At this stage, tumor has been separated from the non-tumorous pathology. Therefore, the goal of this stage is to identify which clusters belong to tumor and label them accordingly.
As described in Section 2.2, of the five clusters, tumor occupies the highest end of the T1 spectrum and can occupy one, two, or three classes. Hence, it is possible label three of the five classes with two simple rules. The highest class in T1 space is automatically labeled as tumor, while the lowest two classes in T1 space are labeled as non-tumor. At this point, we should note that two of the three clusters given training and initialization pixels described in Section 4.4 were immediately identifiable and labeled. In a sense, the knowledge dictated the ssFCM training decisions, which in turn guided the ssFCM routine to produce clusters that better reflected the knowledge. As knowledge increases and more intuitive training can be inserted, the problem space that subsequent rules must handle is greatly simplified.
With three of the five clusters labeled, two remain. Of the two remaining clusters, the higher T1 cluster is examined first. If a cluster is found to be non-tumor, then no cluster with a lower T1 value can be tumor. Therefore, determining that the second highest T1 cluster is not tumor will allow us to immediately label the third highest cluster as non-tumor. If the second highest T1 cluster is tumor, then the third highest can be processed.
A variety of tests could be used for screening tumor from non-tumor,
including density and relative size (glioblastoma multiforme tumor tends to be
much more compact and smaller than edema pathology), but with hopes
of covering multiple tumor types with a single rule, a different
use of cluster distribution was employed. First used in [2,3] for
finding cases where white matter had been split into two classes,
the basic idea is that a cluster that contains tumor is more likely
to lie closer to a cluster with known tumor than a cluster without
any.
In this case, the highest and lowest T1 clusters (known
tumor and non-tumor respectively) and the unknown cluster
are projected into T1 space. A ratio, which is later thresholded,
is created by dividing the distance (in T1 space) from the
known non-tumor cluster to the unknown cluster by the distance
from the unknown cluster to the known tumor cluster. If the
ratio is less than 
, then the unknown cluster is non-tumor.
This test is applied to both the second highest T1 cluster
and the third highest, in the case that the second highest passes.
If one or two tumor classes are found, they are merged together and processing halts with the glioblastoma multiforme tumor having been successfully segmented. If a third tumor cluster has been found, however, a final stage of reclustering is necessary. This is due to the fact that the third tumor cluster is actually comprised of tumor and non-tumor pathology.
To separate the tumor, the mixed cluster is isolated into a mask and another round of ssFCM using the same training and initialization patterns described above in Section 4.4. The cluster is broken into three sub-classes and the class with the highest T1 value is merged with the rest of the tumor image.