The first of the proposed methods for assessing registration quality uses a generalisation of Tanimoto's spatial overlap measure [7]. We start with a manual mark-up of each image, providing an anatomical/tissue label for each voxel, and measure the overlap of corresponding labels following registration. Each label is represented using a binary image, but after warping and interpolation into a common reference frame, based on the results of NRR, we obtain a set of fuzzy label images. These are combined in a generalised overlap score [1]:
The second method assesses registration in terms of the
quality of a generative statistical appearance model, constructed
from the registered images - for all the experiments reported
here, this was an active appearance model
(AAM) [3]. The idea is that a correct
registration produces an anatomically meaningful dense
correspondence between the set of images, resulting in a better
appearance model. We define model quality using two measures -
generalisation and specificity [18]. Both are
measures of overlap between the distribution of original images,
and a distribution of images sampled from the model, as
illustrated in Figure 1. If we use the generative
property of the model to synthesise a large set of images,
, we can define
Generalisation
:
![]() |
(2) |
where is a measure of distance between
images,
is the
training image, and
is the minimum over
(the set of synthetic images). That is, Generalisation is the average
distance from each training image to its nearest neighbour in the
synthetic image set. A good model exhibits a low value of
,
indicating that the model can generate images that cover the full
range of appearances present in the original image set. Similarly,
we can define Specificity
:
![]() |
(3) |
That is, Specificity is the average distance of each
synthetic image from its nearest neighbour in the original image
set. A good model exhibits a low value of , indicating that the
model only generates synthetic images that are similar to those in
the original image set. The uncertainty in estimating
and
can also be computed.
In our experiments we have defined as the shuffle
distance between two images, as illustrated in
Figure 2. Shuffle distance is the mean of the
minimum absolute difference between each pixel/voxel in one image,
and the pixels/voxels in a shuffle neighbourhood of radius
around the corresponding pixel/voxel in a second image. When
, this is equivalent to the mean absolute difference
between corresponding pixels/voxels, but for larger values of
the distance increases more smoothly as the misalignment of
structures in the two images increases. The effect on the
pixel-by-pixel contribution to shuffle distance as
is
increased is illustrated in Figure 3.
[width=0.5]../EPS/Carole/shuffle_white_lines.png
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[width=]../EPS/Carole/shuffle_dist_example_lighter_shades.png
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[width=]../EPS/Carole/Allthree.png
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