Digital Signal Processing Reference
In-Depth Information
where
w
k
w
k
+
1
=
w
k
.
(2.34)
and
w
k
+
1
s
k
+
1
,
y
k
+
1
=
k
=
0
,...,
N
.
(2.35)
s
k
y
k
belongs to previous pixel
and
w
k
+
1
is the updated eigenvector of the current pixel. The vector
s
k
consists of
the gray values of red, green, and blue component of the current pixel. The value
of the converging parameter
The term
w
k
is the eigenvector with deviation 2
μ
is small that approximates to 10
−
6
. The plus sign in
(
2.33
) will conduct the equation to reach a maximum value that represents the signal
subspace. The minus sign in (
2.33
) will find the noise subspace that is converged to
a minimum value. For iterative computation of the covariance matrix,
R
s
, it can be
updated as
μ
s
k
+
1
s
k
+
1
,
R
s
(
k
+
1
)=(
1
−
α
)
R
s
(
k
)+
α
(2.36)
where
R
s
(
k
)
represents the
k
th covariance matrix of the
k
th sample color pixel and
R
s
(
th sample color
pixel. We can apply following equation to update the eigenvalues without computing
the covariance every time.
k
+
1
)
represents the
(
k
+
1
)
th covariance matrix of the
(
k
+
1
)
2
λ
k
+
1
=(
1
−
α
)
λ
k
+
α
|
y
k
+
1
|
,
(2.37)
where
th eigenvalue.
We can find the mean value of the estimated eigenvectors from (
2.33
). The estimated
mean eigenvectors can be represented as follows:
λ
k
represents the
k
th eigenvalue and
λ
k
+
1
represents the
(
k
+
1
)
w
k
]=
E
[
E
[
I
±
μ
R
s
(
k
)]
E
[
w
k
]
,
(2.38)
where
I
is the identity matrix. Inspecting (
2.38
), we find out that normalized eigen-
vector
w
k
of previous pixel will approximately equal to eigenvector
w
k
of the current
pixel. According to this property, we can select
to adaptively adjust and estimate
the eigenvectors of the successive pixels according to (
2.33
). Using plus and minus
sign in (
2.38
),
w
k
will converge to signal plane and noise planes respectively.
μ
2.3.2
Search Algorithms for Desired Color Object
The AESS algorithm is applied to the desired region with first selecting an initial
pixel. We take the sampled pixel as the starting point of our searching algorithms.
From this starting point, the eigenvectors will be adaptively updated according to
different searching routes. Finally, the desired color object will be segmented. The
quality of the segmented result is heavily influenced by the shading condition, be-
cause the eigenvectors are very sensitive to the color shade. In order to overcome this
