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Validation using Warped Images

Given the 70 image sets described above, each with known average misregistration, $d$, the relationship between $d$ and Specificity, Generalisation, and Generalised Overlap was investigated, by calculating the mean and standard error for each measure over the 10 warp instances for each value of $d$. In total, there were 71 image sets to study. One is the original registered set and the other 70 image sets comprise 10 instantiations for each value of $d$.

It is worth emphasising that no images are actually being registered here. Instead, sets are generated by simulating different levels of misregistration and then studying this misregistration. Each set of 10 instantiations is derived from the same image, but the process is stochastic, so the instantiations are unique.

For each misregistered image set, Specificity and Generalisation were calculated, as described in Section 6.2, using $m$ = 15 modes of variation for the model and $\mathcal{M}$ = 1000 synthetic images drawn from a Gaussian model distribution. This was repeated for values of shuffle radius, $r$, of 1 (Euclidean distance), 1.5, 2.1 and 3.7, as defined in Section , corresponding to circular neighbourhoods contained within 1x1, 3x3, 5x5 and 7x7 pixel patches respectively. These experiments were repeated with 2.5%, 5.0% and 10% Gaussian intensity noise added to the misregistered images, in order to investigate the sensitivity of the model-based measures to image noise. This makes it possible to argue in defence of the robustness of these measures to noise. Figure  shows an example brain image with varying degrees of noise added.

Figure: effect of varying the level of noise applied to the original image (left). Noise levels of 0%, 2.5%, 5%, and 10% (right) are shown.

With the ground-truth annotation, Generalised Overlap with volume, equal, inverse volume and complexity weightings were calculated, as defined in equation 2.1. Different values of $\alpha_{l}$ affected the different components of that equation. The mean and standard error for each measure over the 10 warp instances for each value of $d$ was also calculated.