Digital Signal Processing Reference
In-Depth Information
the desired video objects correctly. In the SEFCM, we modify the matrix
L
j
as in
(
2.46
) that is suitable to extract the signal and noise subspaces. For extracting the
signal space, we can rewrite
L
j
as follows:
⎛
⎞
λ
2
,
j
+
λ
3
,
j
2
−
1
00
⎝
⎠
.
Γ
=
(2.50)
λ
−
1
1
,
j
0
0
j
λ
−
1
1
,
j
0
0
Similarly, we can extract the noise planes by using the following matrix:
⎛
⎞
λ
−
1
1
,
j
0
0
λ
2
,
j
+
λ
3
,
j
2
−
1
⎝
⎠
.
0
0
Γ
j
=
(2.51)
λ
2
,
j
+
λ
3
,
j
2
−
1
0
0
λ
−
1
1
We adopt (
2.50
) to extract the signal plane by using
j
to suppress the noise terms.
,
λ
−
1
In (
2.51
), we use
1
,
j
to suppress the signal terms in order to obtain two noise
planes. We can modify the membership function of (
2.43
) as follows:
(
v
j
)
−
2
T
A
j
(
z
q
−
v
j
)
z
q
−
m
−
1
u
jq
=
1
,
(2.52)
1
(
v
β
)
−
2
c
β
=
T
A
β
(
∑
z
q
−
v
β
)
z
q
−
m
−
V
j
Γ
j
V
j
and
A
β
=
V
T
where
A
j
=
β
Γ
β
V
β
related to class
j
and
β
, respectively. For
class
. The detailed
procedures of the SEFCM are shown in Fig.
2.19
and illustrates as follows:
β
, the index
j
appeared in (
2.50
)and(
2.51
) should changed to
β
1. Sample few desired color object blocks.
2. Compute the covariance matrix and obtain the eigenvectors according to (
2.2
).
3. Transform the color images to signal and noise subspaces with eigenvectors
as (
2.48
).
4. Initialize the modified membership value and center of each cluster. With iter-
ative updating of the covariance matrices using (
2.49
), apply FCM to extract
the segmentation results related to signal and noise planes separately. Either
segmenting on signal or noise planes, we apply (
2.50
)or(
2.51
) to the new mem-
bership function (
2.52
) during the FCM classification procedures.
5. Perform logical operation on the results obtained from Step 4.
2.4.2.2
Coupled Eigen-Based FCM (CEFCM) Method
In order to efficiently segment the desired color objects, we devise a coupled eigen-
based FCM (CEFCM) algorithm (Fig.
2.21
). In considering signal and noise planes
