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International Journal Of Engineering And Computer Science ISSN:2319-7242
Volume 4 Issue 1 January 2015, Page No. 10072-10077
A Novel Fusion Approach by Non-Sub Sampled Contourlet
Transform
Patil. Sujatha 1 N.Nagaraja Kumar 2
1
PG Scholar, Dept of ECE, Rajeev Gandhi Memorial College of Engineering and Technology
2
Assistant Professor, Dept of ECE, Rajeev Gandhi Memorial College of Engineering and Technolog
Abstract
In This project we analyzes the characteristics of the non-sub sampled counterlet Transform and put
forward an image fusion algorithm based on Wavelet Transform and the Second Generation Curvelet
Transform method. We would take the selection principles that all about low and high frequency coefficients
according to different frequency domain after Wavelet and the Second Generation Curvelet Transform. We
first measure the STD (stranded deviation) of low frequency components and high frequency components.
The window property and local characteristics of pixels were analyzed in this method. Totally, the proposed
algorithm in this paper was appalling to the experiments of multi focal image fusion and also
complementary image fusion. In accordance with the final results the proposed method hold useful
information with other method
Transform. In recently it is faster developed was a
multi resolution analysis image fusion method [2].
Introduction
Wavelet Transform has efficient frequency
characteristics. These are applied successfully in
Image fusion is the process that combines
image processing field. Its excellent characteristic
information in multiple images of the same scene.
in one-dimension information can’t be extended to
These images may be captured from different
two dimensions or multi-dimension. In that
sensors, acquired at different times, or having
wavelet which was spanning by one-dimensional
different spatial and spectral characteristics. The
wavelet has limited directivity
object of the image fusion is to retain the most
desirable characteristics of each image. With
Discrete Curvelet Transform
the availability of multi-sensor data in
many fields, image fusion has been receiving
It is a special member of the emerging family of
increasing attention in the researches for a wide
multi scale geometric transforms which is the
spectrum of applications. We use the following
curvelet transform. It was developed in the last
four examples to illustrate the purpose of image
few years for the traditional multi scale
fusion.
representations such as wavelets to overcome
Fusion is a technique which keeps images
inherent. In this Curvelet transform is a multi
data as main research contents. It refers to the
scale pyramid function with many directions and
techniques that integrate multi-resolution images
positions at each and every length scale, and
of the same scene from multiple image sensor data
needle-shaped elements at the fine scales. The
or integrate multi-images of the same scene for
pyramid is non-standard. Then Curvelet have
different times from one image sensor [1]. In this
useful geometric features and then set them apart
image fusion algorithm based on Wavelet
Patil. Sujatha, IJECS Volume 4 Issue 1 January, 2015 Page No.10072-10077
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from wavelets and the likes. For an instance, the
Curvelet obey a parabolic scaling relation, then
each element has an envelope for which is aligned
along a “ridge” of length and width. Then we
postpone mathematical treatment of the Curvelet
transform, and then the focus instead on the
reasons on one might care about the new
transformation and by the extension. That’s why it
might be important to develop accurate discrete
Curvelet transforms.
In the discrete curvelet transform twodimensional Cartesian coordinate system, we use
as a block region with the same center to replace it
(see fig 1).Then local window in Cartesian
coordinate system is expressed as
Here
Fig.1 Discrete curvelet tiling of space of
frequency
Continuous curvelet transform
In two-dimensional space , x stands for spatial
domain variable, stands for frequency domain
variable, r, express polar cordinates. First a
couple of window functions should be brought,
W(r) and V (t) separately express radius window
and corner window, W is supported in
,
V is supported in t [−1,1] , then permitting
condition should be satisfied
For all scales of j
, frequency window of
Fourier frequency domain is expressed as follows
In this | j / 2| stands for j / 2 rounding operation.
