Game Development Reference
In-Depth Information
goal of them is to describe the degree of similarity of two visual signals. In digital
image processing, the simplest way to quantify the suprathreshold distortion is the
mean square error (MSE),
N
1
N
2
MSE
=
1
(
x
i
−
y
i
)
(12.4)
i
=
where
N
indicates the total number of pixels, and
x
i
,
y
i
denote the pixel values for
the original and distorted frames. The definition of MSE can also be generalized with
the
l
p
form as follows:
p
1
/
p
N
E
p
=
1
|
x
i
−
yi
|
.
(12.5)
i
=
The clear physical meaning and attractive features ofMSEmakes it widely applied
in measuring the distance between two signals (Wang and Bovik
2006
). For example,
the energy of the error signal computed by MSE can be preserved after unitary
transforms such as the Fourier transform. Moreover, MSE can be easily applied to
optimization task, as its gradient is easy to be computed and the closed-form of
solutions can be derived. However, MSE has also been widely criticized due to its
poor correlation with the visual quality perceived by HVS. One typical example is
shown in Fig.
12.1
, in which the images are subject to different types of distortions.
Specifically, the image in (c) has the highest PSNR, yet lowest perceptual quality. Due
to their different distortion types, the perceived quality cannot be reflected by pixel
level square error. The main reason lies in that MSE cannot reflect the mechanism
of HVS, as the visual distortion in the primary visual cortex is not computed at pixel
level. It is also widely believed that a perfect quality measure should be dependent
on the signal self, since the visual information is not uniformly distributed in the
spatial domain. By contrast, MSE is additive for independent signal sources.
After realizing that MSE is not a perfect measure when dealing with perceptually
important signals, many alternatives of MSE have been developed. The initial idea
of perceptual quality assessment is to simulate the visual system by decomposing
(a)
(b)
(c)
Fig. 12.1
Lena
image undergone various degradations and the corresponding PSNR.
a
PSNR
=
20
.
33,
b
PSNR
=
18
.
12,
c
PSNR
=
30
.
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