Fusion of Images using DWT and fDCT Methods

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 04 Issue: 08 | Aug -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 489
Fusion of images using DWT and fDCT methods
1Shivanand R. Kollannavar
1PG student, M.tech in Digital Electronics, Department of E&CE,
SDM college of Engineering and Technology,Dharwad,
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Abstract - Image fusion methods has played an important
role in the development of extracting inherent image
information. The applications of image fusion are considered
in fields pertaining to medical imaging, military applications,
commercial applications and satellite imagery. This
necessitates the development of more robust and effective
image fusion techniques. However, when it comes to
practicality of these techniques such as noise considerations
(AWGN based channel noise, etc.), many these methods suffer
limitations. In this paper, two stages are considered, the first
stage consists of pre-processing where the Gaussian noise is
considered along with the removal of noise using median
based filtering approach. The second stage consists of image
fusion using DWT and fDCT based methods. A comparative
analysis is performed of the two methods. Image quality
assessment concerning measures such as PSNR, SNR, SSIM,
MAE, Gradient and standard deviation were performed. Itwas
observed that the fDCT based image fusion methodperformed
with comparatively higher measures than the DWT given the
similar initial conditions. Experimental results show that the
coefficients considering the scale and orientation of fDCT
provides a higher accuracy than compared to coefficients
obtained from DWT method.
Key Words: Gamma correction, DWT, fDCT, Median
Filtering, Gaussian noise,static filtering, fDCTwrapping.
1. INTRODUCTION
Image fusion plays a significant role in many of pre-sent’s
day’s applications ranging from military applica-tions,
healthcare industries, satellite imagery and wireless
systems. The requirement of effectiveandrobusttechniques
for the process of fusion of image is more than necessary in
present day’s scenario. Some of the applications in medical
image fusion include detection and diagnosis of modular
related disorders and conditions. In military applications,
image fusion helps in identifying enemy intrusion through
advanced surveillance system.
However, a major limitation observed in the process of
image fusion is that of practicality in real time applications.
In the context of wireless systems, the data undergoes
transmission stage, channel and receiver stages where it
encounters many types of noise and its effects. For example,
in the transmission stage, during the sampling and
quantization, the image is affected by what is known as
aliasing and quantization noise which is caused due to
sampling errors. When it sent for the encoding process, the
image is affected by certain noise. When the data is
transmitted through a channel, the image is affected what is
known as Additive White Gaussian Noise (AWGN) which
alters the characteristics of the image significantly.
Another major limitation is that of the illuminationiscaused
due to short dynamic range that results from the type of
image acquisition device. Many methods for im-age
enhancement considering the spatial domain is pro-posed,
however, in the context of image fusion, the scope of image
enhancement remains to be dealt with. Image fusion
methods considering the noise factor and the illumination
conditions are limited which otherwise has a greater scope
of applications and significance.
Methods of image fusion mainly involve temporal based
methods which applies imaging techniques on a time se-ries
domain. The implication of transformation function such as
Discrete Wavelet Transformation (DWT), Curve let
transformation, etc are yet to be explored in the context of
image fusion.
It is observed that, though there are many methods which
are available in the context of image fusion, the practicality
associated with these techniques are very li-mited. Hence in
the proposed work, image fusion tech-niques are
implemented considering the aspects of image illumination
and noise factors of the image. A comparative analysis is
performed based on the two methods proposed in the
previous section.
The paper is structured as follows; the first section deals
with the introduction which signifiestheimportanceandthe
limitations pertaining to image fusion methods. The second
section deals with the literature survey, the third section
deals with the proposed system and implementation. The
fourth section deals with the results and discussions
followed by conclusion.
1.1 LITERUTURE SURVEY
Image fusion is a process of combining relevant informa-
tion of images into single image information in view to
enhance the image quality assessment. Deepak Kumar et. al
[1] proposes a generalized techniques that are involved in
image fusion process. Some of the methodsmentionedinthis
paper are averaging method, principal component analysis

and discretewavelet transformation(DWT) to name afew.A
comparative analysis is also performed re-garding the
significance and limitations of each method in view of the
image quality.
Y. Zhang et. al [2] performed a study inunderstandingthe
process of image fusion along with its significance and
limitations. Among the various image fusion techniques, the
significant techniques involve HIS (Intensity, Hue and
Saturation) based image fusion, PCA (Principal Component
Analysis) based image fusion arithmetic combinations and
wavelet fusion. Major limitations in these methods involved
variations in parameters concerning spherical distribution,
band combination and colour distortion problems. Hence,
there is a requirement to enhancement the quality of the
image.
