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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. Although this has the merit of simplicity, it does not provide a very well-behaved distance measure since it increases rapidly for quite small image misalignments. This observation led us to consider an alternative distance measure, based on the 'shuffle difference', inspired by the 'shuffle transform' [11]. The idea is illustrated in Fig. 4. 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 more well-behaved distance measure.
Fig. 4. The calculation of Fig. 5. An example of the shuffle difference
a shuffle difference image image (right) when applied to two MR slices (left)