JOURNAL OF INFORMATION, KNOWLEDGE AND RESEARCH IN
ELECTRONICS AND COMMUNICATION ENGINEERING
FRAMELET BASED IMAGE FUSION FOR THE
ENHANCEMENT OF CLOUD ASSOCIATED SHADOW
AREAS IN SATELLITE IMAGES.
1
MR.V.SUNDHARARAJ/ AP, 2JUVVALAPALEMSUMADEEP,3CH.JAYA SAI KISHAN,
4S.MOHANKUMAR
1Asst.Professor,
Department Of ECE, Paavai College Of Engineering, Namakkal,
Tamilnadu.
2,3,4 Students, Department Of ECE, Paavai College Of Engineering,
Namakkal,tTamilnadu. Sumadeep.00@gmail.com,sujiths949@gmail.com
ABSTRACT: In this paper, a framelet-based image sharpening algorithm was developed to
enhance cloud-associated shadow areas in satellite images while preserving details
underneath shadow areas. The developed algorithm utilizes framelet analysis to decompose
cloudy images into several frequency level components. Image details underneath shadow
areas are more preserved in this method compared to wavelet based methods. The developed
technique is implemented on a cloudy Landsat7 Panchromatic sub scene. The results showed
that the developed technique was successful in enhancing the cloudy image through reserving
the obscured details underneath the cloud associated shadow areas. Framelet based
technique is having ability to maintain such details under shadow areas. Generally, two or
three framelet decomposition levels were found to be sufficient for the analysis because the
number of artifacts will increase with increase of number of decomposition levels.
Keywords— Image fusion, shadow, frequency decomposition, Landsat, wavelets, Framelets.
I: INTRODUCTION
Small cloud patches are very common in the images
taken in many parts of the world [1]. Shadows caused
by these clouds represent areas with low illumination
conditions that are harder to detect but have the
potential for enhancement. Fusion techniques were
also used to account for cloud and shadow defects on
certain image using different cloud/shadow free
images [5, 6]. Although these methods are widely
used, they tend to ignore the spatial content
underneath shadow areas. Hence, this study is
devoted to developing a technique to reduce the
effect of cloud associated shadows using image
wavelet decomposition technique. The wavelet based
methods can be done in frequency domain. The
frequency domain provides the flexibility to model
frequency content differently at each wavelet
decomposition level, but there is a problem of lack of
shift invariance and frequency resolution with
standard wavelet transform. Due to these problems,
the information of underneath shadow areas is not
clear. A new framelet (wavelet frame) based method
was introduced to eliminate the drawbacks of wavelet
based methods. Framelet based image fusion is used
to extract the detailed spatial information from the
cloudy and cloudy free images.
One of the objectives of the methodology developed
in this paper is to enhance shadow areas by
preserving details underneath these shadows. A
framelet transform technique is suggested to achieve
this objective by fusing this image with another
cloud-free image The techniques developed in this
study, which utilizes frame let based image fusion to
capture more spatial & edge detail information, was
applied only in shadow areas.
II: THE FRAMELET TRANSFORM
As it is well known, except for the Haar filter bank,
two-band finite impulse response (FIR) orthogonal
filter banks do not allow for symmetry. In addition,
imposition of Orthogonality for the two-band FIR
filter banks requires relatively long filter support for
such properties as a high level of smoothness in the
resulting scaling function and wavelets, as well as a
high approximation
order.
Symmetry and
orthogonality can both be obtained if the filter banks
have more than two bands. Furthermore, due to the
critical sampling, orthogonal filters suffer a
pronounced lack of shift invariance, though the
desirable properties can be achieved through the
design of tight frame filter banks, of which
orthogonal filters are a special case. In contrast to
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orthogonal filters, tight frame filters have a level of
redundancy that allows for the approximate shift
invariance behavior caused by the dense time-scale
plane. Besides producing symmetry, the tight frame
filter banks are shorter and result in smoother scaling
and wavelet functions [4].
A. TIGHT FRAMELET FRAME:
A set of functions {φ1, φ2 ,..….φN−1 }
in a
square integrable space L2 is called a frame if there
exist A > 0, B < ∞ so that, for any function f ∈ L2.
Where A and B are known as frame bounds. The
special case of A = B is known as tight frame. In a
tight frame we have, for all f ∈ L2
We can find the fast wavelet frame (or frame let)
transform, from multi resolution analysis which is
generally used to derive tight wavelet frames from
scaling functions. The frame condition can be
explained in terms of over sampled filters, given a set
of N filters, we define them in terms of their
polyphone components:
Hi (z) = Hi,0 (z2 )+ z−1Hi,1 (z2 ),i = 0,1,2,.....N −1
where
H i,l (z) =∑ hi (2n − l)z−n ,l = 0,1, 2.....
Now we can define the signal X (z) in terms of its
polyphase components,
X (z) = ((X 0 (z) X l (z)))
The equation ( Xl (z)), l =0, 1 is defined in terms of the
time domain signal, x (n), as follows:
X l (z) =∑ x(2n − 1)z− n
n
The given input signal is X (z) and obtained output
signal is X (z ) .these two signals satisfying the
perfect reconstruction condition when
X (z) = X(z)
Similarly in terms of filter banks
HT (z)H(z-1) = I
On the other hand, in our proposed method
we are having a three-band tight frame filter bank
and PR conditions can be expressed in terms of the Z
-transforms of the filters h0,h1,h2 . Moreover, the
perfect reconstruction
(PR) conditions can be easily extended to N filters
down sampled by 2:
X ( z ) = 1 / 2[ H 0 ( z ) H 0 ( z -1 ) + H 1 ( z 1
)H 1 ( z )] X ( z ) +1/ 2[ H 0 (- z ) H 0 ( z -1 ) + H 1 ( z 1
) H 1 (- z )] X (- z )
From the above equation we can get the perfect
reconstruction conditions
H0 (z)H0(z-1)+H1(z-1)H1 (z) = 2;
H0(z-1)H0(-z) + H1(z-1)H1(-z) = 0
The following Figure 1 represents the three band
perfect reconstruction filter bank.
