Digital Signal Processing Reference
In-Depth Information
matrix as described in (
2.53
), where the belongings are treated as the weightings
of
z
q
z
q
that is formed by the data in the eigen-subspaces. From covariance matrix
C
z
j
, we can obtain class
j
's eigenvector
w
j
,
i
and the corresponding eigenvalue
λ
j
,
i
,
where index
i
denotes the
i
th component because we order the eigenvalues as
λ
j
,
1
≥
λ
j
,
2
≥
λ
j
,
3
.
(2.54)
Then, the
j
th cluster center of signal term in the CEFCM can be expressed by
the principal component
v
j
1
=
λ
j
,
1
w
j
,
1
.
(2.55)
The second and the third components are treated as the noise terms. The similar-
ity measure related to the
j
th cluster center expressed as Euclidean distance between
z
q
and
v
j
,
1
now becomes the orthogonal projection to the noise eigenvectors. The
smaller of
z
q
−
v
j
,
1
means that
z
q
and
v
j
,
1
are closer to each other. Based
on
eigen
prop
erties, the smaller projection to both
w
j
,
2
and
w
j
,
3
with respect to
λ
j
,
2
and
λ
j
,
3
indicates that
z
q
and
v
j
,
1
arecloser.Themeasureof
related to
w
j
,
2
and
w
j
,
3
is equivalent to the projection of
z
q
to the normalized noise eigenvec-
tors, which can be expressed as
z
q
−
v
j
,
1
√
λ
j
,
2
w
j
,
2
and
1
√
λ
j
,
3
w
j
,
3
, so that the membership of
1
the
q
th sample can be modified as follows:
1
λ
j
,
2
−
λ
j
,
1
−
2
λ
j
,
1
m
−
1
1
λ
j
,
3
1
z
q
w
j
,
2
2
z
q
w
j
,
3
2
z
q
w
j
,
1
2
+
+
u
jq
=
1
.
1
1
−
λ
β
,
1
−
2
λ
β
,
1
m
−
c
β
=
1
λ
β
,
3
1
z
q
w
β
,
2
2
z
q
w
β
,
3
2
z
q
w
β
,
1
2
∑
λ
β
,
2
+
+
(2.56)
The success of extracting video objects depends on the proportion of three eigen-
values. Inspecting (
2.56
), we have adjusted the iterating processes near the cluster
center in the signal subspace according to its eigenvalue to eliminate too bright or
too dark circumstances. In our experiments, we take fuzzy weighting
m
3, the
class number equals to 6 and feature number equals to 3. Observing the simulation
results, we can obtain more satisfactory ones by just considering the principal plane
and the strongest noise plane. In this case, we set
=
λ
j
,
1
=
λ
j
,
3
=
1,
λ
β
,
1
=
λ
β
,
3
=
1,
and
2in(
2.56
).
After obtaining the segmentation results, almost all the desired color pixels
can be found. The few remaining noise pixels can be easily removed by any
post-processing procedure. The detailed procedures for the CEFCM are listed as
follows:
λ
j
,
2
→
∞
;
λ
β
,
2
→
∞
with
c
=
1. As Step 1 in Sect.
2.4.2.1
.
2. As Step 2 in Sect.
2.4.2.1
.
3. As Step 3 in Sect.
2.4.2.1
.
4. Initialize the membership function and cluster centers. Later, we jointly consider
three eigen-subspaces and iteratively update the covariance matrix with (
2.53
).
