Biomedical Engineering Reference
In-Depth Information
of this clustering process is carried out by optimizing an objective function, in this
case, to minimize a squared error function, as shown in (
3.41
).
K
n
||
x
(
j
)
i
−
c
j
||
2
(3.41)
j
=
1
i
=
1
where n is the number of data, K is the clusters number,
||
x
(
j
)
i
−
c
j
||
2
is the
distance measurement between the data point
x
(
j
)
i
representing the intensity value
of image pixels and the cluster center
c
j
computed from calculating the mean
of each group of pixels. It indicates the distance difference from the data point
to the cluster centre. First, the histogram of the input image is computed. Two
clusters centre will be chosen randomly among the data points followed by con-
structing the distance difference between each data point and the cluster centre.
Subsequently, each data point will be assigned to one of the two clusters centre
depends on the distance difference. When all the data points are assigned to clus-
ter centre, the new cluster centre is then recalculated by computing the mean of
each cluster group. These steps iterate until the objective function achieve a mini-
mum value.
3.4.1 Clustering Algorithm Applied in the Proposed
Segmentation Framework
Algorithm
(A)
Input
:
Data set (image pixels intensity)
=
{
x
i
}
1
, where n represents the total number of
pixels in the image.
(B)
Initiation:
(i) Set the clusters number 'k',
1
≤
k
≤
3
where k is an integer.
(ii) Initiate the cluster center,
C
j
(
T
)
,
1
<
j
≤
k
, T
=
0
(iii) Set the tolerant error value
′
σ
′
where T
=
number of k-means iterations, Initiation value: k
=
1, T
=
0, j
=
1,
and i
=
1
(C)
Computation of Euclidean Distance
The Euclidean Distance between intensity value and cluster center value is
computed as follow:
K
n
D
(
T
)
ji
x
(
j
)
i
−
C
(
T
−
1
)
j
=
w
ji
j
=
1
i
=
1
(3.42)
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