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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Voi. XXXVII. Part B7. Beijing 2008 
rely on the difference of the calculational mehtod of the 
mathematical model parameters. Thus calulating model 
parameters corresponding to the fusion method is the main task 
when implementating the method. Compared to Wang’s work 
(Wang,2005), the paper mainly concentrates on two aspects. 
First, the paper presents a generalized model for remotely 
sensed data pixel-level fusion, which has a wide range of 
applicability. The various commonly used remote sensing data 
fusion algorithms can be deduced to the generalized model. 
Second, the implementation technique base on the generalized 
model only calculates the model parameters impacting the last 
fusion results and discards the processing steps not affecting the 
fusion results, saving computational time. 
3. THE GENERALIZED MODEL 
According to the imaging mechanism and the ideal 
pan-sharpening results of multispectral image, the presented 
generalized model is formulated by, 
(1) 
( ' ,7) : Spatial and textural details extracted from the 
panchromatic band by a certain calculation. 
a 
Oc,i,j). The coefficients modulating 
into 
xs 
L 
(k.ij) 
The presented model expressed by equation (1) can clearly 
describe the mathematical relationships among the original 
multispectral image, the spatial details extracted from the 
high-resolution panchromatic image, and the adopted fusion 
strategy. In another word, the spatial and textural features 
extracted from the panchromatic band are imported into the 
multispectral image in terms of the fusion coefficients and the 
fusion result is the image whose features are enhanced by the 
panchromatic image. The fusion operations are fulfiled pixel by 
pixel, band by band after calculation of 
and } but 
in the course of calculation of and , not only the 
pixel value of location (i,j) of the lower resolution multispectral 
k th band and the panchromatic band but also the whole 
statistical information and neighbor pixels of loacation (i,j) are 
used. 
the methods calculating parameters 
C 
O’D include: 
g 
1) the linear combination method: obtaining the < ~ x ’ y) after 
subtracting multispectral bands’ linear combination from the 
panchromatic band, such as IHS, PCA, RVS, Brovey, 
Block-regression (Zhang and Yang,2006); 
2) filter method and multi-scale analysis method: obtaining the 
(x ' y) after subtracting its filtered or multi-level decomposition 
results from the panchromatic band, such as SFIM, LCM, A 
trous (N'u~nez,1999), GLP (Aiazzi,2002), ARSIS method 
(Ranchin,2003). 
oc 
( k,x,y ) is determined by following factors: the panchromatic 
and multispectral relative spectral response, spectral range of 
the panchromatic and multispectral bands, the GIFOV(Ground 
projected Instantaneous Field Of View) of panchromatic and 
multispectral bands, the landscape properties and land cover 
classes, radiometric calibration method of different sensors, the 
temporal properties, the correlation between the panchromatic 
and multispectral bands, the average value, variance and other 
statictical characteristics of the multispectral and panchromatic 
bands. 
cc 
The methods calculating parameters include: 
1) Constant Value, such as IHS, PCA, RVS, A trous, LCM; 
2) Spectral Distortion Minimum: such as SFIM, Brovey, A 
trous, Block-regression; 
3) Context-based Decision (CBD), such as GLP, ARSIS. 
The model formulated by equation (1) is more comprehensive 
and applicable than Wang’s model. The fusion coefficients of 
wang’s model are limited to the cases of constant value and 
spectral distortion minimum, and can not describe the fusion 
coefficients for LCM, ARSIS and GLP fusion algorithms. For 
the method extracting spatial and textural details, Wang’s 
model include the filter and linear combination mehtods while 
the generalized mode proposed in this paper supports the 
additional methods used in LCM and GLP fusion algorithms. In 
a word, the generalized model can characterize most of 
commonly used remote sensing data fusion algorithms 
including not only the IHS, PCA, A trous, Brovey, HPF 
algorithms but also RVS, GLP, LCM, ARSIS, wavelet 
decomposition plus PCA transform, wavelet decomposition 
plus IHS transform, and the authors proposed Block-regression. 
4. DEDUCTION FOR COMMONLY USED FUSION 
ALGORITHMS 
In this section, three categories of fusion algorithms mentioned 
in section 1 are deduced to the generalized model, i.e. the 
proposed equation (1), through the mathematical transformation. 
Through the deduction, the conclusion can be drawn that 
different fusion technique rely on the difference of the 
S< Cl (k . 
calculation of parameters {l,J> and ( ’ l,J> . 
4.1 Component Substitution Fusion Technique 
The typical algorithms applying component substitution fusion 
technique include IHS, PCA, LCM and RVS fusion algorithms. 
To illustrate the deduction for this technique, following is the 
transformation steps taking PCA fusion algorithm as an 
example. 
XS 
The lower resolution multispectral band k is resampled to 
have the same size as the higher resolution panchromatic band 
P an after those bands are co-registrated: XSk ~ rs P^ xs k) ? and 
after the resampling the implementatiom steps for PCA fusion 
algorithm are as follows (Shettigara, 1992): 
1 ) Calculating the correlation matrix of the n lower resolution 
multispectral bands, ^ is equal to 4;