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with each row representing one grey level of the image and each column a particu-
lar class. Values of voxel object
o
,
are represented by one neuron and defined
i
with
1
if
v
∈
C
⎩
⎨
⎧
i
o
=
(16)
v
,
i
0
otherwise
Each row should consist of only one '1', and the column which this '1' falls under
will indicate that particular grey level class
C
. The connection strength between
two neurons
o
,
represents some other voxel object
that is element of grey level class
C
) is denoted as
W
vi,wj
. A neuron in this net-
work would receive input from all other neurons weighted by
W
vi,wj
. Mathemati-
cally, the total network input to the neuron (
v,i
) is given as [12]
o
,
and
o
,
(where neuron
i
j
j
O
C
∑∑
Net
=
W
v
.
(17)
vi
vi
,
wj
wj
w
j
The neuron with the largest net-input in the same row is declared as the winner,
according to winner-takes-all rule [13] , and the updating of all neurons in the
same row is as follows:
{}
1
if
Net
=
max
Net
⎩
⎨
⎧
v
,
i
v
o
=
(18)
v
,
i
0
otherwise
.
All network states upon convergence will be valid, i.e., no grey levels will be clas-
sified into two or more different classes, and each grey level will be assigned a
class.
The implementation of the neural network in 3D object segmentation on grey
level intensity classes is as follows. At input
O
grey levels of an image and the
number of classes
C
must be defined. Initializing of the neural network is done by
randomly assigning one '1' per row, and setting the rest of neurons in the same
row to '0'. Same procedure is done for all other rows, while ensuring that there is
at least one '1' per column. The next step is loop done for
O
times: one row is
randomly chosen and
Net
v,i
is calculated to all neurons in the same row and a win-
ner-takes-all rule is applied to update all neuron states within the same row. After
performing the whole loop, one epoch is constituted and algorithm is repeating
from initialization step until convergence, i.e. until the network state,
V =
(
o
v,i
), for
previous epoch is the same as for the current epoch.
4 Results
Experimental input volumetric neurodata are shown in Fig. 3 and aim is to seg-
ment it into subvolumes. The segmentation and classification procedure is shown
in Fig. 4. Main task is to detect and isolate brain mass and separate it from the
background. First, region properties are detected. Region properties are denoted
