Digital Signal Processing Reference
In-Depth Information
1
N
(8)
( )
t
+
μ
=
xZ
γ
()
l
i
il
( )
t
+
N
π
i
=
1
l
1
N
( )
t
+
( )2
t
+
C
=
(
x
−
μγ
)
(
Z
)
(9)
l
i
l
il
( )
t
+
N
π
i
=
1
l
The E step and the M step form the iterative relations, they are repeated until all values
have been convergence.
3
Segmentation Using Gaussian Mixture Model and EM
Algorithm
RGB
R
G
B
Suppose
xxxx
=
(
,
,
)
is a pixel of color image, where
x
,
x
,
x
is the RGB
i
i
i
i
components of the pixel respectively, (
i
=
1, 2,...,
N
)
. Image segmentation process is
as follows:
a) Choose
M
, which is the number of region you want to segment, and then
initialize
. To a color image, we
determine subjectively that it is mixed by m single Gaussian. The initial value of each
parameter is:
θ
,
θππ πμμ μ
=
(
,
,...,
,
,
,...,
,
CC
,
,...,
C
)
12
M
12
M
12
M
1
ππ
0
=== =
0
...
π
0
(10)
1
2
M
M
where
.
b) Use the above formula (7), (8) and (9) in the iterative EM algorithm to calculate
the final
μ
0
l
and
C
are given by the above formula (8), (9), (
0
l
=
1, 2,...,
M
)
. In this procedure code of
the paper, the iterative terminal condition is that absolute value of the difference is
less than
θ
,
θππ πμμ μ
=
(
,
,...,
,
,
,...,
,
CC
,
,...,
C
)
12
M
12
M
12
M
10
−
6
between this result and the previous result.
c)
According
to
the
final
obtained
parameter
θππ πμμ μ
=
(
,
,...,
,
,
,...,
,
CC
,
,...,
C
)
, we mark each pixel
x
in the color
12
M
12
M
12
M
image. The mark formula is as follows:
NM
[
]
{
}
(11)
I
=
max
E
ln
p X Z
(
,
|
πμ
,
,
C
)
=
γ
(
Z
) ln
π
+
ln
N x
(
|
μ
,
C
) ,
l
=
1, 2,...,
M
l
il
l
i
l
l
i
==
11
l
4
Experimental Results
In the following experiments, the original color images are flower, tiger, bear in Figure
1. The number
M
of segmentation is respectively 2,5,10. The segmentation results
show in Figure 2, 3, 4.
From the above results, we can see that Gaussian mixture model responses the
distribution of color image information to a certain extent. When the value of
M
increases, the segmentation effect will make better in the experiments.
