The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008
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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 .