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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