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Title
Mapping without the sun
Author
Zhang, Jixian

108
Table 2 shows the process of the decomposition and
reconstruction of the Daubechies wavelet using the lifting
ways.
4. THE SAR IMAGE AND OPTICAL IMAGE FUSION
The image may be decomposed to the low-frequency
sub-image and high-frequency sub-images by the wavelet
transform. For the low-frequency sub-image, the main intention
of the image fusion is to reserve the spectral information of the
optical image, and restrain the noise of the SAR image as much
as possible [5] . Usually, the power average method is used to
integrate the low-frequency sub-images. For the high-frequency
sub-images, which present the variational characteristics of the
targets, the image fusion may be handled using the different
fusion operators in term of the application. The fusion operator
is the keys to integrate the high-frequency sub-images.
4.1 The rule for the low-frequency image fusion
A view of the influence of the noise in SAR image, the regional
average method is firstly used to denoise the SAR sub-image
when integrating the low-frequency sub-images. Then, the
power average method is used to integrate the SAR image and
the optical image.
The low-frequency sub-image of the SAR image is firstly
transformed using the regional average method:
WM lhereeionalaverase > 7)
Then, the SAR image and the optical image are integrated by
the under fuction:
W nM .0J) = w 1 ■fr sa (i,j) + Q-w i )-W„(i,J) (3)
Where
W, is the power coefficient, and its value is [0,1].
4.2 The rule for the high-frequency image fusion
The purpose of the high-frequency image fusion is to integrate
the detail information of the images. Because of the
discontinuity of the SAR high-frequency sub-images, the
method in the paper focuses on integrating the optical high-
frequency sub-images in order to keep the integrality of the
features, which will make a great influence on the reliability of
the image matching, especially for the real aperture radar image
matching. So the fusion image should present the SAR image
characteristics and keep the integrality of the features as much
as possible.
On the basis of the analysis of the high-frequency sub-images,
the ratios of the high-frequency coefficients are calculated
between horizontal and vertical directions in the windows,
which are automatically alterable in according with the
features-size. The noise dots will be detected because the
energy along the horizontal and vertical directions is
approximatively equal if the feature is a noise dot. After the
noise is retained, the method based on the ratio of the variance
is used to integrate the SAR and optical high-frequency
sub-images.
Namely, according to the speckle noise, the windows may be
automatically changed from 3x3 to 9x9. The higher
variance in the windows will be regarded as the pixel value of
the high-frequency sub-images fusion if the feature in the SAR
sub-images isn’t a noise dot. The equation is followed as:
W F»,iolU) =
w 0P (Uj)
KAU)
Wsar(U)
if speckle
z / ^op — ^SAR
if (4)
Where
the variance of the window is defined as id is the size of
the windows):
<7*(Uj) = , 1 2 X -W k (m + i,n+j)f
(2£7 "FI) m=-d n=-d
w o,j)= 1 2 X XXo n +i, n +j)
yZu + l) m=-d n=-d
4.3 Integrating the SAR image and optical image
Because the speckle noise makes a great influence on the
feature extraction, it is more important to restrain the noise and
integrate the spectrum and features information of the optical
image. After the images of the SAR and optical image have
been registered, the calculation processes of this method follow
as:
1) Decomposing respectively the SAR and optical images
using lifting wavelet technique. Generally, the level is 3.
2) For the low frequency sub-image fusion, the average
coefficients based on the power is adopted. In order that the
image could show the characteristic of the SAR imagery, the
power value over 0.5 is assigned to the SAR image. For the
SAR low frequency sub-image of the first level, the
sub-images will be integrated after SAR sub-image is filtered
using the regional average ways.
3) For the high frequency sub-image fusion, the ratios of the
high-frequency coefficients are firstly calculated between the
horizontal direction and the vertical one. Then, a new scheme,