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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.