The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
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wc L 
L . 1,2,...., n 
So if we decompose an image / into wavelet coefficients, then we 
can write: 
1 = £ w c, + v 
i=i 
where I r is a residual image. 
In this approach all wavelet planes have the same number of 
pixels as the original image. There are two approaches for image 
fusion based on wavelet decomposition: 1) substitution method 
which replaces some wavelet coefficients of the multispectral 
image by the corresponding coefficients of the high resolution 
image and 2) additive method which adds high-resolution 
coefficients to the multispectral data. The first method of the 
wavelet decomposition in combination with the PCA method we 
applied to merge multispecral image and panchromatic image in 
this study. But the result showed that the PCA transformation and 
additive wavelet transformation has their own advantages and 
disadvantages more serious distortion of spectral 
characteristics in the PCA (Principal Component Analysis) 
transformation while better in preserving spectral information and 
lack of spatial in the atrous wavelet transformation. So, we 
developed a new technique, based on additive wavelet 
decomposition and PCA transformation, for the merging and data 
fusion of such images. 
3 IMAGE FUSION ALGORITHM 
1.1 Preprocessing of input images 
In image fusion, the first step is to prepare the input images for the 
fusion process. This includes registration and resampling of the 
input images (Zhou, 1998). Registration is to align corresponding 
pixels in the input images. This is usually done by geo-referencing 
the images to a map projection such as UTM (Universal 
Transverse Mercator). If the images are from the same sensors and 
taken at the same time, they are usually already co-registered and 
can be directly used for fusion processing. However, if the images 
are from different sensors, and even if they are georeferenced by 
the image vendors, a registration process is likely still necessary to 
ensure that pixels in the input images exactly represent the same 
location on the ground. 
Image registration can be performed with or without ground 
control. The most accurate way is to rectify the images using 
ground control points. However, in most cases, it is not possible to 
find ground control points in the input images. In such situations, 
taking the panchromatic image, which has a better spatial 
resolution, as the reference image and registering the multispectral 
images with respect to the panchromatic one can be a good 
solution to refine the rectified multispectral images. 
Then we got the new principle components from the new 
multispecral image, with most image information contained 
in the first component of the fusion image. Finally, the atrous 
wavelet transformation was applied to merge the 
multispectral image with the first component generated from 
the PCA transformation to substitute the original high-spatial 
resolution panchromatic band. 
In the substitution method the wavelet coefficients of 
multispectral image were discarded and substituted by the 
wavelet coefficients of the new first component of the PCA 
fusion image. 
Figure. 1. Flowing chart of image fusion based on the 
PCA+astrous method 
1.3 Test Data 
Now we give the specific operational procedure for the 
proposed PCA+atrous image fusion approach. The 
operational procedure is a generic one, although Quickbird 
images were taken as an example in order to illustrate the 
method. First, multispectral QuickBird images (ground 
resolution was 2.8 meters) over the pyramids are fused with 
the QuickBird panchromatic image (ground resolution was 
0.7 meters), they were both acquired in 2003. 
4 RESULTS AND EVALUATION 
1.2 Implementing wavelet transform 
4.1 Fusion of QuickBird images 
This approach was done in the following way. Firstly a fusion 
image was obtained by using the PCA transformation to merge the 
multiresolution image and high-resolution panchromatic image. 
Since both images are taken at the same time and from the 
same sensor, no registration or rectification is needed. The 
resolutions of the multispectral image and the panchromatic 
one are 2.8 m. and 0.7 m respectively. They have been