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1. All approaches 
.SURES 
always unknown, 
signing objective 
; would produce is 
a very difficult task but such metrics are highly desired. Among 
the limited number of methods that have been proposed in the 
literature for image fusion quality assessment without an ideal 
image, most of them are not very suitable [15, 16]. Some 
researchers assess the results by using subjective tests [17]. 
However, although subjective tests can sometimes be accurate 
if performed correctly, they are inconvenient, expensive, and 
time consuming. Further, it is impossible to use them to 
continually adjust system parameters in a real time manner. 
There are a few objective metrics which do not require the 
availability of an ideal image in the literature. 
In the article, we present representational and some new 
quality metrics for the experiments. Some useful conclusion can 
draw out through comparing. One type of metrics is Standard 
Deviation (SD), Entropy (EN); the other type is cross entropy 
(CE), mutual information (MI), and universal index (UI) [18], 
which utilizes the features of both the fused and source. 
3.1 A Standard Deviation (SD) 
As we know, SD can provide some contrast information. For 
a fused image of size N X M, its standard deviation can be 
estimated by 
SD = 
N M 
/=1 jm 1 
where C(i, j) is the (i, j)th pixel intensity value and lfl is the 
sample mean of all pixel values of the image. It is known that 
SD is composed of two parts, the signal part and the noise part. 
This measurement will be more efficient in the absence of noise. 
3.2 Entropy (EN) 
l FA (/»«)= 
PFA(f> a ) 
P F (f)P A ( a ) 
1 F B (f’ b )= Y.Pfb(/¿) log 2 
f,b 
p FB (f’ b ) 
PÁf)PÁ b ) 
Performance is measured by the value of 
Mlf = l FA (f, a) + \ FB (f ,b) 
3.5 Universal Index (UI) 
Based on the SSIM measure [20] gives an indication of how 
much of the salient information contained in each of the input 
images has been transferred into the fused image. First calculate 
SSIM (a, /|w) and SSIM (b, /|w) which are the structural 
similarity measures between the input images and the fused 
image in a local window w. Then a normalized local weight A. 
(w) indicate the relative importance of the source images. The 
index is calculated by the function 
UI = ~X( k (oASSIM(a,f\ m ) 
\W\ aeW 
+ (\-X((ù))SSIM(b,f\(ù)) 
where SSIM is the structural similarity measure of two 
2 
sequences, let fl x , G x ,and O xy be the mean of x, the 
variance of x, and the covariance of x and y, respectively. Then 
SSIM compute as 
CT 
SSIM = —2L 
G y ct 
2 M x M y 2a x a y 
2 2 2 2 
Mx + My CT x + a y 
An index to evaluate the information quantity contained in an 
image. Entropy has often been used to measure the information 
content of an image. Entropy is define as 
L-1 
£ = -Xft l0 §2 Pi 
/=0 
where L is the total of grey levels, p-{po, Pi, Pi-i} is the 
probability distribution of each level. 
3.3 Cross Entropy (CE) 
The source images A, B and fused image F, the cross entropy 
is defined as (p A is p for image A) 
CE= CE(A, F) + CE(B, F) 
2 
where CE(A, F)(CE(B, F)) is the cross entropy of the source 
image A(B) and fused image F 
CE(A,F)= f>,(/)log 2 £ig 
i=0 P F (l) 
CE(B,F)= f> s (/)log 2 MJ 
,=o P F ( 0 
3.4 Mutual Information (MI) 
A higher value of the index indicates that the fused image 
contains fairly good quantity of information in both images. 
Define the joint histogram of source image A (B) and the fused 
image F as P FA (f, a) (P FB (f, b)). The mutual information 
between source image and the fused image is [19] 
4. EXPERIMENTS AND ANALYZING 
We applied the above methodologies and assessment system 
to fuse SAR and SPOT panchromatic images which has 5m 
pixels (Figure 1). The experiments compared the different 
alternatives for each procedure of the generic fusion framework 
described in Figure 2. It is worth noticing AMO in method (b) 
to search the Pareto optimal weights of the coefficients and 
compared the results with popular method (a) in figure 2. The 
abbreviations used in the paper are described in table l.The 
performance of method (WA-WBA+NG+AMO+RBV) using 
different decomposition levels are shown in the table 2. In the 
table 2, the first column shows the combinations of alternatives 
in figure 2 for the procedures, and the second column lists the 
different alternatives MSD for the current procedure. Columns 
3-7 show the performance using the criteria we introduced in 
Section 3. 
(a) SAR (b) SPOT 
Figure 1. Source images