There are main differences of dilation factor
between V and W. In the time domain, dilation
factor of W is
shorter, dilation factor of W is
Longer, that is 2 width lengths, this is also
called as anisotropy scaling relation stands for a
wedge window in polar coordinates, and it is
expressed such as Fig.2:
Fig.2 Example of an image with acceptable
resolution
FUSION ALGORITHM
There are the three levels of fusion; those
are namely pixel level fusion, feature level fusion
and decision level fusion [3]. In this project we
adopted the pixel level fusion. Then we can take
operation on pixel directly, and then the fused
image could be obtained. For the source image we
can keep as more information as possible.
Because the Wavelet Transform takes block based
operation to approach the singularity. Thus
isotropic will be expressed the geometry of
singularity is ignored. The Curvelet Transform
takes wedge base to approach the singularity. It
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has the angle directivity compared with the
Wavelets, and an isotropy will be expressed.
When we approaches the direction of base
matches
the
geometry
of
singularity
characteristics,
Then the Curvelet coefficients will be bigger [4].
First, we need to pre-processing, and then cut the
same scale from waiting of fused images
according to selected regions of a sources image.
Subsequently, after that we are dividing the
images into sub-images which are different scales
by Wavelet Transform. Then the local Curvelet
Transforms of every sub-image should be taken,
as its sub-blocks are different from each others on
scales change. The steps of using Curvelet
Transform to fuse two images are as follows
 We can correct original images and
distortion image so that the two of the
image
have
similar
probability
distribution. Then Wavelet coefficient are
similar component will stay in the same
magnitude .and Resample and registration
of original images.
 By using the Wavelet Transform to
decompose original images into subbands.in that one low-frequency which is
approximate component and three highfrequency detail components which are
horizontal l, vertical and diagonal.
 Here we are taken the Curvelet Transform
of individual acquired low frequency
approximate
component
and
high
frequency detail components from both of
the original images ,in that the
neighborhood interpolation method is used
and the details of gray can’t be changed in
the fused images.
 According to the definite standard to fuse
images, the local area variance is chose to
measure definition for low frequency
component. First, divide low-frequency
into individual four square subblocks which are
( 3×3 or 5× 5 ),
then calculate local area variance of the
current sub-block:
 Where,
stands for lowfrequency, coefficient (approximation)
mean of original images. If variance is
bigger, then it shows that the local
contrast of original image is bigger, this is
nothing but shown in below
 The
other
components
activity
is defined as a fusion standard
of high-frequency components. First, the
images are divide high-frequency subband into sub-blocks, and then calculate
the STD of sub-blocks.
In which,
on.
means (3×3 or 5× 5), and so
 The reconstructed images will be fusion
images .when all sub band are inverse
transformation of the all coefficients
NON-SUBSAMPLED CONTOURLETS AND
FILTER BANKS
Non-sub sampled Contourlet Transform:
Fig. 3.
Non-sub sampled Contourlet
transform. (a) NSFB structure that implements
the NSCT. (b) Idealized frequency partitioning
obtained with the pro-posed structure.
Patil. Sujatha, IJECS Volume 4 Issue 1 January, 2015 Page No.10072-10077
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The above figure shows the proposed NSCT.
The structure consists in a bank of filters that
splits the 2-D frequency plane in the sub-bands
which is show in the figure (3-b). Our proposed
transformation can be divided into two shiftinvariant parts:
1) Pyramid structure that ensures the
Multiscale property
2) Directional Filter Bank (DFB) structure that
gives directionality.
Non-sub sampled Pyramid (NSP):
The multi focus property of the NSCT is
obtained from a shift-invariant filtering structure
that achieves sub band decomposition likely to
Laplacian pyramid. This can be achieved by using
two-channel non sub sampled 2-D filter banks.
Which is shown in Fig. 3 the figure demonstrate
that proposed non sub sampled pyramid (NSP)
decomposition with J=3 stages. So such expansion
is conceptually similar to the (1-D) NSWT
computed with the taros algorithm [9] and has J+1
redundancy [5]. Where J denotes the number of
decomposition stages the ideal pass band filter
support of the low-pass filter at the
stage is the
region
accordingly, the ideal support of
the equivalent high-pass filter is the complement
of the low-pass.
