Quality Assessment - 3DTV: Processing and Transmission of 3D Video Signals - page 180

of the error signal in each of the identified depth plane are evaluated. Error
signal, e i , refers to the difference of the pixel values between the processed
and the original depth planes. For depth plane i the standard deviation of
error can be identified as:

⎡ ⎤

1
2

e j − μ

e

N

1
N

⎣ ⎦

i
e

i

σ =

(6.18)

j = 1

where, e i

e is the mean value of the error signal for plane i .
Summation of the standard deviation of the error for all the depth planes
defines M 2 :

x i y i

= − and μ

n

e

M 2 =

1 σ

(6.19)

i =

CalculatingM 3 : StructuralComparison
Third, to evaluate M 3 after removing the mean intensity from the signals X
and Y they are normalized by its own standard deviation, thus the two signals
being compared have unit standard deviation. As a result, measurement
techniques M 1 , M 2 ,and M 3 are statistically independent of each other. The
structure comparison is conducted on these normalized signals

( X − μ x )

σ x

and

− μ y )
σ y . Note that the correlation between the above unit vectors is equivalent
to the correlation coefficient between X and Y. In image processing, the
covariance between these signals is considered as a simple but effective
measure to quantify the structural similarity. Structural comparison measure
in SSIM is utilized for this purpose [4]. Structural comparison is evaluated on
the entire depth image (i.e. image containing all depth planes). Each image
frame is divided into 16

( Y

16 macroblocks and the structural comparison
(SC) is computed on macroblock basis. Structural comparison is defined as
follows:

×

k 1
σ x · σ y +

σ xy +

SC = (6.20)

k 1

σ xy represent the standard deviations and covariance of signals
X and Y . A small constant is introduced to both numerator and denominator
to avoid instability when

σ x , σ y and

σ x .σ y is very close to zero.

l ) 2

k 1 = ( c · (6.21)

is chosen where c is the dynamic range of the pixel values (255 for 8-
bit greyscale representation) and l as 0.001. σ xy in Equation (6.20) can be

estimated as:

L

1
L

σ xy = ( x j − μ x )( y j − μ y ) (6.22)

j = 1