EN s (i,j)= ¿r[M s (k,l)-E{M s )] 2
kJeD(iJ)
EN°(i,j) = £[M°(*,/)-E{M°)f
k,leD(i,j)
(9)
Where D(i,j) is the neighbor window of point (i,j)- The
window size of D(i,j) usually is 3*3 or 5*5.
The fused wavelet coefficient CW(i,j) at point (/ } j) is
obtained as following
\w s {i,j) EN s (i,j)>EN°(i,j) (10)
\w°(i,j) EN 4 S (i, j) < EN° (/', j)
And then, the inverse DT-CWT is carried out for composing the
new merged images at this level.
(5) The 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 contains both the spectral
information of multi-spectral optical images and the object
structure information of SAR image.
We find much more details of urban area have been lost for
speckle noise in SAR image, but the lake at center and some
buildings at right are distinct, because water reverberates less
electromagnetic wave but the building produces strong echo.
The buildings with strong echo are white points in the SAR
image, and they clearly show us positions and shapes of the
buildings and roads in the city. So these object features are
what we need to fuse with multi-spectral optical image.
Figure 4. SAR image (left) and SPOT5 multi-spectral image
composed of XS1, XS2 and XS3 bands (right)
4. EXPERIMENTS
We chose two images in experiments. One is a Radarsat-1 SAR
image (acquired in 6 th November 2002, along-track slant range
resolution is 8.82 meters, across-track slant range resolution is
5.56 meters) and a SPOT5 multi-spectral image composed of
XS1, XS2 and XS3 bands (acquired in 1 st October 2002,
ground resolution is 10 meters). They are shown in figure 4.
They have been registered strictly at the same scale. We fuse
the images with DWT and DT-CWT at 1, 2, 3 level.
Proportions of the fused images are listed in figure 5.
Figure 5. Proportions of images fused by: (a) 1-level DWT, (b)
2-level DWT, (c) 3-level DWT, (d) 1 -level DT-CWT, (e)
2-level DT-CWT, (f) 3-level DT-CWT
In figure 5 the features in SAR image have been successfully
integrated with SPOT5 image. Parts of urban area have been
enhanced and spectral information has been conserved well.
Figure 5 (a), (b), (c) are fused by DWT at 1, 2, 3 level
respectively, and figure 5 (d), (e), (f) are fused by DT-CWT at 1,
2, 3 level respectively. We observe (a) is similar with (d) but (d)
is vivider. And it is clear that (b) and (c) lost more spectral
