Digital Signal Processing Reference
In-Depth Information
Equation 12.20 and also in Equation 12.75. This was already noticed in the
scheme of Smith and Brady
25
(Equation 12.8), who did not take the central
pixel into the averaging process, which is equivalent to setting
λ
∗
=
1. That is
λ
∗
=
why we set
1inEquation 12.75 to define the new DPAF filter Equations
12.74 and 12.75.
The superiority of this approach over the classic scheme is clearly seen in
Figure 12.9, where especially for highly corrupted images, the difference in
terms of PSNR is quite significant (see also Tables 12.4 and 12.5 in Section
12.6.2).
In a similar way, the DPAL filter can be defined as
exp
η
p
0
,p
1
,p
2
,
,p
η
{
−
β
·
W,
...
·
F
p
η
,p
η
}
p
1
,p
2
,p
3
,
...
F
x
=
F
p
0
exp
η
p
0
,p
1
,p
2
,
,p
η
=
−
β
·
W,
...
{
,p
η
}
p
1
,p
2
,
...
w
∗
p
0
,p
η
·
=
F
p
η
,
(12.78)
p
η
which can be written as
N
F
0
=
1
w
k
F
k
,
(12.79)
k
=
where
N
denotes the number of pixels surrounding
F
0
in the filtering window.
Analogously to Equation 12.76, we can introduce the general form of DPAL
defined by Equation 12.78
N
F
0
=
(
−
λ
∗
)
F
0
+
λ
∗
1
w
k
F
k
,
1
(12.80)
k
=
and its iterative version
N
F
t
+
1
0
−
λ
∗
)
F
t
0
+
λ
∗
1
w
k
F
k
,
=
(
1
(12.81)
k
=
w
k
are the normalized weighting coefficients from Equation 12.78.
The concept of the DPAF and DPAL filters is presented in Figure 12.6. The
weights assigned to the pixels surrounding the central pixel
F
0
are determined
in different ways. In the DPAF approach, the weights in Equation 12.74 are
calculated exploring all digital paths starting from the central pixel and cross-
ing its neighbors (Figure 12.6a), and then a weighted average of the nearest
neighbors of the central pixel is calculated (Equation 12.75).
In the DPAL approach, the weights are obtained by exploring all digital
paths leading from the central pixel to any of the pixels in the filtering window
(Figure 12.6b), and then a weighted average of all pixels contained in that
window is calculated (Equation 12.81).
where
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