Game Development Reference
In-Depth Information
×
32,
and logical transform (LOT) is utilized as one dimension of residual blocks is larger
than 32, e.g., 64
For the consideration of complexity, the largest transform size is up to 32
64. That is, LOT is applied when the maximum
physical transformsize is quarter size of the residual block. More specifically, in LOT,
for a 64
×
64, 64
×
16, or 16
×
64 residual block, a 2-D 5-3 integer wavelet transform is firstly performed,
then for the 32
×
32 LL-band signal, a normal DCT is applied. For simplicity, we
use one dimensional wavelet transform as an example. Assuming the input vector is
X
×
, the output X [
[
64
]
32
]
is computed as
X [2 i
2]
+
2 X [2 i
1]
+
6 X [2 i ]
+
2 X [2 i
+
1]
X [2 i
+
2]
+
4
,
i
=
1
,...,
30
8
X [ i ]
2 X [2]
+
4 X [1]
+
6 X [0]
+
4
=
.
,
i
=
0
8
X [60]
+
2 X [61]
+
5 X [62]
+
2 X [63]
+
4
,
i
=
31
8
(5.14)
With LOT, the transform process is roughly equivalent to only derive the 32
×
32
low-frequency component of an 64
×
64 DCT, but the complexity is lower than a
full 64
64 DCT definately. The LOT transform design works efficiently for the
smooth picture regions which typically cover the majority regions in high resolution
video. The LOT is beneficial for smooth regions, and large transforms are typically
preferred in terms of coding efficiency.
For non-square intraprediction (e.g. 32
×
16), or the
second level transform of asymmetric interprediction, non-square transform is used.
For one M 1 ×
×
8
/
8
×
32, or 16
×
4
/
4
×
M 2 non-square prediction residual matrix X , the transform can be
expressed as:
T M 2 .
Y
=
T M 1 ×
X
×
(5.15)
The transforms applied in AVS2 keep the 16-bit arithmetic by introducing two
shifting operations after the horizontal and vertical transform. More specifically, for
vertical transform, the following is applied:
Y 1 = (
T N ×
X
+ (
1
<< (
s 1
1
))) >>
s 1 ,
(5.16)
where X represents the input residual block, T N represents the N
×
N transform
matrix, s 1
11 indicates the number of bits to be shifted after the
vertical transform, and n specifies the bit-depth of prediction residual. For horizontal
transform, the following is applied:
=
n
+
log 2 N
T N
Y 2 = (
X
×
+ (
1
<< (
s 2
1
))) >>
s 2 ,
(5.17)
 
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