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