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Results

Figure  plots each of the four variants of the generalised overlap measure, as a function of $d$, the degree of misregistration. As expected, the value decreases monotonically with increasing misregistration in each case. This shows that the two gold-standard measures of misregistration (mean pixel displacement and ground-truth overlap) are in agreement, which validates the experimental framework. The measure of overlap is also monotonic wrt the level of distortion that simulates and corresponds to misregistration, which validates the perturbation method.

Similarly, Figure  plots Generalisation and Specificity as functions of $d$, for different values of shuffle radius $r$. The results are qualitatively similar to those obtained for generalised overlap, except that both measures increase monotonically with increasing misregistration, as expected (see Section ). These results show that, over the range of misregistrations investigated, the model-based measures are good surrogates for $d$, the mean pixel misregistration. Since the warps used to introduce controlled misregistration were of very general form, there is no reason to suppose that this result is dependent on the pattern and specifics of misregistration.

Figure: Mean sensitivity of different NRR assessment methods over the full range of deformations $d$, shown with $\pm$one standard error errorbars