Digital Signal Processing Reference
In-Depth Information
With greater weighting coefficients, this filter takes those pixels of the neigh-
borhood, whose intensity are close to the intensity of the central pixel
F
0
, and
does not take into consideration the value of
F
0
, when defined as
16
-
20
n
n
1
Z
F
0
=
[1
−|
F
0
−
F
k
|
]
·
F
k
,
Z
=
[1
−|
F
0
−
F
k
|
]
,
(12.5)
k
=
1
k
=
1
which leads to a more robust filter performance. Similar structure has the
gradient inverse weighted operator, which forms a weighted mean of the
pixels belonging to a filter window. Again, the weighting coefficients depend
on the difference of the gray-scale values between the central pixel and its
neighbors:
17
,
19
n
1
Z
F
k
F
0
=
,
max
{
γ
,
|
F
0
−
F
k
|}
k
=
0
n
1
Z
=
,
(
in Reference 17
γ
=
0
.
5
).
(12.6)
max
{
γ
,
|
F
0
−
F
k
|}
k
=
0
Lee's local statistics filter
18
,
21
,
22
estimates the local mean and variance of
the intensities of pixels belonging to a specified filter window
W
and assigns
to the pixel
F
0
the value
F
0
F
, where
F
is the arithmetic
mean of the image pixels belonging to the filter window and
=
F
0
+
(
1
−
α)
α
is estimated
2
0
2
2
0
2
0
as
α
=
max
{
0
,
(σ
−
σ
)/σ
}
, where
σ
is the local variance calculated for the
2
is the variance calculated over the whole
samples in the filter window and
σ
image. If
σ
σ
, then
α
≈
1 and no changes are introduced. When
σ
σ
,
0
0
then
0 and the central pixel is replaced with the local mean. In this way,
the filter smoothes with a local mean when the noise is not very intensive and
leaves the pixel value unchanged when strong signal activity is detected.
In Reference 23 and 24 a powerful adaptive smoothing technique related
to anisotropic diffusion (which will be discussed in the next section) was
proposed. In this approach, the central pixel
F
0
is replaced by a weighted
sum of all the pixels contained in the filtering mask:
α
=
exp
,Z
n
n
2
1
Z
−
|
G
k
|
F
0
=
0
w
k
F
k
,
with
w
=
=
0
w
k
,
(12.7)
k
β
2
k
=
k
=
where
is the magnitude of the gradient calculated in the local neighbor-
hood of the pixel
F
k
and
|
G
k
|
is a smoothing parameter.
In Reference 25 another efficient adaptive technique was proposed:
β
exp
exp
N
k
2
1
Z
−
ρ
−
|
F
k
−
F
0
|
F
0
=
·
F
k
,
(12.8)
1
2
β
β
k
=
1
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