Filters for motion compensation interpolation with reference down-sampling
The present disclosure provides systems and methods for processing video content using motion compensation interpolation. The methods include: in response to a target picture and a reference picture having different resolutions, applying a band-pass filter to the reference picture, to perform a motion compensated interpolation with reference down-sampling to generate a reference block; and encoding or decoding a block of the target picture using the reference block.
1. A computer-implemented method for processing video content, comprising:
encoding or decoding a picture block by applying a first filter to a reference picture,
wherein the applying of the first filter performs both motion-compensation interpolation and downsampling of the reference picture, and
wherein the first filter is a band-pass filter having a plurality of integer coefficients derived from a cosine windowed-sinc function, a sum of the plurality of integer coefficients being equal to a power of 2.
2. The method according to claim 1 , wherein the cosine windowed-sinc function is
f
(
n
)
=
f
c
r
Sin
c
(
f
c
r
n
)
cos
(
π
n
L
-
1
)
,
wherein
n
=
-
L
-
1
2
,
.
.
.
,
L
-
1
2
,
wherein f c is a cutoff frequency of the cosine windowed-sinc function, L is a kernel length, and r is a downsampling ratio.
3. The method according to claim 1 , wherein the plurality of integer coefficients is derived from the cosine windowed-sinc function by:
calculating a plurality of values based on the cosine windowed-sinc function; and
rounding the plurality of values to a plurality of integers, respectively.
4. The method according to claim 3 , wherein the rounding of the plurality of values:
causes a sum of the rounded plurality of integers to be equal to a power of 2; and
minimizes or maximizes a cost function associated with the first filter.
5. The method according to claim 4 , wherein the cost function is a sum of absolution difference (SAD) or a sum of squared error (SSE) between:
the rounded plurality of integers, and
the plurality of values, respectively.
6. The method according to claim 4 , wherein the cost function is a sum of absolution difference (SAD) or a sum of squared error (SSE) between:
frequency responses of the rounded plurality of integers, and
frequency responses of a plurality of reference coefficients, respectively.
7. The method according to claim 6 , wherein the plurality of reference coefficients comprises:
the plurality of values calculated based on the cosine windowed-sinc function, or
a plurality of coefficients of a second filter.
8. The method according to claim 7 , wherein the second filter has more taps than taps of the first filter.
9. The method according to claim 1 , wherein the first filter is an 8-tap filter with 16 phases, the plurality of integer coefficients comprising:
Interger coeffeiecnts
Phase p
p0
p1
p2
p3
p4
p5
p6
p7
0
−4
2
20
28
20
2
−4
0
1
−4
0
19
29
21
5
−4
−2
2
−4
−1
18
29
22
6
−4
−2
3
−4
−1
16
29
23
7
−4
−2
4
−4
−1
16
28
24
7
−4
−2
5
−4
−1
14
28
25
8
−4
−2
6
−3
−3
14
27
26
9
−3
−3
7
−3
−1
12
28
25
10
−4
−3
8
−3
−3
11
27
27
11
−3
−3
9
−3
−4
10
25
28
12
−1
−3
10
−3
−3
9
26
27
14
−3
−3
11
−2
−4
8
25
28
14
−1
−4
12
−2
−4
7
24
28
16
−1
−4
13
−2
−4
7
23
29
16
−1
−4
14
−2
−4
6
22
29
18
−1
−4
15
−2
−4
5
21
29
19
0
−4.
10. The method according to claim 1 , wherein the first filter is a 4-tap filter with 32 phases, the plurality of integer coefficients comprising:
Interger coeffeiecnts
Phase p
p0
p1
p2
p3
0
17
30
17
0
1
17
30
18
−1
2
16
30
18
0
3
16
30
18
0
4
15
30
18
1
5
14
30
18
2
6
13
29
19
3
7
13
29
19
3
8
12
29
20
3
9
11
28
21
4
10
10
28
22
4
11
10
27
22
5
12
9
27
23
5
13
9
26
24
5
14
8
26
24
6
15
7
26
25
6
16
7
25
25
7
17
6
25
26
7
18
6
24
26
8
19
5
24
26
9
20
5
23
27
9
21
5
22
27
10
22
4
22
28
10
23
4
21
28
11
24
3
20
29
12
25
3
19
29
13
26
3
19
29
13
27
2
18
30
14
28
1
18
30
15
29
0
18
30
16
30
0
18
30
16
31
−1
18
30
17.
11. A system for processing video content, comprising:
a memory for storing a set of instructions; and
at least one processor configured to execute the set of instructions to cause the system to perform:
encoding or decoding a picture block by applying a first filter to a reference picture,
wherein the applying of the first filter performs both motion-compensation interpolation and downsampling of the reference picture, and
wherein the first filter is a band-pass filter having a plurality of integer coefficients derived from a cosine windowed-sinc function, a sum of the plurality of integer coefficients being equal to a power of 2.
12. The system according to claim 11 , wherein the at least one processor is configured to execute the set of instructions to cause the system to derive the plurality of integer coefficients from the cosine windowed-sinc function by:
calculating a plurality of values based on the cosine windowed-sinc function; and
rounding the plurality of values to a plurality of integers, respectively.
13. The system according to claim 12 , wherein the rounding of the plurality of values:
causes a sum of the rounded plurality of integers to be equal to a power of 2; and
minimizes or maximizes a cost function associated with the first filter.
