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) 
J N 
In (3), fl represents the number of u . g v f , N the number of 
samples. 
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 
^43 
flm 
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 
(6) 
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. 
3. OBJECTIVE ASSESSMENT 
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 
analysis. 
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), 
A 
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-\ 
^•iiTTT^ZZ 
angular second moment 
L-1 l-1 A 2 
/1=11^ 0'J) 
/=0 7=0 
contrast 
L-\ \ L-1 ¿-1 A ] . 
/ 2 =Z« 2 LÏ>(U) ’ 
»-0 l<=0 j=0 J 
entropy 
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. 
image 
similarity 
/s=xz /(** Pso, j) /.1X1/ 0, j)] 2 . X Z k( f - -/)] 2 [ 
7=0 /=0 / [ V y-° 1=0 V j =0 »-° J 
image 
fidelity 
II 
1 
M-\N-l /M-l N-l 
Z Z1/ (». J) - *(«. y)] 2 / Z Z1/ ( f . »] 2 
y=0 ¡=0 / 7=0 /=0 J