Results

**Figure 6:** Appearance model which was built automatically by group-wise registration. First mode is shown, $\pm 2.5$ standard deviations.
[scale=0.38]../EPS/exp_C5_model.png

Overall, the above approach was applied 10 times using 10 different perturbation seeds to ensure that both methods are consistent and results unbiased. Results of the proposed measures for increasing registration perturbation are shown in Figure 5. Note that Generalisation and Specificity plotted for different shuffle neighbourhood radius are in error form, i.e. they increase with decreasing performance. All metrics are generally well-behaved and show a monotonic decrease in registration performance. Such results directly validate the model-based metrics, which are shown be in agreement with the ground truth embodied in the region overlap based measure.

These results also demonstrate that, for all sizes of shuffle neighbourhood, the specificity and generalisation values increase (get worse) with increasing mis-registration. The results for different sizes of shuffle neighbourhood demonstrate that the range of mis-registration over which distinct values of specificity and generalisation are obtained increases as the neighbourhood size increases. We observe similar behaviour as the value of $\alpha_{l}$ is altered.

Finally, in order to obtain a quantitative comparison of the proposed algorithms we explore sensitivity of the proposed metrics, where the slighter the difference which can be detected reliably, the more sensitive the method. Sensitivity is in this case defined as the rate of change in the measure for a given perturbation range, normalised by the average uncertainty in the measurement over that range. More formally, sensitivity can be defined thus:

$\displaystyle \frac{m-m_{0}}{d}/\overline{\sigma}$

(2)

where

is the quality measured for a given value of displacement, $m_{0}$ is the measured quality at registration,

is the degree of deformation and $\overline{\sigma}$ is the mean over the error bars. Sensitivity is evaluated for all three of the proposed metrics and shown in Figure 3 with errors bars based on both an inter-instantiation error and a measure-specific error. The Specificity measure is the most sensitive for any radius of the shuffle distance followed by the overlap metric and Generalisation, with shuffle radii of 1.5 and 2.1 (equivalent to 3x3 and 5x5 neighbourhoods) giving optimal sensitivity.

[scale=0.3]../EPS/BW_MIAS_sensitivity_label.png

Figure 2. The sensitivity of the different registration assessment methods.