14. The system according to claim 13 , wherein the cost function is a sum of absolution difference (SAD) or a sum of squared error (SSE) between:
the rounded plurality of integers, and
the plurality of values, respectively.
15. The system according to claim 13 , wherein the cost function is a sum of absolution difference (SAD) or a sum of squared error (SSE) between:
frequency responses of the rounded plurality of integers, and
frequency responses of a plurality of reference coefficients, respectively.
16. The system according to claim 15 , wherein the plurality of reference coefficients comprises:
the plurality of values calculated based on the cosine windowed-sinc function, or
a plurality of coefficients of a second filter.
17. The system according to claim 11 , wherein the first filter is an 8-tap filter with 16 phases, the plurality of integer coefficients comprising:
Interger coeffeiecnts
Phase p
p0
p1
p2
p3
p4
p5
p6
p7
0
−4
2
20
28
20
2
−4
0
1
−4
0
19
29
21
5
−4
−2
2
−4
−1
18
29
22
6
−4
−2
3
−4
−1
16
29
23
7
−4
−2
4
−4
−1
16
28
24
7
−4
−2
5
−4
−1
14
28
25
8
−4
−2
6
−3
−3
14
27
26
9
−3
−3
7
−3
−1
12
28
25
10
−4
−3
8
−3
−3
11
27
27
11
−3
−3
9
−3
−4
10
25
28
12
−1
−3
10
−3
−3
9
26
27
14
−3
−3
11
−2
−4
8
25
28
14
−1
−4
12
−2
−4
7
24
28
16
−1
−4
13
−2
−4
7
23
29
16
−1
−4
14
−2
−4
6
22
29
18
−1
−4
15
−2
−4
5
21
29
19
0
−4.
18. The system according to claim 11 , wherein the first filter is a 4-tap filter with 32 phases, the plurality of integer coefficients comprises:
Interger coeffeiecnts
Phase p
p0
p1
p2
p3
0
17
30
17
0
1
17
30
18
−1
2
16
30
18
0
3
16
30
18
0
4
15
30
18
1
5
14
30
18
2
6
13
29
19
3
7
13
29
19
3
8
12
29
20
3
9
11
28
21
4
10
10
28
22
4
11
10
27
22
5
12
9
27
23
5
13
9
26
24
5
14
8
26
24
6
15
7
26
25
6
16
7
25
25
7
17
6
25
26
7
18
6
24
26
8
19
5
24
26
9
20
5
23
27
9
21
5
22
27
10
22
4
22
28
10
23
4
21
28
11
24
3
20
29
12
25
3
19
29
13
26
3
19
29
13
27
2
18
30
14
28
1
18
30
15
29
0
18
30
16
30
0
18
30
16
31
−1
18
30
17.
19. A non-transitory computer readable medium storing a bitstream of a video for processing according to a method comprising:
encoding or decoding a picture block by applying a first filter to a reference picture,
wherein the applying of the first filter performs both motion-compensation interpolation and downsampling of the reference picture, and
wherein the first filter is a band-pass filter having a plurality of integer coefficients derived from a cosine windowed-sinc function, a sum of the plurality of integer coefficients being equal to a power of 2.
20. The non-transitory computer readable medium according to claim 19 , wherein the first filter is an 8-tap filter with 16 phases, the plurality of integer coefficients comprising:
Integer coefficients
Phase p
p0
p1
p2
p3
p4
p5
p6
p7
0
−4
2
20
28
20
2
−4
0
1
−4
0
19
29
21
5
−4
−2
2
−4
−1
18
29
22
6
−4
−2
3
−4
−1
16
29
23
7
−4
−2
4
−4
−1
16
28
24
7
−4
−2
5
−4
−1
14
28
25
8
−4
−2
6
−3
−3
14
27
26
9
−3
−3
7
−3
−1
12
28
25
10
−4
−3
8
−3
−3
11
27
27
11
−3
−3
9
−3
−4
10
25
28
12
−1
−3
10
−3
−3
9
26
27
14
−3
−3
11
−2
−4
8
25
28
14
−1
−4
12
−2
−4
7
24
28
16
−1
−4
13
−2
−4
7
23
29
16
−1
−4
14
−2
−4
6
22
29
18
−1
−4
15
−2
−4
5
21
29
19
0
−4
21. The non-transitory computer readable medium according to claim 19 , wherein the first filter is a 4-tap filter with 32 phases, the plurality of integer coefficients comprising:
Integer coefficients
Phase p
p0
p1
p2
p3
0
17
30
17
0
1
17
30
18
−1
2
16
30
18
0
3
16
30
18
0
4
15
30
18
1
5
14
30
18
2
6
13
29
19
3
7
13
29
19
3
8
12
29
20
3
9
11
28
21
4
10
10
28
22
4
11
10
27
22
5
12
9
27
23
5
13
9
26
24
5
14
8
26
24
6
15
7
26
25
6
16
7
25
25
7
17
6
25
26
7
18
6
24
26
8
19
5
24
26
9
20
5
23
27
9
21
5
22
27
10
22
4
22
28
10
23
4
21
28
11
24
3
20
29
12
25
3
19
29
13
26
3
19
29
13
27
2
18
30
14
28
1
18
30
15
29
0
18
30
16
30
0
18
30
16
31
−1
18
30
17