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Measuring Distances Between Images

The most straightforward way to measure the distance between images is to evaluate the mean absolute difference between them, or alternatively treat them as vectors by concatenating pixel/voxel values and take the Euclidean distance. Although this has the merit of simplicity, it does not provide a very robust distance measurement. In the context of model and image registration evaluation considered here, these approaches result in measures of distance that increases rapidly, even for quite small image misalignments. Robustness can be enhanced by considering a `shuffle distance', inspired by the `shuffle transform' [15]. The idea is to seek correspondence with a wider area around each pixel. Instead of taking the mean absolute difference between exactly corresponding pixels, we take each pixel in one image in turn, and compute the minimum absolute difference between it and pixels in a shuffle neighbourhood of the exactly corresponding pixel in the other image. This approach is less sensitive to small misalignments, and provides a more robust measure of image distance. The sensitivity to misalignment is determined directly by the size and shape of the shuffle neighbourhood. One obvious choice is a square box around the corresponding pixel, but this is inherently anisotropic. Instead, we consider a shuffle disc, of radius $r$, which contains all pixels within a distance $r$ of the central pixel.

Figure 3 shows examples of shuffle distance between an original image and a misaligned version evaluation, for varying values of the radius $r$. The effect of the shuffle neighbourhood radius on the sensitivity to misalignment is obvious as the contribution to distance perceivably decreases in areas of limited misalignment, as we go from $r=0$ to $r=3.7$ (roughly equivalent to a $7\times 7$ square window).

Figure: Shuffle distance evaluation: Left: original image, Right: warped image, Centre, from left to right: images showing contributions to shuffle distance, for $r = 0\:$(abs. diff.)$,\:1.5,\: 2.1$    & $3.7$ respectively.

[width = 0.9 ]../Graphics/shuffle_dist_example.png