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Perturbing the Initial Registration

In order to perform a systematic evaluation of the effects of misregistration, multiple image sets were created, based on the MGH Dataset, but with controlled degrees of misregistration. To create a misregistered set, the original image set was taken and had applied to it a set of smooth pseudo-random spatial warps, based on biharmonic Clamped Plate Splines []. The warp for each image was controlled by 25 randomly placed knot-points, each displaced in a random direction by a distance drawn from the positive half of a zero mean Gaussian with SD ${\sigma}$, which controls the degree of misregistration. This provided a very general family of warps. The degree of misregistration was quantified by measuring $d$, the magnitude of pixel displacement averaged over the whole image. A total of 70 misregistered image sets were generated - 10 warp-set instantiations for each of 7 different values of $d$ (0.0643, 0.249, 0.685, 1.36, 2.21, 2.76, and 4.15 pixels). Examples of warped images are shown in Figure .

The sets of chosen warps preserved the topology of the images while the magnitude of localised warps ensured that there was no problematic distortion. The spatial spread of these small warps was assured to occupy different regions of the image and thus affect most image pixels as well. No warps were applied next to image borders, so as to avoid pixels from being scattered and pushed outside the image.

Figure: An original image from the MGH Dataset (top left) and examples of warped versions of the same image obtained using different values of $d$, the mean pixel displacement (shown on each image).

Although this is not an ideal way to ensure that introduced distortion mimics what one would find in real brains, such distortions are identical to those which are applied in order to solve the registration problem (just working in reverse) and all the warped brains look like possible actual brains.

I tested a variety of sets and observed the effect of the warps on images in order to ensure that warped images did not lose their natural topology. The intensity of the warps I eventually applied was quantified by program-specific values of 10, 40, 110, 220, 370, 460, and 670. Rather than provide arbitrary numbers which are specific to an algorithm, I refer to pixels-quantified units ($d$) in the experiments that follow.

The scales of deformation were carefully chosen such that they provided more insight into the behaviour of the experiments at points near the correct solutions. The deformations at the lower end of the scale were greater in terms of number and sample points in the graphs likewise. The greatest level of deformation was not exceeded in these experiments because greater deformation did not seem to result in brain images whose appearance looked quite so reasonable. A deformation too great would explore situations that are less likely to be encountered in practical applications.