The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
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weighting parameters of a and b for G and B bands are 0.75 
and 0.25, respectively. 
However, since the above two weighting parameters are totally 
depends on the IKONOS imagery, these parameters cannot be 
applied to other satellite image fusion. Therefore, a control 
parameter, y3, will additionally be suggested in this paper. This 
will be selected when the mean value of the difference between 
the PAN image and the ft * I' image is a minimum, so as to 
minimize the radiance difference between two images. 
The proposed hybrid method for IKONOS image fusion is as 
follows: 
F{R) 
F(G) 
F{B) 
FINIR) 
R + ^ W(PAN-^«l') k 
k=l 
G + V w 
^ (PAN-^*I*) k 
k=l 
B + i W (PAN _,. I% 
k-1 
NIR + ^ W (PAN; ,,,, )k 
(19) 
In sum, we employed the FIHS method in order to reduce the 
computational cost of the original hybrid method along with the 
simplification of the mathematical model, and suggested the 
control parameter and the framelet transform in order to 
enhance the overall performance of the fused images. 
4. EXPERIMENTAL STUDY AND ANALYSIS 
To verify the performance of the proposed method, an IKONOS 
PAN image and MS images of the Korean city of Daejeon, 
which were acquired on 9 March 2002, were used. The 
IKONOS imagery contains a lm PAN image and four-band 4 m 
MS images. The data for this experiment comprised a PAN 
image and four R, G, B, and NIR MS images. 
elHS 
eSW- 
eSWI- 
eFSWI- 
Wavelet 
s 
Trous 
Framelets 
bias (%) 
R 
16.68 
0.00 
0.00 
0.00 
(ideal 
G 
16.87 
0.00 
0.00 
0.00 
value: 0) 
B 
18.85 
0.00 
0.00 
0.00 
NIR 
18.81 
0.00 
0.00 
0.00 
CC 
R 
0.95 
0.96 
0.97 
0.97 
(ideal 
G 
0.95 
0.96 
0.97 
0.97 
value: 1) 
B 
0.93 
0.95 
0.96 
0.96 
NIR 
0.94 
0.95 
0.96 
0.96 
SD (%) 
R 
10.78 
9.53 
8.51 
8.36 
(ideal 
G 
10.39 
8.62 
7.84 
7.66 
value: 0) 
B 
12.12 
10.18 
9.29 
9.15 
NIR 
11.27 
10.13 
8.77 
8.79 
sCC 
R 
0.99 
0.94 
0.98 
0.98 
G 
0.99 
0.94 
0.98 
0.98 
B 
0.99 
0.93 
0.98 
0.98 
NIR 
0.98 
0.95 
0.98 
0.98 
ERGAS 
5.26 
2.41 
2.15 
2.12 
SAM(deg.) 
3.71 
3.42 
3.10 
3.09 
Q4 
0.58 
0.92 
0.94 
0.94 
Table 2. Comparison of IKONOS Fusion Results 
In order to assess the quality of the fused MS images, reference 
MS images with the same spatial resolution as the PAN image 
were needed. However, since such MS images were unavailable, 
spatially degraded PAN and MS images, which were generated 
by a lowpass filtering and sub-sampling procedure, were 
considered (Wald et al., 1997). 
4.1 The Quality Indices for Quantitative Analysis 
The spectral and spatial quality indices for quantitative analysis 
have been used in (Ranchin et al,2000; Alparone et al., 2004): 
namely, the bias; the standard deviation (SD); the correlation 
coefficient (CC); the relative global dimensional synthesis error, 
which is known as the erreur relative globale adimensionelle de 
synthèse (ERGAS); the spectral angle mapper (SAM); the 
global quality index, Q4; and the spatial correlation index 
proposed by Zhou et al. (sCC). 
Note that the bias, SD, CC, ERGAS, SAM and Q4 are applied 
at degraded scale, but sCC is applied only at full scale without 
any degradation. 
4.2 Quantitative Analysis 
Table 2 shows the results of a comparative analysis of the 
IKONOS image fusion with the seven quality indices. 
The comparison presented in Table 2 shows that the extended 
IHS method (elHS) has lower CC and Q4 values but greater 
bias, SD, ERGAS, SAM values than the extended substitutive 
wavelet method (eSW-Wavelets). Therefore, the spectral 
quality of the images fused by the eSW-Wavelets method is 
greater than that of the images fused by the elHS method. 
However, since the sCC values of the elHS method are greater 
than those of the eSW-Wavelets, the spatial quality of the 
images fused by the elHS method is greater than that of the 
images fused by the eSW-Wavelets. 
On the other hand, the hybrid method between the elHS and 
eSW methods (eSWI-Trous) has lower bias, SD, ERGAS, and 
SAM values but greater CC, sCC and Q4 values than both the 
elHS and the eSW methods. Consequently, the spatial and 
spectral quality of the images fused by the eSWI-Trous method 
is greater than those of the images fused by both the elHS and 
the eSW methods. That is to say, the hybrid fusion method was 
able to eliminate drawbacks of the IHS and wavelet-based 
methods, while keeping the advantages. 
In addition, Table 2 shows that the proposed fast hybrid method 
(eFSWI-Framelets) has lower bias, SD, ERGAS, and SAM 
values but greater CC, sCC and Q4 values than the eSWI-Trous 
method. Therefore, the spatial and spectral quality of the 
images fused by the eFSWI-Framelets method is greater than 
those of the images fused by the eSW-Trous method. This is 
why the control parameter and the framelet transform are 
suggested in this paper. 
4.3 Visual Analysis 
Figure 5 shows the results of full-scale visual fusion. For Fig. 5 
(b), aliasing artifacts induced during the interpolation process 
are apparently visible. Such impairments disappear in images 
fused by the elHS method and are easily explained by Eq. (15),