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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
variances of the panchromatic image and the k-th band, and 
the covariance between them. mean(F k ) is the mean of the 
fused band, p Q and fi k are the means of the corresponding 
panchromatic image and the k-th band of the multispectral 
image. 
Combination of Criterion-1 and Criterion-2 provides a fused 
image that has the same variance as the panchromatic image 
and the same mean as the multispectral one. Therefore, the 
fused image is forced to have the same spatial variation as the 
panchromatic image which enables the injection of the spatial 
detail content of the panchromatic image into the fused 
multispectral one. In addition, the fused image is forced to have 
the same color content as the original multispectral image since 
the mean of the fused image is required to be the same as the 
mean of the multispectral one. 
Criterion 3: This is to keep the inter-band relationships among 
the original multispectral bands after fusion. This criterion is 
inherited from the Brovey type fusion method 
F k (m,n) = C(m,n)-I k (m,n) (9) 
where C is a common coefficient for all N bands at pixel 
(m,n) , which assures that the ratio among the original 
multispectral bands are kept in the fused bands. It should be 
noted that the C factor varies from pixel to pixel. 
Combining all the above four equations (Eq.6-9) will lead to an 
equation system for each pixel. At each pixel, each equation is 
written N times (one equation for each panchromatic and 
multispectral band) where N is the total number of 
multispectral bands. Therefore, a total of 4N equations are 
written. There are 3N unknowns (F k , a ,b for each band) in 
Eq. 6-8 and one unknown C in Eq. 9, which is common for all 
N bands. Therefore, there are r = (4N ~(3N + l))= N -l 
redundant equations for each pixel, i.e., the redundancy is one 
less than the total number of multispectral bands. 
The solution to the equation system is obtained using the least 
squares technique. For the initial values of F k , the pixel values 
of the corresponding original multispectral bands are used. 
Initial value of C is taken as 1, and the initial values of a k and 
b k are taken as 0.5. The criteria-based method employs small 
local windows on both panchromatic and resampled 
multispectral bands to find a k , b k and C. Hence, the variance 
and the mean values are calculated for the local windows. 
Besides, a lxl window at the original multispectral image is 
chosen as the computation unit. Let M be the ratio of the 
resolutions of the multispectral and the panchromatic images. 
The area on the panchromatic and the resampled multispectral 
image corresponding to the smallest window on the original 
multispectral image is represented with a window size of MxM . 
Larger window will yield sharper fused image, however, colour 
distortion will occur as pointed out by (Gungor and Shan, 2005). 
If the pixel values within the local window on the panchromatic 
image are very uniform or all the same on occasion, the 
variance of panchromatic image ^ essentially becomes zero. 
No spatial detail transfer is to be expected in this case; therefore, 
pixel values of the multispectral bands are kept unchanged and 
used for the fused pixels. 
4. EVALUATION AND DISCUSSIONS 
The proposed GIHS method and the criteria-based method are 
tested by using QuickBird panchromatic (0.6m resolution) and 
multispectral images (2.4 m resolution). The imagery is over 
urban area in Purdue University campus in West Lafayette, 
Indiana. The fused multispectral images are shown in Figure 2 
(GIHS method) and Figure 3 (criteria-based method). 
Figure 2. IHS (left) and GIHS (right) methods with B-G-R (top) 
and B-G-IR (bottom) display 
It is evident from Figure 2 that the results of the classical IHS 
method, which are produced using blue, green and red bands, 
have significant colour distortion. The green colour of forest 
and grass becomes purple in these images. However, the results 
of the classical IHS method have good colour performance 
when blue, green and infrared bands are used. This is because 
the green colour of vegetation corresponds to high intensities 
(large gray values) in infrared band when compared to the other 
bands. This also affects the corresponding panchromatic image. 
The gray values of the panchromatic image become relatively 
larger than blue, green and red bands due to the effect of the 
infrared region. Therefore, discarding the infrared band in the 
intensity calculation causes more severe colour distortion than 
discarding the red band. On the other hand, the generalized IHS 
method uses all available bands to calculate the overall intensity. 
For this reason, the details to be added to each multispectral 
band are calculated by the contribution of all available bands. 
As seen from Figure 2 that the generalized IHS method gives 
better and more stable fusion results when the fused image is 
displayed using any three fused bands.