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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 because it is very sensitive to
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 to produce a shuffle difference image
(see
Figure 3). The shuffle distance is given
by
where
are
the elements of
. 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 , which contains all pixels within a distance
of the central pixel.
Figure 3:
Calculating the shuffle difference image

Figure:
Shuffle distance calculation: Left:
original image, Right: warped image, Centre, from left
to right: shuffle difference images for
respectively.

Figure 4 shows examples of shuffle distance
between an original image and a misaligned version evaluation, for
varying values of the radius . 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 to (roughly
equivalent to a square window).
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Roy Schestowitz
20070311