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Perturbing Ground Truth

The evaluation now proceeded by considering perturbations about this found registration.

A test set of different registrations was created by applying smooth pseudo-random spatial warps (based on biharmonic Clamped Plate Splines [#!CPS!#]) to each image in the registered set. Each warp was controlled by 25 randomly placed knot-points, each displaced in a random direction by a distance drawn from a Gaussian distribution whose mean controlled the average magnitude of pixel displacement over the whole image. Example images from the test set are shown in Figure .

Figure: Examples of registration degradation for increasing scales of smooth CPS warps. Mean pixel displacement for each image is shown.

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Overall, the above approach was applied 10 times using 10 different random seeds. The 10 different warp instantiations were generated for each image and for each of seven progressively increasing values of average pixel displacement.

The perturbed correspondence across the set is then that given by applying the originally-found correspondence from the initial registration, but now applied to the deformed image sets. Hence the correspondence becomes progressively worse as the degree of image deformation increases.

Figure: Generalisation & Specificity (with corresponding error bars) for the brain dataset as a function of the degree of degradation of the registration correspondence, and for varying definitions of image distance, that is, varying radius of the shuffle neighbourhood.

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