Information Technology Reference
In-Depth Information
(
)
K
()
(
v
)
∑
=
p
o
|
l
=
π
p
o
,
v
∈
G
.
(14)
Γ
v
Q
k
k
v
k
1
Assuming grey values of the image are condition-independent, the joint probabil-
ity density function of
o
, given the context labels
l
, is
G
K
( )
( )
(
v
)
∏
∑
= =
P
o
|
l
=
π
p
o
(15)
k
k
v
v
1
k
1
(
)
where
.
Instead of mapping the whole data set using a single complex network, it is
more practical to design a set of simple class subnets with local mixture clusters,
each of which represents a specific region of the knowledge space. It can be as-
sumed that there is more data classes with more class clusters. Since the true clus-
ter membership for each voxel is unknown, cluster labels of the data can be treated
as random variables. There is a difference between the mixture model for model-
ling the voxel image distribution over the entire image where the voxel objects are
scalar valued quantities, whereas here a mixture distribution within each class is
assumed and the class index in the formulation and modelling of the feature vector
distribution is specified. Also, all data points in a class are identically distributed
from a mixture distribution.
l
=
l
;
v
=
1
,...,
G
v
3.3 Neural Network Based Segmentation
In previous sections there are described different algorithms based on threshold-
ing, region growing, edge detection or voxel classification based on kernels. Neu-
ral networks with applications to various stages of image processing can also be
addressed to solve the image segmentation problem [10, 11]. This method in-
volves mapping the problem into a neural network by means of an energy func-
tion, and allowing the network to converge so as to minimize the energy function.
The iterative updating of the neuron states will eventually force the network to
converge to a stable and preferably valid state, with the lowest energy. The final
state should ideally correspond to the optimum solution.
The neural network model for the 3D object, with size
N
×
N
×
N
, segmen-
x
y
z
tation problem can be described with
×× neurons, where
C
is num-
ber of classes, i.e. regions on which the scene is segmented. As previous described
methods, this method of segmentation also uses spatial information and is thus
image-size dependent. To optimize the algorithm in terms of the computational
time and resources when the image size or the number of classes required is large,
neural network based segmentation method can employ the grey level intensities
distribution instead of spatial information, and thus has the advantage of being im-
age-size independent, using fewer neurons and therefore requiring lesser computa-
tional time and resources. Such method uses
O
neurons representing
O
grey levels
and
C
classes of subvolumes, so the neural network consisting of
O×C
neurons,
N
N
N
×
C
x
y
z
