International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
  
and registered multi-spectral images with complex wavelet 
transform to form their multi-resolution and multi-directional 
descriptions. At the same time, the magnitudes of their complex 
wavelet transform are achieved. 
(4)Image fusion begins with the coarsest level, the low 
frequency parts are replaced by the corresponding parts of 
multi-spectral images respectively. The high frequency parts at 
each scale cannot be replaced directly by the high frequency 
parts of panchromatic image, since the high frequency parts of 
the multi-spectral image don’t only include spatial information, 
but also include spectral information. Considering that the 
complex wavelet transformation of the images can be 
interpreted as a complex process including real parts and 
imaginary parts and the magnitudes can show clear 
directionality, we fuse the high frequency parts according to the 
magnitudes. The details is illustrated in fig.6. 
The wavelet coefficients at point (;, j) of real and imaginary 
parts in the high resolution image are denoted as 7j//(; j) and 
W/ (i, j) respectively. The wavelet coefficients at point (;, j) 
of real and imaginary parts in the low resolution image are 
denoted as  jw(i,j) and  w/(i j) respectively. The 
magnitudes at point (;, j) in the high resolution image and the 
low resolution image are achieved respectively by 
M" G, y» Az G D) -w" o. n) 
(wc, D) + WG, p) usu 
    
MO, N= 
The wavelet coefficient cw (;, j) at point (;, j) in the fused 
image is obtained as following 
wha, j) Ma, j= MG, J) 167] 
J 
CW, j)= 
en fe M" (i, j) « M* (i, J) 
And then, the inverse wavelet transformations are carried out 
for composing the new merged images at this level. 
(5)The replacement and composing procedure in (4) are carried 
out recursively at their top levels until the first level is processed. 
This results in three new images. 
(6) The three new produced images are compounded into one 
fused image. The fused image does not only contain the spectral 
information content of original multi-spectral images and the 
structure information content of panchromatic image, but also 
enhance the original spectral and spatial information. 
5. EXPERIMENTS 
We chose two group images in experiments. One group includes 
a SPOT panchromatic image (acquired in 2002, ground 
resolution is 10 meters) and a Landsat7 TM multi-spectral 
image composed of 4", 5" and 7^ bands (acquired in 2000, 
ground resolution is 30 meters). The other 
532 
Real Part e Feal Part 
    
  
| agi nary 
Part 
r 11 magi nary 
Part 
Figure 6. Procedure of image fusion based on complex wavelet 
transform 
includes a IKONOS panchromatic image (ground resolution is 1 
meters) and a IKONOS multi-spectral image (ground resolution 
is 4 meters), they are both acquired in 2003. The two groups of 
images are shown in fig 7 and fig 9. They have been registered 
strictly at the same scale. We fuse the images with different 
methods including direct power average, high pass filter, 
Intensive-Hue-Saturation (IHS) transform, DWT, discrete 
wavelet packet transform (DWPT). These images are used to 
compare with the image fused by CWT. 
First we observe the fused images in fig 8 and fig 10. We find 
that (c) fully conserve spatial information of high-resolution 
image, but evident spectral distortion exist. The spatial 
resolution and spectral resolution of (a) and (b) have been 
improved  limitedly. Then we find that the spectral 
characteristics of (d), (e), (f) are closer to the original 
multi-spectral image than other fused images. Among (d), (e) 
and (f), the spectral characteristic of (d) is closest to the original 
multi-spectral image, the spectral characteristic of (e) is similar 
with (f). Moreover, there is slight sawtooth in (d), (e) , but (f) is 
perfectly smooth and clear. The discrete wavelet transform, 
discrete wavelet packet transform and complex wavelet 
transform are all carried out at two levels, therefore we can put 
them together for comparison. 
Secondly we evaluate the performance of the fusion method 
based on complex wavelet transform using image quality 
indexes. The indexes we selected are average value, standard 
difference, entropy, average grads and fractal dimensions. 
Average value can show the distribution of the image grayscale 
in the rough. Standard difference and entropy can measure the 
information abundance in the image. Average grads shows 
exiguous contrast ,varied texture characteristic and definition of 
the image. Fractal dimensions can describe the abundance 
degree of texture characteristics and the variety of pixel value in 
  
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