Biomedical Engineering Reference
In-Depth Information
It can be shown that this is the optimum measure when two images only
differ by Gaussian noise.
30
For intermodality registration, this will never be
the case. This strict requirement is seldom true for intramodality registra-
tion either, as noise in medical images such as modulus MRI scans is fre-
quently not Gaussian, and also because there has likely been change in the
object being imaged between acquisitions or there would be little purpose
in registering the images!
The SSD measure is widely used for serial MR registration, for example
by Hajnal et al.,
31,32
and by Friston's statistical parametric mapping (SPM)
33,34
software.
The SPM approach uses a linear approximation (often with
iterative refinement) based on the assumption that the starting estimate is
close to the correct solution and the image is smooth, rather than the iter-
ative approach used by other researchers.
The SSD measure is very sensitive to a small number of voxels that have
very large intensity differences between images
. This might arise,
for example, if contrast material is injected into the patient between the
acquisition of images
A
and
B
or if the images are acquired during an
intervention and instruments are in different positions relative to the sub-
ject in the two acquisitions. The effect of these “outlier” voxels can be
reduced by using the sum of absolute differences, SAD rather than SSD:
A
and
B,
1
----
B
T
x
()
SAD
A
x
()
(3.14)
T
x
A
A
,
B
3.4.5
Correlation Techniques
The SSD measure makes the implicit assumption that after registration the
images differ only by Gaussian noise. A slightly less strict assumption would
be that at registration there is a linear relationship between the intensity values
in the images. In this case, the optimum similarity measure is the correlation
coefficient CC
B
T
x
()
A
x
()
(
A
)
(
B
)
T
x
A
A
,
B
CC
---------------------------------------------------------------------------------------------------------------------------------------------
1
2
2
2
B
T
x
A
(
A
x
A
()
A
)
(
()
B
)
T
T
x
A
A
,
B
x
A
A
,
B
(3.15)
T
where
within the domain , and
is the mean of within . The correlation coefficient can be thought of as
a normalized version of the widely used cross correlation measure
A
is the mean voxel value in image
A
A
,
B
B
T
B
T
A
,
B
C
.
1
----
B
T
x
()
C
A
x
()
(3.16)
T
x
A
A
,
B
One interesting property of correlation techniques is that correlation can be car-
ried out in either the spatial domain or the spatial frequency domain (k-space).
