitivity.

Figure: Overlap measures (with corresponding $\pm$ one standard error errorbars) for the MGH dataset as a function of the degree of degradation of registration correspondence, $d$. The various graphs correspond to the various tissue weightings as defined in Chapter 2.

Figure: Generalisation & Specificity for various definitions of image distance (varying shuffle radius) with corresponding $\pm$ one standard error errorbars as a function of the degree of degradation of the registration correspondence $d$ for the MGH dataset