Figure1: A three-band PR filter bank.
We already knew, about the PR conditions
for the filter banks. We can write these perfect
reconstruction conditions in matrix form as
HT (z)H(z-1) = I
H (z) is a matrix[4 ].
If one filter band h0(n) is compactly supported,
then a solution {h1(n),h2(n) } to the perfect
reconstruction condition exist if and only
hi (z) + hi (−z) < 2, z
=1
The goal is to design a set of three filters that
satisfy the PR conditions in which the low pass filter,
h0(n) is symmetric and the filters h1 (n) and h2(n) are
each either symmetric or anti-symmetric and h2 (n) is
a time reversed version of h1 (n).
The symmetry condition for h0(n) is
h0 (n) = h0 (N −1 − n)
Where N is the length of the filterh0(n).
To show this, suppose that h0(n), h1(n) & h2(n) satisfy
the PR conditions and that
h2 (n) = h1(N − 1 − n)
More details about frames and filter coefficients are
given in
[2], [3], [4]. The 2D extension of filter bank is
illustrated on Figure2.
Figure2: An over sampled filter bank for a 2-D image
III. IMAGE FUSION
Generally, Image Fusion is the process of
combining relevant information from two or more
images into a single image by using certain
algorithms. The resulting image will be more
informative than any of the input images. Fusing two
images in order to get rid of defective parts in one of
the images is a typical image fusion application.
IV. DEVELOPED METHODOLOGY
In our developed algorithm, the defected
cloudy image is fused with another cloud-free image
to form a new enhanced image from the high
frequency components of the cloudy image and the
low frequency information of the cloud-free image.
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ELECTRONICS AND COMMUNICATION ENGINEERING
Figure 3(a) presents schematic diagram of the
methodology adopted in this approach. It should be
mentioned here that developed methodology of
capturing and preserving high frequency component
was applied in shadow areas only. Areas identified as
clouds were simply replaced by corresponding areas
in the cloud-free image.
(a)
(b)
Figure 3: (a) schematic representation of
developed methodology (b). Study area-Nov 2001
Landsat 7 ETM panchromatic sub-scene.
A. Data:
The developed algorithm was implemented
on the panchromatic band of a November 2001
Landsat 7 ETM
satellite sub scenes shown in Figure 3(b). This area
represents part of a city suburb located close to an
airport close to Cairo, Egypt[7]. Features in this
image are partially obscured by existing cloud
patches and their associated shadows. Figure 4
shows the cloud free images of the study area. The
first cloud-free image is another ETM
Panchromatic image of the same resolution taken in
July 2000. The second test image is 30 meters
resolution Landsat ETM taken in May 2001.This
image was pre-processed by conversion to gray
level image and resampling to 15 meter pixel.
(a)
(b)
Figure 4: (a) First cloud-free image-July 2000
Landsat7 ETM panchromatic subscene. (b) Second
cloud-free image–May 2000 Landsat ETM visible
bands subscene converted to gray level image
B. IMAGE
FUSION
USING
FRAMELET
TRANSFORM:
The developed methodology suggests that both
defected and cloud-free images are decomposed
using frame let transform to create different high and
low frequency components. The high frequency
component contains image details such as noise,
edges and details. On the other hand, the low
frequency (approximation) components contain basic
image information. Considering fast wavelet (frame
let) decomposition of the shadow areas of an image,
it could be easily shown that the details components
contain image information located in these areas.
Information beneath shadows could be preserved if
the details information in these areas were used in the
image reconstruction process while neglecting the
approximation component. However, neglecting the
approximation component produces an image with
only high frequency information. To solve this
problem, the approximation component of another
cloud-free image was suggested to replace the
approximation component of the defective image
dominated primarily by the cloud associated shadows.
C. EXPERIMENTAL RESULTS:
The defected and cloud free images were
decomposed using frame let transform filter using
Matlab Software. The resulting image is then
reconstructed from the high frequency component
of the framelet decomposition the original image
and the low frequency component of the framelet
decomposition of the cloud-free image. This
approach could be looked at as a typical image
fusion application based on framelet decomposition
utilized to filter out certain components in one of
the images involved. Details from the original
image in the shadow area mostly exist in the detail
components of the second frame let decomposition
level. Figure 5 shows the resulting image after
applying this approach using second framelet
decomposition level. In this, the details underneath
shadows in the defected image were picked up in
the resulting image.
(a)
(b)
Figure 5: (a) Image reconstructed from second
level decomposition of the cloudy image and the
first high-resolution cloud-free image
(b) Image reconstructed from second level
decomposition of the cloudy image and the
second low -resolution cloud-free image
V. CONCLUSION
The
successful in
shadows from
based on fast
developed
algorithm
was
eliminating cloud associated
a image. The technique was
wavelet transform (framelet)
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decomposition and fusion with another cloudfree image. The developed technique was
successful in enhancing cloud-associated
shadow areas in the image while preserving
details in the shadow areas. Generally, two
wavelet decomposition levels were found to be
sufficient for the analysis. However, higher is
decomposition level, the more artifacts in the
output image. The results obtained using two
images with the same spatial resolution were
found to be better than those obtained when
using images with different spatial resolution.
[1]
[2]
[4]
[5]
[6]
[7]
[8]
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