The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
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registered strictly at the same scale. We fused the images with 
different methods including PCA and astrous. These images were 
used to be compared with the image fused by PCA+astrous. 
4.2 Visual and Quantitative Evaluation 
4.2.1 Visual Evaluation: First the fused images were 
evaluated visually. It is clearly seen from the pictures in Figure 2 
that the spatial resolutions and the spectral resolutions of the 
images after the fusion are improved, in comparison to the original 
images. The spectral information in the original panchromatic 
image has increased, and the structural information in the original 
multispectral images has also been enriched. Hence, the fused 
images contain both the structural details of the higher spatial 
resolution panchromatic image and the rich spectral information 
from the multispectral images. In the original QuickBird images, it 
is very difficult to discern some physical features like small 
buildings. 
But, the colors of the features in the fused images are changed. 
This color distortion effect is the largest in PCA method. We find 
that (c) fully conserve spatial information of high-resolution image, 
but evident spectral distortion exist. Among these three methods, 
astrous transformation gives the best result in terms of color 
conservation. The spectral characteristics of (d) are closest to the 
original multi-spectral image than other fused images, and the 
spectral characteristic of (d) is similar to (b). 
However, the result obtained from PCA+astrous wavelet 
transform approach is superior to those two results, as the colors 
of the features in original multispectral images are nearly the same 
with the fusion image just based on the astrous wavlet. 
The mean gradient (M.G.) reflects the contrast between the 
details variation of pattern on the image and the clarity of the 
image. And the correlation coefficient (C.C.) between the 
original and fused image shows the similarity in small size 
structures between the original and synthetic images. The 
higher the value, the more similar the fused image to the 
corresponding original image, which in turn indicates a good 
spectral information retain in the fused results. Results in 
Table shows that the astrous wavelet transform approach and 
the PCA+astrous keeps over 90% of the spectral content of 
all original multispectral bands, the result of the astrous is the 
best and the PCA+astrous-based image fusion is only slightly 
lower. 
But the mean gradient of the PCA+astrous-based image 
fusion method is greater than those of the astrous wavelet 
based image fusion method, since the details have been 
enhanced in fusion process, roads, bridges, airports, rivers 
and other objects are distinguished more easily. As previously 
stated, if the object of image fusion is to construct synthetic 
images which are closer to the reality they represent, then the 
PCA+astrous-based image fusion method meet this objective 
very well. This is one of the main advantages of using the 
PCA+astrous transform for image fusion. 
In a word, though there is a slight spectral distortion in the 
fused image based on PCA+astrous wavelet transform, its 
spatial resolution and details texture have been enhanced 
remarkably. This demonstrates that the fusion method based 
on PCA+astrous wavelet transform is better than the fusion 
method just based on asttrous wavelet transform or PCA 
transform. 
But the PCA+astrous wavelet gives a better spatial resolution 
when compared to the results from other fusion methods. So in 
this paper, compared with the fused result just from astrous wavlet 
or the PCA alone, the fused result obtained from the PCA+astrous 
wavelet transform has a better visual effect in Quickbird image 
fusion in Figure 2. 
All the above analysis suggests that the wavelet based fusion 
approach provides overall the best results in the methods used 
in our study. Based on the experimental results obtained from 
this study, the PCA+astrous-based image fusion method is 
very efficient for fusing Quickbird images. This new method 
has reached an optimum fusion result. 
4.2.2 Quantitative Evaluation 
In general, a good fusion approach should retain the maximum 
spatial and spectral information from the original images and 
should not damage the internal relationship among the original 
bands. So secondly we evaluate the performance of the fusion 
method based on PCA+astrous wavelet transform using image 
quality indexes. Based on these criteria, the indexes we selected 
are average value, standard difference, entropy, average grads, 
fractal dimensions and correlation coefficients. Average value can 
show the distribution of the image grayscale in the rough. 
Standard difference and entropy can measure the information 
abundance in the image. Average grads shows exiguous contrast, 
varied texture characteristic and definition of the image. 
Table 1 presents a comparison of the experimental results of 
image fusion using the PCA image fusion method, the astrous 
wavelet-based image fusion method, and PCA+astrous method in 
terms of combination entropy, the average gradient and the 
correlation coefficient^. 
The combination entropy (C.E.) represents the property of 
combination between images. The larger the combination entropy 
of an image, the richer the information contained in the image. In 
Table 1, the combination entropy of the PCA+astrous-based image 
fusion is greater than those of other methods. Thus, the 
PCA+astrous-based image fusion method is better than the astrous 
wavelet and PCA methods in terms of combination entropy. 
Method 
C.E 
M.G 
C.C 
Original images 
' (band 1> band2, 
band3, band4) 
Image fused by 
4.80364 
4.91436 
5.01511 
6.37158 
7.16106 
5.9237 
6.2839 
6.6029 
7.7767 
17.3162 
0.62786 
PCA 
7.17243 
17.2208 
0.62657 
(band K band2^ 
7.21094 
17.6439 
0.62712 
band3^ band4) 
7.19666 
18.3797 
0.6512 
Image fused by 
7.11928 
15.8315 
0.94334 
astrous 
7.22269 
16.2062 
0.94166 
(band K band2^ 
7.25106 
16.3050 
0.94431 
band3N band4) 
7.16074 
17.0117 
0.89956 
Image fused by 
7.12787 
19.8423 
0.90557 
PCA+astrous 
7.36655 
20.9268 
0.90967 
(band K band2> 
7.36208 
20.8359 
0.91660 
band3^ band4) 
7.29436 
21.4049 
0.86847 
Table. 1. Information statistics of Quickbird image