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Results

Figure 5: Appearance model which was built automatically by group-wise registration. First mode is shown, $\pm 2.5$ standard deviations.

[width=]../EPS/Carole/exp_C5_model.png

The results of the validation experiment are shown in Figure 4. Note that $O$ is expected to decrease with increasing perturbation of the registration, whilst $G$ and $S$ are expected to increase. All three metrics are generally well-behaved and show a monotonic response to increasing perturbation. This validates the model-based measures of registration quality, which are shown both to change monotonically with increasing perturbation of the registration and to correlate with the gold-standard approach based on manually annotated ground truth.

These results for different values of $r$ (shuffle radius) and $\alpha_{l}$ all demonstrate monotonic behaviour with increasing perturbation, but the 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 Figure 4 is plotted in Figure 6 for all the methods of assessment. This shows that the Specificity measure with shuffle radius 1.5 or 2.1 is the most sensitive of the measures studied, and that this difference is statistically significant.

Figure 6: The sensitivity of the different registration assessment methods.

[width=]../EPS/BW_MIAS_sensitivity_label.png