Methods and systems for upsampling filter design
View Patent ↗Aspects of the present invention relate to systems, methods and devices for upsampling images and design of upsampling filters. Some aspects relate to a determination of a phase offset position in a higher resolution picture relative to a lower resolution picture. Interpolation filter coefficients for some filters may then be selected based on the filter offset. Other aspects relate to selection of coefficients for filters that are not dependent on the phase offset. In certain implementations, a weighting factor may be used to combine the effects of a phase-offset-dependent filter and an independent filter.
1. A method for picture up-sampling from a lower resolution picture to a higher resolution picture said method comprising:
a) determining a lower resolution picture location corresponding to a sample position in said higher resolution picture;
b) determining a phase offset position for said lower resolution picture location, wherein said phase offset position denotes the position of said lower resolution picture location relative to said sample position in said higher resolution picture;
c) selecting a first filter coefficient for a first interpolation filter based on said phase offset position;
d) selecting a second filter coefficient for a second interpolation filter;
e) selecting a weighting factor to control the relative influence of said first interpolation filter and said second interpolation filter; and
f) calculating a picture value for said sample position using a weighted combination of said first interpolation filter and said second interpolation filter, said weighted combination being controlled by said weighting factor.
2. A method as described in claim 1 wherein said second filter coefficient is selected based on said phase offset position.
3. A method as described in claim 1 wherein said selecting a weighting factor is based on image noise.
4. A method as described in claim 1 wherein said selecting a weighting factor is based on proximity to an image block boundary.
5. A method as described in claim 1 wherein said first interpolation filter and said second interpolation filter are controlled by separate weighting factors.
6. A method as described in claim 1 wherein one of said first interpolation filter and said second interpolation filter is a 4-tap filter based on a 4-piece cubic spline.
7. A method as described in claim 1 wherein said first interpolation filter is a 4-tap filter based on a 4-piece cubic spline and said second interpolation filter is derived from the Catmull-Rom function.
8. A method as described in claim 1 wherein said phase offset position and said first and second filter coefficients are determined and selected independently for a horizontal direction and a vertical direction.
9. A method as described in claim 1 wherein one of said first interpolation filter and said second interpolation filter is a 4-tap filter with coefficients defined by the following table:
(4-tap) interpolation
filter coefficients
phase
e[−1]
e[0]
e[1]
e[2]
0
0
32
0
0
1/16
−1
32
2
−1
2/16
−2
31
4
−1
3/16
−3
30
6
−1
4/16
−3
28
8
−1
5/16
−4
26
11
−1
6/16
−4
24
14
−2
7/16
−3
22
16
−3
8/16
−3
19
19
−3
9/16
−3
16
22
−3
10/16
−2
14
24
−4
11/16
−1
11
26
−4
12/16
−1
8
28
−3
13/16
−1
6
30
−3
14/16
−1
4
31
−2
15/16
−1
2
32
−1.
10. A method as described in claim 1 wherein one of said first interpolation filter and said second interpolation filter is a 4-tap FIR filter with tap values given by the following matrix equation:
1
4
*
[
1
x
x
2
x
3
]
*
[
0
4
0
0
-
3
0
3
0
6
-
9
6
-
3
-
3
5
-
5
3
]
wherein said phase offset position is defined as x, where 0<=x<1.
11. A method for picture up-sampling from a lower resolution picture to a higher resolution picture said method comprising:
a) determining a lower resolution picture location corresponding to a sample position in said higher resolution picture;
b) determining a phase offset position for said lower resolution picture location, wherein said phase offset position denotes the position of said lower resolution picture location relative to said sample position in said higher resolution picture;
c) selecting a first filter coefficient for a first interpolation filter;
d) selecting a second filter coefficient for a second interpolation filter;
e) selecting a third filter coefficient for a third interpolation filter;
f) selecting at least one weighting factor to control the relative influence of said first interpolation filter, said second interpolation filter and said third interpolation filter; and
g) calculating a picture value for said sample position using a weighted combination of said first interpolation filter, said second interpolation filter and said third interpolation filter, said weighted combination being controlled by said at least one weighting factor.
12. A method as described in claim 11 wherein one of said first interpolation filter, said second interpolation filter and said third interpolation filter is a 4-tap filter based on a 4-piece cubic spline.
13. A method as described in claim 11 wherein one of said first interpolation filter, said second interpolation filter and said third interpolation filter is a 4-tap FIR filter with tap values given by the following matrix equation
1
4
*
[
1
x
x
2
x
3
]
*
[
0
4
0
0
-
3
0
3
0
6
-
9
6
-
3
-
3
5
-
5
3
]
wherein said phase offset position is defined as x, where 0<=x<1.
14. A method as described in claim 11 wherein one of said first interpolation filter, said second interpolation filter and said third interpolation filter is a 4-tap filter with phase-related coefficients taken from the following table:
(4-tap) interpolation
filter coefficients
phase
e[−1]
e[0]
e[1]
e[2]
0
0
32
0
0
1/16
−1
32
2
−1
2/16
−2
31
4
−1
3/16
−3
30
6
−1
4/16
−3
28
8
−1
5/16
−4
26
11
−1
6/16
−4
24
14
−2
7/16
−3
22
16
−3
8/16
−3
19
19
−3
9/16
−3
16
22
−3
10/16
−2
14
24
−4
11/16
−1
11
26
−4
12/16
−1
8
28
−3
13/16
−1
6
30
−3
14/16
−1
4
31
−2
15/16
−1
2
32
−1.
