Cluster Center Distribution in Feature Space

Each slice processed by the FCM algorithm consists of an intensity image for each of the three features, T1, PD, and T2 respectively. As a result, each FCM class will have a cluster center in . When the number of clusters was in one-to-one correspondence to the number of tissue types, pixels belonging to different tissue classes were often placed in the same cluster. Therefore, during initial segmentation steps in [1,2,3], the FCM algorithm is used to cluster the input slice for an initial set of ten classes. While this generally resulted in some degree of over-segmentation in normal slices, it reduced the chance that tumors were grouped into classes that contain normal tissues. This concept is equally important here in further separating pathological tissue from normal tissue, as well as segmenting tumor from other pathology like edema and necrosis.

At the beginning of the tumor segmentation process, labels for air, extra-cranial tissues, and white matter are already known. Pixels belonging to any of these classes are masked out and the remaining unknown pixels are reclustered into seven classes, again using the strategy of over-clustering. Figure 2(a) shows the seven class centers of a reclustered slice projected into T1 and PD space. Three characters are used to represent classes of gray matter (G), pathology (P), and CSF (C) respectively. Knowledge of the class center distribution (after clustering) is useful in locating regions of interest for focus-of-attention based on the following:

1. CSF always takes the cluster with the lowest T1 value for its centroid.
2. Gray matter always occupies 2 clusters with the lowest values for the PD centroid value.
3. Pathology lies in the high PD spectrum and can reside in up to 3 clusters.
4. Of the ``pathology clusters,'' the cluster with the highest T1 value centroid generally contains the most tumor.

  
Figure 2: Cluster Center Distribution: (a) Normal Tissue and Pathology (b) Tumor and Pathology.

Once the clusters containing CSF and gray matter have been located, they are also masked out and the remaining clusters, containing only pathological pixels, are themselves reclustered into five clusters. Figure 2(b) shows the five class centers of reclustered pathology projected into T1 and PD space with (T) representing glioblastoma multiforme tumor and (P) non-tumor pathology. Given two super-classes, glioblastoma multiforme tumors and non-tumor pathology, the following was observed:

1. Tumor appears at the highest end of the T1 spectrum and may occupy one, two, or three classes.
2. Non-tumor pathology tends to occupy the lowest two classes in PD space.
3. Clusters with tumor lie generally closer in T1 space to the highest T1 cluster (known tumor) than the lowest T1 cluster (known non-tumor). This implies a form of ``separateness'' between tumorous and non-tumorous clusters.

At both stages in the segmentation process, these distribution phenomena provide valuable information that allow us to quickly remove extraneous data and reveal the regions of importance. Furthermore, tissue distribution in feature space provides an excellent way to find training patterns and initializations for FCM. It should be noted, however, that these distributions are known to be approximate or fuzzy and ``exact'' orderings are not expected to hold for every processed slice. Other knowledge must be used to cover clusters not captured by distribution characteristics.