Harry NGross et. al [3] proposed an applicationinvolving
the improvement of image enhancement by considering a
spectral mixture analysis and image fusion techniques. The
spectral mixture analysis is performed to obtain higher
spatialaccuracy which is implementedthroughconventional
unmixing to generate fraction images. Further fusion
methodsareimplementedtocombinethespectralandspatial
images to form a single image which provides more
information to the user.
Methods of evaluation for to assess the performance of
image fusion techniques was proposed by Alparone et. al [4]
concerning the multispectral high resolution pan chromatic
images, The radiometric anddistortionmeasurementswhich
are observed in the pan images are encapsulated in a specific
measurement whichaccounts for factors such as variationin
contrast, mean bias and spectral distortion. Comparitive
analysis is performed among different image fusionmethods
using this quality assessment metrics.
M. Gonzalez et. al [5] proposed a new method involving
fusion of multispectral and panchromatic images using IHS
and PCA based methods which is performed on a wavelet
based decomposition technique. The image is first
decomposed using the wavelet transformation to extract the
detail coefficients which is then processed usingIHSandPCA
methods which consecutively merges both spectral and
spatial aspects of the image leading to higher resolution of
the image. Experimental results showed that when using
undecimated algorithm is used in wavelet transformation,
improved performance in the methods was observed.
Myungjin Choi [6] proposed a new method involving IHS
based image fusion, the significance of this method was to
fuse massive amount of images which are obtained from the
satelliteimages, further a trade-off is performedbetweenthe
spectral and spatial aspects of the image to improve the
image qualityassessments. The significanceofthisapproach
is easy and fast implementation of the image fusion process.
C. Pohl and J. L Van Genderen [7]performedanevaluation
on the different methods involving image fusion along with
its possible applications. The methods of image fusion in this
works mainly involve pixel based image fusion. The
geometric correction of the image data concernsfactorssuch
as geometric model, groundcontrol points,digitalevaluation
model and resampling methods. The objectives of image
fusion involves sharpening of images, improving the
geometric corrections and enhancing featuresnotvisibleina
single data alone. Another aspect observed in thisworkisthe
significance of band selection and its role in the image fusion
process.
Yoonsuk Choi and Shahram Latifi [8] performed a review
on the different image fusion techniquesforsatelliteim-ages.
The main focus of the work is the reviewing of the
background of the transformation theory, analysis of
standard colours and contour-let based schemes, hybrid
schemesandwavelettransformationbasedschemes.Ofthese
methods, the wavelet transformation based image fusion
produced improved results in context of standardizationand
minimization of colour distortion. This inturn has better
performance as compared to IHS and PCA based methods.
This is further signified in the following work.
Krista Amolins et. al [9] performed astudyofapplications
of image fusion considering the wavelet based
transformations. It was observed that the standard image
fusion methods such as IHS and PCA based methods that
though the spatial information is improved in the image
information, the colour distortion was produced which
significantly deteriorates the quality of the image data.
Various methods of wavelet based transformation was
applied for image fusion process and it was observed that
even the simplest of wavelet based image fusion produced
improved quality of performance in the context of image
quality assessment as compared to the standard methods of
fusion techniques such as IHS and PCA. This is especially
prevalent in panchromatic satellite imagery.
Myungjin Choi et. al [10] emphasied the use of curvelet
transformation forimage fusion. A comparativeanalysiswas
compared to other standard methods such as IHS, PCA and
wavelet based methods. The main objective of image fusion
was to obtain good details of the spectral and spatial
information of the image data. However, the DWT method
produced better accuracy in the context of spatial
information by representing the edges. The proposed
curvelet transformation resulted in better accuracy in terms
of representing the edges in the image which further
improved the accuracy of the image spatial information.
Filippo Nencini et. al [11] proposed an image fusion me-
thod using curvelet based transformation considering the
panchromatic images. First, the directional detail edge
coefficients were derived which further soft thresholded to
reduce the noise. It was observed that the noise reduction

was better when compared to Discrete Wavelet
Transformation (DWT). Experimental results showed an
improved result in image quality such as image sharpening
and reduction in local inaccuracies.
1.2 PROPOSED SYSTEM
The proposed system is basically divided into three
modules involving pre-processing, image fusion using
Discrete Wavelet Transformation and image fusion using
Discrete Curvelet Transformation. The pre-processingstage
consists of addition of noise and noise removal me-thod.The
fusion method concerning the DWT considers the image
fusion method based on the haarwaveletandthedaubechies
basis function, and finally the curvelet based method
considers the wrapping and usage of 2nd order static filter
for fusion of image.
