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Mapping without the sun
Zhang, Jixian

compression quality assessment. The method is a qualitative
one and the following is the principle procedures of it:
2.1 Establishing element set and grade factor set
To find different factors in describing image compression
quality and put forward factor set:
U = {w,,w 2 , w 3 ,•••, Uj,■••,«„}, y = l, 2,. ..,m (1)
In (1), u ■ represents the j th evaluation element and Uj can be
divided further. According to Chinese specification ‘Digital
surveying and mapping products check and quality assessment
(GB/T 18316-2001)’, four assessment grades can be determined:
excellent (V[), good (v 2 ), fair (v 3 ) and poor (v 4 ):
v = {vi, v 2 , v 3 , v 4 } (2)
For each u ., r tj represents the degree of membership on u , to
v, (i = 1,2,3,4):
r. =- (3)
In (3), fl represents the number of u . g v f , N the number of
R is denoted the fuzzy matrix of element U . on grade V f :
r n
r 2l
r n
r 4l
r \2
r 22
r 32
r 42
R =
r n
r 23
r 33
r 2m
r 3m
2.2 Establishing weight coefficient matrix
In fuzzy evaluation, every evaluation element has different
contribution to image quality. Thus, to determine the weight
coefficient matrix of evaluation element:
A = {a l ,a 2 ,a 3i ...,a J ,....,a m \,j = (5)
2.3 Establishing comprehensive evaluation matrix of
evaluation elements
Y=A-R={a i ,a 2 ,a } ,...ç j ,...ç n
'11 '21 '31 '41
'12 '22 '32 '42
'13 '23 '33 '43
l/im r 2n, r *n]
Y is a fuzzy vector which not only represents all evaluation
elements’ contribution, but also reserves all degree of
membership of every grade.
Subjective tests are tedious, time consuming and expensive, and
the results depend on various factors such as the observer’s
background, motivation, etc., and really actually only the
display quality is being assessed. Therefore an objective
measure that accurately predicts the subjective rating would be
a useful guide when optimizing image compression algorithms.
[Ismail Avcibas et al, 2002].
As to remote sensing image quality assessment, objective
assessment has two aspects: one is imaging quality, the other is
geometric quality.
3.1 Imaging quality assessment
Imaging quality is also named interpreting quality, referring to
image intelligibility and indentifiability. In recent years, there
have been efforts by worldwide scholars and experts to
establish an objective measurement of image quality. The most
common used indexes are based on mathematics, such as mean
squared error (MSE), peak signal to noise ratio (PSNR), root
mean squared error (RMSE), etc. A new trend in imaging
quality assessment is to use human vision system(HVS) in
predicting image quality, while this method has shown any
clear advantage over simple mathematical measures such as
RMSE and PSNR under strict testing conditions and different
image distortion environments [Zhou Wang et al, 2002b].
According to the contents of imaging quality assessment, it can
be divided into three aspects: first is image character analysis;
second is image comparison analysis; the last is application
3.1.1 Image character analysis
In order to compare original image and reconstructed ones, the
change of grey value is employed to analyze the effects of
compression on image characters. Principal indexes include
histogram, mean gray value, standard deviation, angular second
moment, contrast and entropy, etc. Their definition see table 1.
The definition of angular second moment, contrast and entropy
is based on GLCM (Gray-Level Co-occurrence Matrix),
denoted as p(i,j)- More information see [Jia Yonghong, 2003].
mean gray value
i M-\ N-\
m= W ZZ /('»j)
standard deviation
i M-Ï N-\
angular second moment
L-1 l-1 A 2
/1=11^ 0'J)
/=0 7=0
L-\ \ L-1 ¿-1 A ] .
/ 2 =Z« 2 LÏ>(U) ’
»-0 l<=0 j=0 J
ww A A
/3 = “Z X J) 1o 82 P(U j)
1=0 j=0
Table 1 Definition of mean gray value, standard deviation,
angular second moment, contrast and entropy
3.1.2 Image comparison analysis
In virtue of statistics, it is an important method to compare the
original image and the reconstructed ones in terms of the
numerical differences between their pixel values [Ferwerda, J.A.
et al, 2003]. This method belongs to image comparing analysis
and can be used to study the effects of lossy compression on
images with the increase of image compression ratio. Table 2
shows some useful image comparison analysis indexes.
/s=xz /(** Pso, j) /.1X1/ 0, j)] 2 . X Z k( f - -/)] 2 [
7=0 /=0 / [ V y-° 1=0 V j =0 »-° J
M-\N-l /M-l N-l
Z Z1/ (». J) - *(«. y)] 2 / Z Z1/ ( f . »] 2
y=0 ¡=0 / 7=0 /=0 J