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Overlap, Specificity and Generalisation

Registration quality was measured, for each level of registration degradation (perturbation), using several variants of each of the proposed assessment methods:

• Generalised Tanimoto overlap of the ground-truth data labels (1) for varying values of the label weighting $\alpha_{l}$.
• Specificity & Generalisation ((7) & (9), $\lambda=1$), for varying values of the shuffle neighbourhood radius.

Figure 9 shows the results for the Tanimoto overlap measure (1). All overlap variants decay monotonically as a function of misregistration, showing that our perturbed dataset does indeed have the systematic behaviour we require.

Results for the proposed specificity $S$ (7) and generalisation $G$ (9) measures as a function of the displacement magnitude are shown in Figures 10(a) & 10(b). Results are given for varying values of the shuffle neighbourhood radius $r$, including Euclidean distance, $r=1$. Note that Generalisation and Specificity are in error form, and increase monotonically with increasing misregistration, for all values of shuffle radius. The strong qualitative agreement with the results for the overlap measure demonstrates the validity of the model-based measures.