15. A method as described in claim 11 wherein one of said first interpolation filter, said second interpolation filter and said third interpolation filter is a 4-tap filter with phase-related coefficients taken from the following table:
(4-tap) interpolation
filter coefficients
phase
e[−1]
e[0]
e[1]
e[2]
0
0
128
0
0
1/16
−5
127
7
−1
2/16
−9
124
15
−2
3/16
−12
119
24
−3
4/16
−14
113
34
−5
5/16
−14
105
44
−7
6/16
−14
96
55
−9
7/16
−13
86
65
−10
8/16
−12
76
76
−12
9/16
−10
65
86
−13
10/16
−9
55
96
−14
11/16
−7
44
105
−14
12/16
−5
34
113
−14
13/16
−3
24
119
−12
14/16
−2
15
124
−9
15/16
−1
7
127
−5.
16. A method as described in claim 11 wherein one of said first interpolation filter, said second interpolation filter and said third interpolation filter is a 6-tap filter with phase-related coefficients taken from the following table:
(6-tap) interpolation filter coefficients
phase
e[−2]
e[−1]
e[0]
e[1]
e[2]
e[3]
0
0
0
128
0
0
0
1/16
1
−6
127
7
−2
1
2/16
2
−10
124
15
−4
1
3/16
3
−13
119
24
−6
1
4/16
4
−16
113
34
−8
1
5/16
4
−17
105
45
−11
2
6/16
4
−17
97
56
−13
1
7/16
4
−17
87
66
−15
3
8/16
3
−16
77
77
−16
3
9/16
3
−15
66
87
−17
4
10/16
1
−13
56
97
−17
4
11/16
2
−11
45
105
−17
4
12/16
1
−8
34
113
−16
4
13/16
1
−6
24
119
−13
3
14/16
1
−4
15
124
−10
2
15/16
1
−2
7
127
−6
1.
17. A method as described in claim 11 wherein said first interpolation filter is a 4-tap filter based on a 4-piece cubic spline and said second interpolation filter is derived from the Catmull-Rom function.
18. A method as described in claim 11 wherein said first interpolation filter is a 4-tap filter based on a 4-piece cubic spline, said second interpolation filter is derived from the Catmull-Rom function and said third interpolation filter is a 6-tap filter based on a 6-piece cubic spline.
19. A method as described in claim 11 wherein said first interpolation filter is a 4-tap filter with phase-related coefficients taken from the Table I below:
TABLE I
(4-tap) interpolation
filter coefficients
phase
e[−1]
e[0]
e[1]
e[2]
0
0
32
0
0
1/16
−1
32
2
−1
2/16
−2
31
4
−1
3/16
−3
30
6
−1
4/16
−3
28
8
−1
5/16
−4
26
11
−1
6/16
−4
24
14
−2
7/16
−3
22
16
−3
8/16
−3
19
19
−3
9/16
−3
16
22
−3
10/16
−2
14
24
−4
11/16
−1
11
26
−4
12/16
−1
8
28
−3
13/16
−1
6
30
−3
14/16
−1
4
31
−2
15/16
−1
2
32
−1,
wherein said second interpolation filter is derived from the Catmull-Rom function and said third interpolation filter is a 6-tap filter with phase-related coefficients taken from the Table II below:
TABLE II
(6-tap) interpolation filter coefficients
phase
e[−2]
e[−1]
e[0]
e[1]
e[2]
e[3]
0
0
0
128
0
0
0
1/16
1
−6
127
7
−2
1
2/16
2
−10
124
15
−4
1
3/16
3
−13
119
24
−6
1
4/16
4
−16
113
34
−8
1
5/16
4
−17
105
45
−11
2
6/16
4
−17
97
56
−13
1
7/16
4
−17
87
66
−15
3
8/16
3
−16
77
77
−16
3
9/16
3
−15
66
87
−17
4
10/16
1
−13
56
97
−17
4
11/16
2
−11
45
105
−17
4
12/16
1
−8
34
113
−16
4
13/16
1
−6
24
119
−13
3
14/16
1
−4
15
124
−10
2
15/16
1
−2
7
127
−6
1.
20. A system for picture up-sampling from a lower resolution picture to a higher resolution picture said system comprising:
a position processor for determining a lower resolution picture location corresponding to a sample position in said higher resolution picture;
a phase calculator for determining a phase offset position for said lower resolution picture location, wherein said phase offset position denotes the position of said lower resolution picture location relative to said sample position in said higher resolution picture;
a first interpolation filter;
a second interpolation filter;
a first coefficient selector for selecting a first filter coefficient for said first interpolation filter based on said phase offset position;
a second coefficient selector selecting a second filter coefficient for said second interpolation filter;
a weighting factor calculator for selecting a weighting factor to control the relative influence of said first interpolation filter and said second interpolation filter; and
a filter application for calculating a picture value for said sample position using a weighted combination of said first interpolation filter and said second interpolation filter, said weighted combination being controlled by said weighting factor.