Game Development Reference
In-Depth Information
2
μ
x
μ
y
+
C
1
l
(
X
,
Y
)
=
l
(μ
x
, μ
y
)
=
(11.1)
μ
x
+
μ
y
+
C
1
where the
μ
x
and
μ
y
represent the mean value of original and distorted images
given by
N
1
N
μ
x
=
x
i
(11.2)
i
=
1
and the constant
C
1
is included to avoid instability when the denominator is very
close to zero. The second contrast comparison
c
(
X
,
Y
)
is calculated by the standard
deviation as the signal contrast,
2
˃
x
˃
y
+
C
1
c
(
x
,
y
)
=
c
(˃
x
, ˃
y
)
=
(11.3)
x
+
˃
y
+
˃
C
1
where
1
N
2
1
2
N
˃
x
=
1
(
x
i
−
μ
x
)
(11.4)
−
1
i
=
Third, the signal is normalized by its standard deviation, satisfying that the two
signals have the identical deviation. Then the structure comparison
s
(
X
,
Y
)
can be
performed on the normalized signals as follows,
s
X
−
m
μ
x
˃
x
Y
−
m
μ
y
˃
y
C
3
˃
x
+
˃
y
+
˃
xy
+
s
(
X
,
Y
)
=
,
=
(11.5)
C
3
Finally, the overall SSIM index is obtained by combining the three components
as one,
)
]
ʱ
·[
)
]
ʲ
·[
)
]
ʳ
SSIM
(
X
,
Y
)
=[
l
(
X
,
Y
c
(
X
,
Y
s
(
X
,
Y
(11.6)
where
ʱ
,
ʲ
and
ʳ
are parameters controlling the relative importance of the three
parts. For simplicity,
ʱ
=
ʲ
=
ʳ
=
1 for most applications, and then the SSIM is
with a specific form as follows,
(
2
μ
x
μ
y
+
C
1
)(
2
˃
xy
+
C
2
)
SSIM
(
X
,
Y
)
=
(11.7)
x
+
μ
y
+
x
+
˃
y
+
(μ
C
1
)(˃
C
2
)
11.1.2.2 VSNR
The Visual Signal-to-Noise Ratio (VSNR) is another efficient metric based on the
wavelet domain. This scheme combines the ideas of both the near-threshold and
the suprathreshold models. In the first stage, contrast thresholds for detecting the
