The anatomical structure of the brain varies with
different planes of imaging and different positions in a
plane [9]. In this study, slices of interest
are approximately 7 to 8cm from top of the head
in the axial plane. These slices can be considered the
``center'' of the brain in the axial plane and
have the best uniformity of signal within our MR coils.
Each slice consists of three feature images: T1-weighted
(pulse repetition time 600ms, echo time 20ms), proton density (PD)
and T2-weighted (pulse repetition 3000ms, echo time 80ms) [1].
There are two sources of knowledge: (1) the anatomical
structure of brain tissue and (2) the tissue distribution in
feature space. Knowledge was acquired from imaging
anatomy [9] and experimental observation.
A. Modeling and Matching of Tissues:
Figure 1(a) depicts a normal brain slice.
The labeled tissues are: white matter (white), gray
matter (black), and cerebro-spinal fluid (CSF) (inner gray.)
Figure 1(b) shows an abnormal slice. The tumor
(light gray) occupies an area which would typically
belong to white matter and CSF. Due to tissue variation
between different
patients and slice positions within the neighborhood of
interest, it is a nontrivial effort to quantitatively
model the shape of white matter and CSF. The models we
have defined for normal white matter and CSF are instead
qualitative. For example, in normal slices, white matter
is contiguous along both sides of a ventricular area,
though the continuity may be slightly interrupted by
gray matter.
The CSF is symmetrical on a vertical axis through the
center of the ventricular area.
A default logic [10] is utilized to match the
qualitative models to the input slice: unless there are
expected deformations or a mismatch in an instance of a
model, classify the instance into a normal class.
If a deformation is small,
the decision is delayed until further
evidence is collected.
Figure 1: Slices of interest: (a) a normal slice (b) an abnormal slice.
B. Tissue Distribution in Feature Space:
The FCM algorithm is used to segment MR slices initially
and to acquire the knowledge of tissue distribution in
feature space. An image slice with three features is
clustered into ten classes. We decided upon ten classes
empirically. Each class
has a cluster
center 
. Figure 2(a)
shows the ten class centers of a slice in the T1, PD and
T2 space. Six characters are used to represent, from
left to right, classes of air (A), skull tissues (B),
white matter (W), gray matter (G), tumor (T) and CSF (C)
respectively. The class centers in feature space can be
better illustrated by projecting them into T1 and T2
space, as shown in Figure 2(b).
The knowledge of the class
center distribution can be used in locating regions of interest for
focus-of-attention based upon their relation
in the T2 spectrum (Figure 2(c)). For example,
air appears in the lowest one or two classes
as a separate class.
Figure 2: Class centers in feature space.
The relative ordering provides heuristics that allows us to quickly remove extraneous information, such as the clusters representing air and skull tissues, and provide help in labeling the remaining clusters.