The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
g = 
1 
3. IMAGE FUSION AND QULITY APPRAISAL 
3.1 Image fusion 
Wavelet-based fusion technique integrates the high-frequency 
components of the higher resolution data with the low- 
frequency components of the lower resolution data (or the lower 
resolution data) in a Multi-Resolution Analysis (MRA). 
Currently wavelet-based image fusion methods used are mostly 
based on two computation algorithms: the Mallat algorithm 
(Mallat,1989; Ranchin et al,2000) and the a trous algorithm 
(Aiazzi et al,2002; Shensa,1992).In this paper the Mallat 
algorithm is used. The fusion process has been well described 
(Yocky,1996; Aiazzi et al,2002). The first step is to co-register 
two images precisely. It is generally preferable to register the 
lower resolution image to the higher resolution image. In other 
words the high resolution image is used as reference image. 
However if the lower resolution image has georeference that is 
to be retained, it may be desirable to use it as the reference 
image, the process includes two sides:locality transform and 
resampling. Secondly it is to calculate the ratio of spatial 
resolution between different resolution images. If the result is 
integer w,the value would be adopted as dimension of muti- 
band wavelet transform .The high-resolution image would be 
decomposed based on w-band biorthogonal wavelet transform. 
Accordingly if the w is not integer ,the Lease common multiple 
of the resolution of two images must be calculated.Then 
interpolation of high-resolution image is carried on based on 
lease common multiple Following this ,the decomposition of 
new high-resolution is processed based on multi-band 
biorthogonal wavelet transform.A low frequency image and w 2 
-1 high frequency images are accquired.Then the low frequency 
image of the higher resolution image is replaced by the low 
resolution image . Finally, an inverse wavelet transform is 
applied. The result is an image which merges the high- 
resolution image and the low-resolution image. 
3.2 Quality analysis and appraisal 
In this paper several parameters including combination 
entropy correlation coefficient ,mean gradient and standard 
deviation , as used in other studies such as Wald et al.(l997), 
Sun et al.( 1998), and Li et al.( 1998),are adopted to value 
quality of the fusion image. Standard deviation and correlation 
coefficient are parameter we are familiar with, so combination 
entropy and mean gradient are only presented in this 
paper.According to Shannon information theory, the larger the 
entropy of image is , the richer the information and the better 
quality of a image is . 
(JV,-1)(JV -1) 
XV(a/, 2 +a/;)/2 oo) 
H(x)=- ZPJog.P, 
/=o 
where H (c) = the entropy of image 
/ = the grey value of pixel 
n = the number of pixel of image 
=the probability of i 
(9) 
Where g is mean gradient 
./V r , N v , is the number of colums and lines respectively 
A/ 2 , A/ 2 is the square sum of difference of adjacent pixel 
4. EXAMPLE AND FUSED IMAGE ANALYSIS 
As an experimental study, the multi-band biorthogonal 
wavelets-based image fusion method was applied to the 10m 
resolution Spot panchromatic image and three 30m resolution 
Landsat multispectral images.Because the ratio of spatial 
resolution is three,we adopt three-band biorthogonal wavelet to 
merge two images.Menwhile ,this paper also fuses two images 
based on PCA,IHS and Brovey in order to appraise the fused 
image based on three-band biorthogonal wavelet. 
From the fused images Figure2 ,it should be noted that both the 
spatial and spectral resolution have been enchanced. The fused 
images contain the spatial information of high-resolution Spot 
panchromatic and multi-spectral information of TM 
image.Fused image based on three-band biorthogonal wavelet 
has a better visual rusult in comparison with other three fused 
images.Moreover this paper appraises the fused image 
quantitively by four parameters standard deviation ,mean 
gradient, combination and correlation. The result is Table 1 
Figure2 the fused images based on,3-band biorthogonal 
wavelet, PCA, IHS and , Brovey 
In general the standard deviation and combination entropy can 
reflect the information of image and deviation from original 
image to a certain degree. The fused image based on three-band 
biorthogonal wavelet transform has the most entropy among all 
fused images.So this technique fuses more information than 
other fusing techniques.In addition, the standard deviation of 
the biorthogonal wavelets based image fusion is more, close to 
the standard deviation of original images than these of other 
methods,which indicates this method has less distortion of 
spectral characteristics .