The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
the multiplicative data set, reduces the data to a combination 
reflecting the mixed spectral properties of both data sets: 
MLT = yjaxbxPan¡jxMS 4 
(1) 
2.4 SFIM Algorithm 
The SFIM algorithm is a ratio method that the high-resolution 
image is divided by a simulated low-resolution image and the 
result is then multiplied by the low-resolution image. Liu 
(2000a, b) defined the algorithm as follows: 
Where MLT is the output image and i and j are pixels of band k. 
Pan and MS are the panchromatic data and multi-spectral data 
respectively. To compensate for this effect, weighting coefficients 
a and b can be used. As Cliche and Bonn (1985, p. 316) noted, 
“however arbitrary, the weights used for the panchromatic and 
infrared channels increase the spatial resolution from 20 to 10 m 
and preserve much of the infrared information.” 
2.2 MB Algorithm 
Since the original Brovey Transform can only allow three bands 
to be fused, the transform has to be modified in this study. The 
Modified Brovey algorithm is a ratio method where the data 
values of each band of the MS data set are divided by the sum of 
the MS data set and then multiplied by the Pan data set. The MB 
algorithm attempts to maintain the spectral integrity of each band 
by incorporating the proportionate value of each band as related to 
the MS data set before merging it with the Pan data set. By 
adjusting for the effects of the Pan data set’s spectral properties 
when combining the data sets, the spectral quality of the MS data 
set is mainly preserved: 
SFIM= (MS' i.j.k x Pan ,J' Mean :J 
(4) 
MB,,, = 2 x (MSij.„ 1 Z MSi.jjJ x Pan,.) 
(2) 
where MB is the output image and i and j are pixels of band k. 
Pan and MS are the panchromatic data and multi-spectral data 
respectively. The result is multiplied by 2 to increase the digital 
numbers (DNs) of the resulting fused image. 
2.3 HPF Algorithm 
The High-Pass Filter model was first introduced by Schowengerdt 
(1980) as a method to reduce data quantity and increase spatial 
resolution potential for Landsat MSS data. Chavez et al. (1991) 
extended this idea to more diverse multispatial data sets when 
they merged Thematic Mapper (TM) data with a digitized 
National High Altitude Program (NHAP) aerial photograph. The 
HPF method submits the high spatial resolution imagery to a 
small convolution mask (3x3) which acts upon the high- 
frequency spatial information (Pohl, 1998), effectively reducing 
the lower frequency spectral information of the high spatial 
resolution image. The filtered result is then added to the MS data 
and the result divided by two to offset the increase in brightness 
values: 
HPF.jk = (MS,„ + FP,) 12 
(3) 
Where SFIM is the output image and i and j are pixels of 
band k. Mean is a simulated low resolution pixel derived 
from the high-resolution image using an averaging filter for a 
neighbourhood equivalent in size to the spatial resolution of 
the low-resolution data. Pan and MS are the panchromatic 
data and multi-spectral data respectively. For example, 
suppose the high resolution image consisted of SPOT 10x10 
m panchromatic data and the low-resolution image consisted 
of Landsat ETM+ 30x30 m data. In this case the Mean value 
would be the average of the nine 10x10 pixels centred on the 
pixel under investigation in the high-spatial-resolution dataset. 
Liu (2000a) suggests that the SFIM can produce optimally 
fused data without altering the spectral properties of the 
original image if the co-registration error is minimal. 
3. QUALITY ASSESSMENT CRITERIA 
Quality refers to both the spatial and spectral quality of 
images (Wald, 1997). Image fusion methods aim at increasing 
the spatial resolution of the MS images while preserving their 
original spectral content. Spectral content is very important 
for applications such as photo interpretation and classification 
that depend on the spectra of objects. The evaluation of the 
fusion results is based on the quantitative criteria including 
spectral and spatial properties and definition of images 
(Xu,2004). Numerical statistical methods such as Bias of 
Mean(BM), Standard Deviation(SD), Entropy, Average 
Grads(AG), Correlation Coefficient(CC) are used in this 
study to quantitatively assess the fused images produced 
using the above algorithms. 
3.1 Spectral Fidelity 
The basic principle of spectral fidelity is that the low spatial 
frequency information in the high-resolution image should 
not be absorbed to the fusion image, so as to preserve the 
spectral content of original MS image. The indexes which/ 
can inflect the spectral fidelity of fusion image include: 
3.1.1 Bias of Mean: BM is the difference between the 
means of the original MS image and of the fused image 
(Stanislas de Bethune,1998). The value is given relative to 
the mean value of the original image. The ideal value is zero. 
Let F refers to the fused image. 
MS„^, - F„ 
MS_ 
(5) 
MS. 
Where HPF is the output image and i and j are pixels of band k. 
FP is the filtered result of High-Pass Filter, This technique Where BM is the Bias of Mean, MS is the multi-spectral data, 
preserves the MS data while incorporating the spatial resolution of 
the PN data. 
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