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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
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using SWT, the original image is transformed into four pieces 
which can be labeled as ZZ , LH , HL and HH . The ZZ piece 
is the low-band or called approximated component, the 
remaining pieces LH , HL and HH are high-bands or called 
detail components. All of the components have the same size as 
the original image due to shift-invariant character. 
In the wavelet domains of the two transformed images, 
low-bands coefficients are integrated using the weighted 
average, the fusion equation is as below: 
LL(x,y) =a *LL\(x,y) + b *LL2(x,y) (16) 
3. OUR PROPOSED FUSION ALGORITHM 
An important preprocessing step in image fusion is image 
registration. It ensures that the information from each of the 
images refers to the same physical structure in the environment. 
In this paper, we assume that images to be combined have 
already been co-registered. The proposed multifocus image 
fusion algorithm is composed of computing SML for each 
focus image, SWT decomposition, image fusion and inverse 
SWT. 
where LL represents the new low-band coefficient after 
fusion, a and b denote weighted coefficients, their 
summation is always 1. 
The high-bands coefficients are first integrated using 
choose-max as follows: 
J HH 1(jc, y) HH l(x, y) > HH2(x, y) 
[HH2(x,y) HHl(x,y) < HH2(x,y) 
(17) 
Firstly, we choose SML as focus measure to compute the 
clarity of each focus image. With the SML, we can get two 
initial binary decision maps by setting two thresholds to the 
SML difference between two focus images, which can be 
represented with the following equations: 
Map\{x, y) 
SML\(x, y) - SML2(x, y) > T1 
SML\{x, y) - SML2(x, y) < 7T 
(14) 
Map2(x, y) 
SML\(x,y) - SML2{x,y) < T2 
SML\(x,y) - SML2(x,y) > T2 
(15) 
Then the two SML decision maps are used to refine the fusion 
rule. 
HH(x,y) = < 
HH\(x,y) 
HH2{x,y) 
HH(x,y) 
A/apl(x,y) = 1 
AZap2(x, y) = 1 
others 
(18) 
The similar fusion rules are performed on LH and HL 
high-bands in each decomposition level. 
At last, the fused image will be obtained by reconstructed with 
the fused approximate coefficients and detailed coefficients. 
where Map1 and Map2 denote two decision maps. SML\ 
and SML2 represent the SML values of two focused 
images respectively. 71 and T2 are two thresholds. 
Secondly, two focus images are decomposed into multiscale 
coefficients with SWT respectively. Due to the decomposition 
The proposed approach is implemented in personal computers 
with MATLAB 6.5 programs under Microsoft Windows XP 
environment. 
4. EXPERIMENTAL RESULT AND EVALUATION 
To illustrate the performance of the proposed method, two 
groups of different focus but co-registered images are taken as 
examples in this paper. In order to compare fusion effect, 
discrete wavelet fusion method is performed as reference. 
computed to evaluation image quality quantitatively (Wang et 
al.,2002). The bigger of the average gradient, the more 
The wavelet function sym4 is adopted and the input images are 
decomposed to 2 levels in this paper. The thresholds 71 and 
T2 are set to 0.2 and -0.2 respectively. Both low-band 
weighted coefficients a and b are equal to 0.5. The 
simulation experiment results are shown as Figure 1 and Figure 
2. 
It is difficult to evaluation the quality of a fusion image (Wald 
et al., 1997). Generally, the visual perception and quantitative 
analysis are used to compare image quality. From the visual 
perception, it is obvious form Figure 1 and Figure 2 that the 
proposed method has reserved more detail information than the 
wavelet transform method. The average gradient of image is 
clear-cut of the image is. The equation of the average gradient 
is as follows, 
J M-\ N-1 
If 
09) 
2 ax. dyj