Gamma
correction
Gaussian
Noise
Median
filtering
Image 1
Image 2
Select region to blur
image
Image 1 Image 2
Select basis function
Select level of
decomposition
AC DC
Perform mean based
image fusion
Perform fDCT wrapping
Set scale and orientation
Perform 2nd order static filtering
Select level of
decomposition
Perform inverse fDCT wrapping
Image Pre-processing
Discrete Wavelet
Transform
Discrete Curvelet Transform
Fused image Fused image
Fig 1: block diagram of proposed System Architecture
The functionalities mentioned above will have an in depth
analysis with respect to its working. This is given as follows.
a. Pre-processing
As mentioned in the previous section, the pre-processing
stage consists of two stages involving image enhancement
and noise removal process. The image enhancement is
performed using gamma correction method which is based
on spatial based image enhancement having an adjusting
parameter of gamma factor that depends on the image
considered. The gamma correction method is given as
follows,
(1)
Where, I (x, y)  input image,
T(x, y)  transformed image
The gamma correction method considering thetransformed
image is given as,
(2)
Where,  gamma factor
Once, the image is enhanced, it is further processed
considering the noise removal process, the noiseconsidered
in this context is the Gaussian noise, which reflects the
channel noise (AdditivewhiteGaussianNoise:AWGN)thatis
prevalent in the wireless communication system. The
characteristic observed in the Gaussian noise is an implicit
random distribution of high intensity values (1’s and 0’s)
which makes distorts the respective histogram of the image.
The Gaussian noise distribution considered is given in eq. X
as follows,
(3)
Where,
z gray level of the image
 Mean value
 Standard deviation
The filtering method consideredinthiscontextisthemedian
filter (also known as the averaging filter). Thesignificance of
median filtering is its ability to preserve the edges in an
image while maintaining minimum system and
computational complexity. The median filter calculates the
median which is obtained from the defined pattern from the
adjacent pixels in numerical order, consequently the
computed median value is replaced with the middle pixel
value. The size of mask considered in this filter is of order 3
X 3 which is given as follows,
b. Discrete Wavelet Decomposition
In the decomposition stage, a preferable technique used
in decomposition stage is the Discrete Wavelet
Transformation (DWT), the selection criteria for DWT was
based on its computational efficiency, practicality and
simplicity.
The pre-processed image data is further multiplied with the
basis function considering the ‘haar’ and the ‘db4’. This
results in two types coefficients mainly derived from low
pass filter and the high pass filter known as Approximation
Coefficients (AC) and the Detail Coefficients (DC)
respectively. The decomposition is performed up to 3 level,
however, this parameter could be adjusted considering the
nature of image. The image fusion method consideredinthis
context is the mean based image fusion. In this method, the
mean of AC components of two images is performed, along
with computing the mean of DC components of two images,

upon reconstruction of the image (considering the updated
AC and DC components) using the inverse DWT, the fused
image is obtained.
c. Fast Discrete Curvelet Transformation (fDCT)
The pre-processed image is first transformed into real
valued curvelet components, the probabilities for the
curvelet at the finest level is type wavelet. The number of
scales considering the coarsest wavelet level is givenin eq. X
as shown below,
The number of angles st the 2nd coarsest level considering a
minimum of 8 must be a multiple of 4. The obtained curvelet
coefficients consists of two types mainly ‘sine’ and ‘cosine’
components in the case of real valued curvelet components
which is present in the first two quadrants and the last two
quadrants respectively. The scaling is performed on the
integer varying from finest to coarsest scale, and the
orientation (angle) varies from top-lestcornerandincreases
clockwise.
At level 3 decomposition the scaled and oriented curvelet
components are sent to the 2nd order static filtering which
controls the way the matrix boundaries are added, This
method is considered equivalent to the structuring element
used in the morphological operations. The number of 1’s
(considering the pixel intensities) in the imageisconsidered
for which zeros and ones are padded consideringsymmetry.
Finally an inverse fDCT wrapping is performed to
reconstruct the fused image using the curvelet components
post filtering process.
2. RESULTS AND DISCUSSIONS
This section deals with the obtained simulation results along
with its description and significance with respect to the
project. The parametric evaluations along withitsdescription
are also mentioned in this section.
The pre-processing stage in the proposed system consists of
image enhancement using gamma correction and noise
removal process using the median based filtering method.
The pre-processed image is measured by two measures
namely Peak Signal to noise Ratio (PSNR)andSignaltoNoise
Ratio (SNR).
Peak signal to noise ratio (PSNR): Peak signal-to-noise
ratio, often abbreviated PSNR, is an engineering termfor the
ratio between the maximum possible power of a signal and
the power of corrupting noise that affects the fidelity of its
representation. Because many signals have a very wide
dynamic range, PSNR is usually expressed in terms of the
logarithmic decibel scale.
Signal to Noise Ratio (SNR): Signal-to-noise ratio is defined
as the ratio of the power ofa signal (meaningful information)
and the power of background noise (unwanted signal)
Where, P is average power. Both signal and noise power
must be measured at the same and within the same system
bandwidth.
