The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
Figure 2 shows the filters for a = 1.0720. Figure 3 shows the 
resulting scaling function and wavelets. Table I lists the 
coefficients of the filters \ , \ and h 2 . 
2.3.5 Two-Dimensional Extension: The 2D extension can 
be obtained by alternating between rows and columns, as is 
usually done for typical discrete wavelet transforms. The 
corresponding filter bank, which is illustrated in Fig.4, is 
iterated on the lowpass branch (the first branch). 
3. THE PROPOSED FUSION METHOD 
To apply any of the methods of image fusion described in this 
paper, the MS image and the PAN image must be accurately 
superimposed. Thus, both images must be co-registered, and the 
MS image resampled to make its pixel size the same as the 
PAN image. In order to achieve this, a robust registration 
technique and a bi-cubic interpolator were used. 
Figure 4. An oversampled filterbank for a 2-D image 
3.1 FIHS Fusion Method 
The FIHS fusion for each pixel can be formulated by the 
following procedure (Tu et al., 2001): 
F(R) 
R + (PAN - I)' 
F(G) 
= 
G + (PAN - I) 
F(B) 
B + (PAN - I) 
where F(X) is the fused image of the X band, for X = R, G, and 
B, respectively. 
3.2 The Hybrid Method proposed by Gonzilez-Audicana et 
al. 
A multiresolution wavelet decomposition is used to execute the 
detailed extraction phase, and the IHS procedure is followed to 
inject the spatial detail of the PAN image into the MS image. In 
other words, instead of using the PAN image in Eq. (15), the 
results of the PAN image and the intensity image fused by the 
substitutive wavelet method is used. The fusion results of the 
PAN image and the intensity image are expressed as follows: 
U=i, + Zw rABt , (16) 
k=l 
where I r is the low-frequency version of the wavelet- 
n 
transformed intensity image and ]>] W PANk is the sum of high- 
k=l 
frequency versions of the wavelet-transformed PAN image. 
3.3 The Proposed Hybrid Method 
Assume that, without the loss of generality, the hybrid method 
is based on the FIHS fusion method instead of on the traditional 
IHS method. This is because Eq. (15) holds. 
The hybrid method can be simplified with the following 
procedure: 
R + Z W (PAN.|) k 
k= I 
F(R) 
R + (I n „ 
- I)' 
k= 1 
F(G) 
= 
G + (I new 
- I) 
= 
G + £ W (PAN , K 
F(B) 
B + (I„ e „ 
- 
k® 1 
b + £ w (PAN , )k 
k=l 
where ^ W (PAN _ 1)k is the sum of the high-frequency versions of 
k=l 
the wavelet-transformed difference image of the PAN image 
and the I image. 
As a result, we easily obtained fused images with the fast 
scheme of the hybrid method: We simply added to each MS 
image the detailed information extracted from the difference 
image of the PAN image and the intensity image. Therefore, the 
proposed hybrid method is much simpler and faster than the 
hybrid method. 
3.4 IKONOS Pan-sharpening Technique 
When IHS-like fusion methods are used with IKONOS imagery, 
there is a significant color distortion, due primarily to the 
extensive range of wavelengths in an IKONOS PAN image. 
This difference obviously induce the color distortion problem in 
IHS fusion as a result of the mismatch; that is, the PAN image 
and the intensity image are spectrally dissimilar. To minimize 
the radiance differences between the I image and the PAN 
image, Tu et al. (2004) introduced the near-infrared (NIR) band 
with spectral adjustment applied to the I image, considering that 
j,_R + a*G + 6*B + NIR 
where a and b are weighting parameters defined to take into 
account that the spectral response of the PAN image does not 
cover that of the blue and green band. The value of these 
parameters was estimated experimentally after the fusion of 92 
IKONOS images, covering different areas. According to the 
experimental results obtained by Tu et al. (2004), the best 
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