Biomedical Engineering Reference
In-Depth Information
2.4.3.2
Voxel Similarity Measures Applied to Images from Different
Modalities—Entropy as a Measure of Alignment
In the past five years there has been significant progress, worldwide, in
using statistical relationships between voxel intensity values to align
images acquired from different modalities. This work stems from the obser-
vation that while images from different modalities exhibit complementary
information, there is usually also a high degree of shared information
between images of the same structures. For example, the human observer
is able to fuse stereoscopically very different images such as MR and CT of
the same structure provided the images' brightness and contrast are adjusted
appropriately.
Any algorithm that is used to register images from two different modalities
must be insensitive to modality-specific differences in image intensity associated
with the same tissue, and also accommodate differences in relative intensity
from tissue to tissue. The first successful application of a voxel similarity-based
algorithm to the registration of images from different modalities was that pro-
posed by Woods for MR-to-PET registration.
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We refer to this algorithm as par-
titioned intensity uniformity (PIU). The algorithm assumes that at each
intensity in the MR image the range of the corresponding PET intensities is
small. Implementation involved an almost trivial change to the original
source code of the program for VIR but proved to be robust for the registra-
tion of MR and PET images of the head, provided the scalp was first removed
from the MR images. Van den Elsen
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proposed another algorithm, this time
specific to MR-to-CT registration, in which the CT intensities were remapped
or transformed so that soft tissue was bright, while both bone and air were
dark. This had the effect of making a CT scan look a little like an MR image
so linear correlation of intensities could be used as a measure of alignment.
While effective in certain circumstances for aligning images of the head and
spine, it never really caught on.
The initial success of these algorithms in specific applications inspired the
search for a more general registration algorithm that would work with mul-
timodality data. The required breakthrough came when a new way of look-
ing at the intensities of the two images was suggested.
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Each point in one
image will correspond to a point in the other, and these two points each have
an image intensity associated with them. We can generate a scatter plot of
these image intensities, point by point. These are two-dimensional plots of image
intensity of one image against corresponding image intensity of the other.
The resulting plot is a type of two-dimensional histogram. This is sometimes
called a joint intensity histogram and, when divided by the number of con-
tributing pixels, is equal to the joint probability distribution. For each pair of
image intensities in the two images, the joint probability distribution pro-
vides a number equal to the probability that those intensities occur together
at corresponding locations in the two images. Examples of this for a pair of
registered MR and PET images are given in Figure 2.9 (left). Interesting things
