Biomedical Engineering Reference
In-Depth Information
13.2.1.3
K
-means Clustering
In a digital image, regions with the same structure may have corresponding
spikes in their intensity distributions. Intervals of the intensity distribution are
more likely to have a higher variance if the same structure region is not in the
same interval. For example, in standard CT or MR images, which in general
contain different structure regions, such as background, cortical bone, white
matter, gray matter, and cerebrospinal fluid (CSF). In the joint-histogram we
would like to see the same structure is assigned to the same bin, i.e., for each
bin to have a high probability of the same structure so that less dispersion in
the joint-histogram is achieved. The method proposed here is to make all the
voxels of background map to one bin by background segmentation using region
growing, and have the remaining voxels map to the rest of bins (with a variable
bin size for each bin) by
k
-means clustering, i.e., minimizing the variance of
intensities within each bin [22].
Following is the
k
-means clustering algorithm used:
1. Initially partition the image voxels into
k
bins.
(1a) Put all the background voxels into bin 0.
(1b) Calculate
the
step
size
for
the
other
k
−
l
bins
using
MaxIntensity
−
Minlntensity
k
−
1
. Each bin will be assigned all voxels whose
intensity falls within the range of its boundary.
(1c) Calculate the centroid of each bin.
2. For each voxel in the image, compute the distances to the centroids of its
current, previous, and next bin, if it exists; if it is not currently in the bin
with the closest centroid, switch it to that bin, and update the centroids
of both bins.
3. Repeat step 2 until convergence is achieved; that is, continue until a pass-
through all the voxels in the image causes no new assignments, or until
a maximum number of iterations is reached. The maximum number of
iterations was set to 500.
13.2.1.4
Normalized Mutual Information
Mutual information (MI) can be thought of as a measure of how well one image
explains the other, and when maximized indicates optimal alignment.
