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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B-YF. Istanbul 2004 
4. THE IMAGE FUSION METHOD BASED ON THE 
CURVELET TRANSFORM 
We now give the specific operational procedure for the 
proposed  curvelet-based image fusion approach. The 
operational procedure is a generic one, although IKONOS 
images were taken as an example in order to illustrate the 
method. 
(1) The original IKONOS pan and multispectral images are 
geometrically registered to each other. 
(2) Three new IKONOS pan images 1, , 1, ,and I, are 
produced, whose histograms are specified according to 
the histograms of the multi-spectral images R, G, and B, 
respectively. 
(3) By using well-known wavelet-based image fusion 
method, we obtained fused images LR, 1, FG, and 
|, +B, respectively. 
(4) I, , L, and I, are decomposed into J +1 subbands, 
respectively, by applying *“ "a trous” subband filtering 
algorithm. Each decomposed image includes d which is 
a coarse or smooth version of the original image and 
. oe . ~ -j 
w which represents “the details of 7 ” at scale 2 
J 
(5) Each c, 
from (3). 
is replaced by fused image which obtained 
(6) The ridgelet transform is then applied to each block. 
(7) Curvelet coefficients (or ridgelet coefficients) are 
modified in order to enhance edges in the fused image. 
(8) The Curvelet reconstructions are carried out for I,, 1, , 
and I, , respectively. Three new images (F ,F,, and F, ) 
are then obtained, which reflect the spectral information 
of the original multi-spectral images R, G, and B, and also 
the spatial information of the pan image. 
(9) F ,F,, and F, are combined into a single fused image 
F. 
In this approach, we can obtain an optimum fused image which 
has richer information in the spatial and spectral domains 
simultaneously. Therefore, we easily can find out small objects 
in the fused image and separate them. This is the reason why 
curvelets-based image fusion method is very efficient for image 
fusion. 
63 
S. EXPERIMENTAL STUDY AND ANALYSIS 
5.1 Visual analysis 
Since the curvelet transform is well-adapted to represent pan 
image containing edges and the wavelet transform preserves 
spectral information of original multispectral images, the fused 
image has high spatial and spectral resolution simultancously. 
From the fused image in Figure 3, it should be noted that both 
the spatial and the spectral resolutions have been enhanced, in 
comparison to the original images. The spectral information in 
the original panchromatic image has been increased, and the 
structural information in the original multispectral images has 
also been enriched. Hence, the fused image contains both the 
structural details of the higher spatial resolution panchromatic 
image and the rich spectral information from the multispectral 
images. Compared with the fused result by the wavelet, the 
fused result by the curvelets has a better visual effect in 
IKONOS image fusion in Figure 3. 
  
(a) (b) ! (c) 
Figure 3. (a) Original IKONOS colour images (b) Wavelet- 
based fusion result (c) Curvelet-based fusion result 
5.2 Quantitative analysis 
In addition to the visual analysis, we extended our investigation 
to a quantitative analysis. The experimental result was analysed 
based on the combination entropy, the mean gradient, and the 
correlation coefficient, as used in Shi et al. (2003). 
  
  
  
  
  
  
  
  
  
Method CE M.G CC 
Original 20.9771 as 
Images 9.5632 22.2667 — 
(R,G,B) 21.6789 = 
Image : 
fused bv 22.7275 0.9261 
> 22.3452 23.7696 0.9196 
^ eet 23.9975 0.8690 
pir l3 
Image m 
feti i 25.8385 0.9457 
Cr And 26.9948 26.9576 0.9463 
: Cuv ert 28.4971 0.9289 
1. 1'2. 3 
Image 
fused b 23.4475 0.9692 
x Y 16.5482 23.6813 0.9951 
(FF F1) 23.7283 0.9581 
LT 
  
Table 1. A comparison of image fusion by the wavelets, 
the curvelets, and IHS methods. 
Table 1 presents a comparison of the experimental results of 
image fusion using the curvelet-based image fusion method, the 
wavelet-based image fusion method, and IHS method in terms 
of combination entropy, the mean gradient, and the correlation 
coefficient.