Biomedical Engineering Reference
In-Depth Information
fairly minor change to the source code of his previously published RIU tech-
nique (see section 3.4.6), but transformed its functionality. The RIU algo-
rithm is based on an idealized assumption that “all pixels with a particular
MR pixel value represent the same tissue type so that values of correspond-
ing PET pixels should also be similar to each other.” The algorithm therefore
partitions the MR image into 256 separate bins (or isointensity sets) based on
the value of the MR voxels, then seeks to maximize the uniformity of the PET
voxel values within each bin. Once again, uniformity within each bin is max-
imized by minimizing the normalized standard deviation.
In the discussion above, we have described the algorithm in terms of MR and
PET registration only. We can now formulate the algorithm more generally in
terms of images
. It is important to note that the two images are treated
differently, so there are two different versions of the algorithm, depending on
whether image
A
and
B
is partitioned.
For registration of the images
A
or image
B
, the PIU can be calculated in two
ways: either as the sum of the normalized standard deviation of voxel values
in
A
and
B
B
for each intensity
a
in
A
(PIU
) or the sum of the normalized standard
B
deviation of voxel values in
A
for each intensity
b
in
B
(PIU
).
A
n
a
-----
B
a
()
n
b
-----
A
b
()
--------------
---------------
and
PIU
B
(3.19)
PIU
A
B
a
()
A
b
()
a
b
where:
1
1
n
a
n
b
T
T
a
a
1
n
a
B
T
x
()
1
n
b
A
()
x
A
B
a
()
A
b
()
-----
-----
T
T
a
b
2
1
n
b
2
1
n
a
()
B
T
x
A
(
A
x
A
A
b
()
)
(
()
B
a
()
)
B
a
()
A
b
()
-----
-----
a
T
T
The PIU algorithm was widely used for MR-PET registration. It requires the
scalp to be first removed from the MR image to avoid a breakdown of the ide-
alized assumption described above. The technique was never widely used
for registration of other modalities, but its success inspired considerable
research activity aimed at identifying alternative voxel similarity measures
for intermodality registration.
3.4.8
Information Theoretic Techniques
Image registration can be described as trying to maximize the amount of
shared information in two images. In a very qualitative sense, we might say
that if two images of the head are correctly aligned, then corresponding struc-
tures will overlap so that we will have two ears, two eyes, one nose, and so
