Biomedical Engineering Reference
In-Depth Information
of the 20 bee brains was taken as the raw image and automatically segmented
using every one of the remaining 19 brains as an atlas. This resulted in 19 seg-
mentations per brain. These 19 segmentations were then combined into a final
segmentation.
The most straightforward method for combining multiple classifications into
one is the so-called “Vote Rule” decision fusion [26]. For each voxel in the raw
image, the outputs of the individual atlas-based classifiers are determined. Their
“votes” are then counted, and the label that received that highest number of votes
is assigned to the voxel. It is worth, however, to take a closer look at the way an
atlas-based classifier works: by looking up a label according to a transformed
image coordinate. The label map is discrete, arranged on a 3D grid of labeled
voxels. Yet the coordinates of the raw image voxels that we are trying to label
hardly ever directly fall on grid points in the atlas. Therefore, looking up the
correct label requires some sort of interpolation. The simplest label interpolation
method is nearest neighbor (NN) interpolation, resulting in a single unique label
per atlas-based classifier. These can easily be combined using vote fusion as
described above.
A slightly more complex interpolation technique that can be applied to labels
is partial volume interpolation (PVI) as introduced by Maes
et al.
[36]. Here, the
labels of all eight neighbors of the interpolated coordinate are determined and
weighted with the trilinear interpolation coefficients of their respective grid
nodes. Therefore, the output of an atlas-based classifier using PVI is a vector
of weights between zero and one, which are assigned to each of the possible
labels. One can interpret the weights as the confidence of the classifier in the
respective label being the correct answer. These weighted decisions from all
classifiers can be combined by so-called “Sum Rule” fusion [26]. The weights for
each label are added over all classifiers, and the label with the highest sum is
taken as the combined decision.
11.5
Quantifying Segmentation Accuracy
In addition to presenting selected algorithms for atlas-based segmentation,
this chapter provides a quantitative comparison among different methods. For
each segmentation that we perform, its accuracy is computed. The accuracies
