With three to four clusters/tissues labeled and removed, this leaves three to four clusters to examine. Empirical observation has shown that pathology occupies one to three of these unlabeled clusters. Of these pathology containing clusters, tumor can occupy one or two of the clusters, but in order to completely separate pathology from normal tissues, we will locate all of these pathology clusters and build a ``pathology mask'' from which the system looks for tumor in earnest.
The unlabeled clusters are sorted along the PD feature and the three highest (in the case of four unlabeled clusters) are kept. These three clusters are then sorted along the T1 feature and will be named as ``Candidates'' for specific examination.
Figure 4: Building the Pathology Recluster Mask. Pathology (a) and (b) was
accepted into the mask (d), while gray matter (c) failed.
The candidate with the highest T1 value, ``Candidate Tumor''
is most likely
to contain the majority of the tumor. The remaining
two ``Candidate Edema1'' and ``Candidate Edema2'' respectively,
may contain some tumor, but contain mostly non-tumorous
pathology, edema and necrosis. To confirm this, however,
a density measure similar to the one described in
Section 4.3
is employed to verify their makeup. The density thresholds
for the candidates were:
Candidate Tumor: 
Candidate Edema1: 
Candidate Edema2: 
It should be noted that these thresholds can be fuzzified as the types of tumors handled by the system increase. For glioblastoma multiformes', the thresholds as given appear sufficient. All candidate clusters passing their respective density test are merged together into the pathology mask and passed to the next reclustering stage. Clusters that fail are removed from further consideration. In Figure 4, (a) and (b) represent some typical pathology clusters while (c) contains CSF and gray matter. Figure 4(d) shows the final pathology mask after (c) failed the density test.
With the region of pathology segmented away from the rest of the brain slice, segmenting specifically for tumor is begun. Like the previous stages, over-clustering is also used here to enhance separation between tissue types. Five clusters were used at this stage.
Since the system has further isolated the mask within two classes, tumor and non-tumor pathology, the knowledge concerning their distribution in feature space is sufficient to enable its incorporation into the next reclustering stage. This was done by using ``semi-supervised fuzzy c-means'' (ssFCM) [7]. The ssFCM algorithm allows pixels whose labels are either known or have very high membership in a class, to be used as ``training.'' Pixels we suspect of being in a particular class, but are not sure enough to use as training, can still serve a purpose, if their initial membership is preset to the cluster representing its suspected tissue type. Initialized pixels are biased towards membership in a particular cluster, but can change if the algorithm finds stronger membership in a different cluster.
Based on the knowledge described in Section 2.2 concerning the cluster distribution for tumor versus non-tumor pathology, training data was provided for three of the five classes the pathology mask was to be clustered into. Since tumor occupies the highest T1 pixels, the top 5% pixels in T1 space were selected for training and the next 5% (after the first 5%) as initialization. A similar method was used for two other classes that would contain non-tumor pathology, except these deal with the pixels lowest in T1 and PD, respectively. The remaining two clusters have no training data, and are used to cluster pixels not captured by the three ``trained'' clusters. Once the training and initialization pixels have been gathered and fed into ssFCM reclustering begins.