Game Development Reference
In-Depth Information
Fig. 7.10
Adaptive loop
filter shape
Rc
=
V
,
(7.25)
⊡
⊣
ʩ
t
r
p
0
t
r
p
0
ʩ
t
r
p
1
t
r
p
0
ʩ
t
r
p
N
−
1
t
r
p
0
⊤
⊦
+
+
+
+
···
+
+
ʩ
t
r
+
p
0
t
r
+
p
1
ʩ
t
r
+
p
1
t
r
+
p
1
ʩ
t
r
+
p
N
−
1
t
r
+
p
1
···
R
=
,
.
.
.
.
.
.
ʩ
t
r
p
0
t
r
p
N
−
1
ʩ
t
r
p
1
t
r
p
N
−
1
ʩ
t
r
p
N
−
1
t
r
p
N
−
1
+
+
+
+
···
+
+
(7.26)
s
[
r
]
t
r
p
0
⊡
⊤
+
⊣
⊦
ʩ
s
[
r
]
t
r
p
1
+
ʩ
V
=
.
(7.27)
.
s
[
r
]
t
r
p
N
−
1
+
ʩ
Here
R
is the auto-correlation matrix of the to-be-filtered pixels, and
V
is cross-
correlation vector of the to-be-filtered pixels and the original ones, respectively.
Gaussian elimination algorithm can be applied to solve Eq. (
7.25
) for the optimal
filter coefficients. In order to efficiently coding these coefficients, the solved floating-
point coefficients fromwiener-Hopf are limited into a given precision. The noncenter
filter coefficients are limited within [
1, 1] and the center filter coefficient is limited
within [0, 2]. The precision of filter coefficients in the fractional part is limited within
6 bits. Then, the derived filter coefficients shall be quantized into integer value with
this precision. Based on the fact that the sum of coefficients approaches one and the
center coefficient usually much larger than noncenter coefficients, differential coding
method is applied to center coefficient and its prediction is that in Eq. (
7.28
).
−
N
−
2
f
p
[
N
−
1
]=
(
1
<<
NUM_SHIFT_BIT
)
−
2
×
f
[
j
]
.
(7.28)
j
=
0
Here
NUM_SHIFT_BIT
is related with the precision of the coefficients.