The filters for subsequent stages are obtained by
up sampling the filters of the first stage. This
gives the multi scale property without the need for
additional filter design. The proposed structure is
thus different from the separable NSWT. In
particular, one band pass image is produced at
each stage resulting in redundancy. By contrast,
the NSWT produces three directional images at
each stage, resulting in 3J+1 redundancy
Directional Filter Bank (DFB) structure that
gives directionality:
It is constructed by combining critically-sampled
two channel fan filter banks and resampling
operations. Finally, the result is a tree-structured
filter bank that splits the image in 2-D frequency
plane into directional wedges. A shift-invariant
directional expansion is obtained with a
nonsubsampled DFB (NSDFB). The NSDFB is
constructed by eliminating the down samplers and
up samplers in the DFB[6]. This can be done by
switching off the down samplers or up samplers in
each two channel filter bank in the DFB tree
structure and up sampling the filters respectively.
These results in a tree composed of two channels
NSFBs. which is shown in Fig. 4.this figure
demonstrate that the four channel decomposition.
Note that in the second level, the up sampled fan
filters,
checker board
frequency support. When combined with the
filters in the first level give the four directional
frequency decomposition which shown in Fig. 4.
The synthesis filter bank is obtained similarly.
Just like the critically sampled directional filter
bank, all filter banks are in the nonsubsampled
directional filter bank tree structure are obtained
from a single NSFB with fan filters .However,
each filter bank in the NSDFB tree has the same
computational complexity as that of the building
block NSFB.
Fig. 4. Four-channel nonsubsampled directional
filter bank constructed with two-channel fan filter
banks. (a) Filtering structure. The equivalent filter
in each channel (b) Corresponding frequency
decomposition.
RESULTS AND ANALYSIS
Hear we use multi-focus images after standard
testing. Fig.5 (a) shows that left-focus image, on
the tiger head was not clear Fig.5 (b) shows rightfocus image, hear the tiger leg was not clear. In
our paper three fusion algorithms are adopted to
contrast fusion effects. We separately use Discrete
Wavelet Transform (DWT), the Second
Generation Curvelet Transform that is Fast
Curvelet Transform (FCT); Non sub sampled
counterlet transform which is proposed in this
paper. According to DWT and FCT, We use
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different fusion standard in different sections. For
standard for high-frequency sub-band from other
the fusion we are choosing the low-frequency subscales. Fig.5 (c), (d), (e) separately express
band as fusion operator. Based on the biggest
corresponding fusion results.
absolute value is used as a fusion standard for
Fig.5 shows that two algorithms and
three high-frequency sub-band from the highest
proposed algorithm all acquire good fusion
scale. Choosing the fusion operator based the
results, focus difference has been
biggest local area variance is used as a fusion
TABLE I. EVALUATION OF THE MULTI-FOCUS IMAGE FUSION RESULTS
Fusion method
Entropy
Cross
RMS error
PSNR
correlation
DWT
7.2726
0.9875
0.43996
55.2625
FCT
7.7303
0.9822
0.61864
56.4732
NSCT
7.5011
0.9889
0.05248
73.7296
Fig.5 Multi-focus lab images and their image fusion. (a) left-focus (b) right-focus (c) fused image of DWT
(d) fused image of FCT (e) fused image of NSCT
Transform and non sub sampled Curvelet
eliminated, definition of original images have
Transform. It includes the multi resolution
been proved. The result of DWT looks worse by
analysis to check the ability in Wavelet transform,
contrast, we can see evident faintness in edges.
and also has better direction identification ability
False contours of edges appear in the FCT. We
for the edge feature of awaiting describing images
acquire the best subjective effect in NSCT. The
in the non-sub sampled Curvelet Transform. In
fused image is the clearest, and detail information
this method could better describe the edge
is kept as more. Table 1 show the experimental
direction of images, and analyzes feature of the
results of three methods
fused images better. According to this paper we
uses a Wavelet and the Second Generation
Curvelet Transform and also non-sub sampled
CONCLUSION
Curvelet Transform into fusion images and , then
In this paper we put forward a better image
makes deep research on fusion standards and this
fusion algorithm based on transformation
paper puts forward corresponding fusion projects.
techqunics Wavelet
Transform, the Second
Generation Curvelet
References
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