Biomedical Engineering Reference
In-Depth Information
no structure or a very small amount of structure in the difference image,
whereas with increasing misregistration, the amount of structure would
increase. The structure could be quantified, for example, by the sum of
squares of difference values, the sum of absolute difference values, or the
entropy of the difference image. An alternative intuitive approach (at least
for those familiar with signal processing techniques) would be to find
by
T
cross-correlation of images
.
With intermodality registration, the situation is quite different. There is, in
general, no simple relationship between the intensities in the images
A
and
B
A
and
B
. No simple arithmetic operation on the voxel values is, therefore, going to
produce a single derived image from which we can quantify misregistration.
There have been some interesting attempts to overcome this difficulty by
preprocessing the images to make them more alike. One approach is to
make one of the images being registered look like the other. This has been
applied to MR-CT registration by remapping the high CT intensities to low
intensities to make the CT images look more like MR images,
28
and to MR
and PET registration by simulating a PET image from the MR image.
33
A
second approach is to generate similar derived images from each modality,
e.g., by applying scale-space derivatives to both images in order to identify
intensity ridges, which, at an appropriate scale, should be similar between
modalities.
29
Recent algorithm developments have, perhaps surprisingly, resulted in
techniques applicable to both intermodality and intramodality registra-
tion, and which work well for a wide variety of applications without the
need for modality-specific preprocessing. The most successful of the current
approaches are based on ideas that come from information theory.
In Sections 3.4.4 to 3.4.8 we describe some of the most widely used voxel
similarity measures for medical image registration. With all these similar-
ity measures it is necessary to use an optimization algorithm to iteratively
find the transformation
that maximizes or minimizes the value of the
measure, as appropriate. It is also necessary to implement appropriate re-
sampling and interpolation techniques for use in each iteration, taking into
account the issues raised in Section 3.2.
T
3.4.4
Minimizing Intensity Difference
One of the simplest voxel similarity measures is the sum of squared intensity
differences (SSD) between images which is minimized during registration.
For voxel locations
x
in image
A
, within an overlap domain
T
comprising
A
A
,
B
N
voxels:
1
----
B
T
x
()
2
SSD
A
x
()
(3.13)
T
x
A
A
,
B
The measure, like other voxel similarity measures, needs to be normalized
so that it is invariant to the number of voxels
T
N
in the overlap domain
A
,
B
.
