N-dimensional filter and method for n-dimensionally filtering an original image pixel
View Patent ↗Known N-dimensional filters 100 and methods for N-dimensionally filtering apply noise reduction to an original image pixel. However, carrying out only noise reduction to a pixel of an image is often not enough when a good picture quality is required. Thus, additionally, sharpness enhancement (peaking) is carried out. However, noise reduction and peaking have contrasting spectral behaviors which lead to non-optimal results when both operations, noise reduction and peaking, are implemented in series. By appropriately defining coefficients α(p, n) or β(p, n) of the transmission function, the transmission function is capable of applying both noise reduction and sharpness enhancement to the input signal of the N-dimensional filter 100.
1. An N-dimensional filter having a transmission function for applying noise reduction to an original image pixel p being provided to the N-dimensional filter by a received input signal,
wherein at least one filter coefficient of the transmission function is defined such that the transmission function applies both noise reduction and sharpness enhancement, simultaneously, to the signal input to said N-dimensional filter, and wherein the transmission function is defined as follows:
F
f
(
p
)
=
G
(
p
)
·
[
F
(
p
)
+
γ
∑
n
∈
N
1
α
(
p
,
n
)
·
F
(
p
+
n
)
+
δ
∑
n
∈
N
2
β
(
p
,
n
)
·
F
f
(
p
+
n
)
]
wherein
p(x,y,t): represents the spatial and temporal position of the original or a neighbor pixel;
N1, N2: are vectors defining a one, two or three dimensional neighborhood of the original pixel;
n represents the position of a current neighbor pixel in a neighborhood N1, N2;
G(p): is a normalization factor;
α, β: are groups of filter coefficients α(p, n) and β(p, n) of the transmission function;
γ, δ: are constants; and
F(p): is an input luminance signal applied to said N-dimensional filter,
characterized in that α(p, n) represent the filter-coefficients of a first group a of filter coefficients and being defined as:
α
(
p
,
n
)
=
{
w1
:
Δ
(
p
,
n
)
<
Th
1
w2
:
Th
1
≤
Δ
(
p
,
n
)
<
Th
2
p
:
Th
3
≤
Δ
(
p
,
n
)
≤
Th
4
0
:
otherwise
and β(p, n) represent the filter-coefficients of a second group β of filter coefficients and being defined as:
β
(
p
,
n
)
=
{
w1
:
Δ
f
(
p
,
n
)
<
Th
1
w2
:
Th
1
≤
Δ
f
(
p
,
n
)
<
Th
2
p
:
Th
3
≤
Δ
f
(
p
,
n
)
≤
Th
4
0
:
otherwise
wherein:
Th 1 –Th 4 : are threshold values,
P: is a negative programmable parameter, and
w1, w2: are positive programmable parameters; and
wherein the parameters Δ and Δ f are defined as follows:
Δ( p, n )=| F ( p+n )− F ( p )|
Δ f ( p, n )=| F f ( p+n )− F ( p )|.
2. The N-dimensional filter as claimed in claim 1 ,
characterized in that each filter coefficient of said transmission function is respectively assigned to a different one of neighboring pixels being comprised in a N-dimensional neighborhood of said original pixel and defines if the assigned neighbor pixel contributes either to noise reduction or to sharpness enhancement of the original pixel.
3. The N-dimensional filter as claimed in claim 1 ,
characterized in that the original pixel as well as the neighbor pixels p(x, y, t) T having the time component t are used either for noise reduction or sharpness enhancement.
4. The N-dimensional filter as claimed in claim 1 ,
characterized in that the input signal is a selected spectral component of a video signal.
5. The N-dimensional filter as claimed in claim 1 ,
characterized in that if the parameters Δ and Δ f do not lie between Th 3 and Th 4 , the filter coefficients α(p,n) or β(p,n) have a + sign, and if the parameters Δ and Δ f lie between Th 3 and Th 4 , the filter coefficients α(p,n) or β(p,n) have a − sign.
6. The N-dimensional filter as claimed in claim 1 ,
characterized in that the N-dimensional filter is embodied in an application specific integrated circuit (ASIC).
7. A display apparatus for displaying images, said display apparatus comprising the N-dimensional filter as claimed in claim 1 .
8. A method for N-dimensionally filtering an original image pixel with respect to noise reduction according to a transmission function, the method being characterized by the step of;
defining at least one filter-coefficient of the transmission function such that the transmission function applies both noise reduction and sharpness enhancement, simultaneously, to the original image pixel applied to an N-dimensional filter, wherein the transmission function is defined as follows:
F
f
(
p
)
=
G
(
p
)
·
[
F
(
p
)
+
γ
∑
n
∈
N
1
α
(
p
,
n
)
·
F
(
p
+
n
)
+
δ
∑
n
∈
N
2
β
(
p
,
n
)
·
F
f
(
p
+
n
)
]
wherein
p(x,y,t): represents the spatial and temporal position of the original or a neighbor pixel;
N1, N2; are vectors defining a one, two or three dimensional neighborhood of the original pixel;
n represents the position of a current neighbor pixel in a neighborhood N1, N2;
G(p): is a normalization factor;
α, β: are groups of filter coefficients α(p, n) and β(p, n) of the transmission function;
γ, δ: are constants; and
F(p): is an input luminance signal applied to said N-dimensional filter,
characterized in that α(p, n) represent the filter-coefficients of a first group a of filter coefficients and being defined as:
α
(
p
,
n
)
=
{
w1
:
Δ
(
p
,
n
)
<
Th
1
w2
:
Th
1
<
_
Δ
(
p
,
n
)
<
Th
2
p
:
Th
3
<
_
Δ
(
p
,
n
)
<
_
Th
4
0
:
otherwise
and β(p, n) represent the filter-coefficients of a second group β of filter coefficients and being defined as:
β
(
p
,
n
)
=
{
w1
:
Δ
f
(
p
,
n
)
<
Th
1
w2
:
Th
1
<
_
Δ
f
(
p
,
n
)
<
Th
2
p
:
Th
3
<
_
Δ
f
(
p
,
n
)
<
_
Th
4
0
:
otherwise
wherein:
Th 1 –Th 4 : are threshold values,
P: is a negative programmable parameter, and
w1, w2: are positive programmable parameters; and wherein the parameters Δ and Δ f are defined as follows:
Δ( p, n )=| F ( p+n )− F ( p )|
Δ f ( p, n )=| F f ( p+n )− F ( p )|.