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Measuring Distances in Between Images

The most straightforward way to measure the distance between images is to treat each image as a vector formed by concatenating the pixel/voxel intensity values, then take the Euclidean distance. It means that each point in one image is compared against its spatially corresponding point in another image. Although this has the merit of simplicity, it does notprovide a very well-behaved distance measure since it increases rapidly for quite small image misalignments [26]. This observation led us to consider an alternative distance measure, based on the 'shuffle difference', inspired by the 'shuffle transform' [14]. The idea is illustrated in Fig. 5. Instead of taking the sum of squared differences between corresponding pixels, the minimum absolute difference between each pixel in one image and the values in a shuffle neighbourhood around the corresponding pixel is used. This is less sensitive to small misalignments, and provides a better-behaved distance measure. The tolerance for misalignment is dependent on the size of the neighbourhood which is considered, so we investigate the effect of expanding that neighbourhood (see Fig. 7).

Figure 5: The calculation of a shuffle difference image

On several occasions we considered the symmetrical shuffle distance, as illustrated in Fig. 6. It applies the shuffle transform in both direction and averages over the sum of the two, thus accounting the the contribution of both. We noted that it entailed no significant improvements. Therefore, experiments in the remainder of this paper choose one image and compute the shuffle distance in just one direction, which is more more efficient and provides equally-valid results.

Figure 6: Examples of the shuffle difference image: from one image to a second image (left), from the second image to the first (centre), and the symmetrical shuffle distance image (right)

Figure 7: A comparison between shuffle distance evaluation types. On the left: original image; on the right: warped image; in the centre (from left): shuffle distance with $r=0$(absolute difference), $1.5,2.9$ and $3.7$.