Structural Similarity Index (SSIM)
The structural similarity (SSIM) index is a method for
predicting the perceived quality of digital television and
cinematic pictures, as well as other kinds of digital images
and videos. SSIM is used for measuring the similarity
between two images. The SSIM index is a full reference
metric; in other words, the measurement or prediction of
image quality is based on an initial uncompressed or
distortion-free image as reference.
Where,  average of x
 Average of y
 Variance of x
 Variance of y
 Covariance of x and y
,  stabilization of division with weak
denominator
Mean Absolute Error (MAE): It is defined as the measure of
two continuous variables which is given as follows,
It is also measured as the average vertical and horizontal
distance between each point Y-X.
Measures of analysis for image fusion method,
1. Standard deviation: The standard deviation is used to
measure the amount of variation which gives an estimate of
the range of values that is prevalent in the image data. Italso
gives an estimate of the validity of the population which is
used to derive statistical conclusions.
The overall observations for the images consideredaregiven
in the following table X as shown below for controlling
parameter as given in table 1

Table -1: controlling parameter
sl.no parameter value
1. Gamma factor 0.71
2. Noise scaling 2
3. compression scaling 0.62
4. image size 245 X
428
Table 2: Observations for DWT based image
fusion
sl.no Image PSNR SNR SSIM MAE Std.
Dev.
1. Image_1 30.33 25.40 1.4 0.95 58.12
2. Image_2 27.20 17.92 7.3 0.86 63.15
3. Image_3 35.85 31.35 0.46 0.989 46.10
4. Image_4 30.56 24.14 2.95 0.899 65.82
5. Image_5 34.84 28.94 0.65 0.98 48.56
6. Image_6 36.24 32.20 0.518 0.98 51.45
7. Image_7 36.30 31.76 0.53 0.98 73.53
8. Image_8 37.8 32.28 0.294 0.992 65.82
9. Image_9 34.06 29.17 0.782 0.97 54.48
10. Image_10 36.25 32.78 0.429 0.990 67.80
Table 3: observations for fDCT based image fusion
sl.no Image PSNR SNR SSIM MAE Std.
Dev.
1. Image_1 32.66 27.68 1.25 0.97 58.15
2. Image_2 25.63 16.35 7.9 0.83 63.15
3. Image_3 37.25 32.74 0.368 0.993 43.03
4. Image_4 25.91 19.49 4.925 0.754 63.17
5. Image_5 36.05 30.15 0.56 0.98 47.92
6. Image_6 37.30 33.27 0.32 0.99 51.42
7. Image_7 39.05 34.50 0.24 0.99 73.53
8. Image_8 39.71 34.17 0.226 0.994 63.17
9. Image_9 36.90 32.01 0.474 0.99 54.45
10. Image_10 35.10 31.63 0.380 0.991 66.80
3. CONCLUSIONS
The overall proposed method for image fusion method
involves mainly pre-processing,imagefusionusingDWT and
fDCT methods and a comparative analysis of the two
methods. Image quality assessment concerning measures
such as PSNR, SNR, SSIM, MAE, Gradient and standard
deviation were performed. It was observed that the fDCT
based image fusion method performed with comparatively
higher measures than the DWT given the similar initial
conditions. Therefore, the inference can be made that the
coefficients considering the scale and orientation of from
fDCT provides a higher accuracy than compared to
coefficients obtained from DWT method.
In future works, more image fusion techniques could be
considered for a varietyofapplicationsrangingfrommedical
diagnostics to satelliteimagery.Practicalityofthetechniques
could be tested on real time imaging data to test the
feasibility, performance and robustness of the image fusion
techniques, finally different methods of obtaining the
coefficients for image fusion could be identified which leads
to more effective methods of image fusion given for a
particular type of image.
ACKNOWLEDGEMENT
I am highly obliged to Department of Electronics and
communication Engineering, SDM College of Engineer-ing
and Technology.
REFERENCES
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[3]Gross, Harry N., and John R. Schott. "Application of
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(1998): 85-94.
[4]Alparone, Luciano, et al. "A global qualitymeasurementof
pan-sharpened multispectral imagery."IEEEGeoscience and
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[7]Pohl, Cle, and John L. Van Genderen. "Review article
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BIOGRAPHIES
Mr.SHIVANAND R.
KOLLANNAVAR
Graduated from Basaveshwar
Engineering College Bagalkot,
Karnataka, India in B.E
(Instrumentaion Technology)
in the year of 2015. He’s
currently pursuing his master
of technology in electronics
and communication from
SDMCET, Dharwad,
Karanataka, India in 2016-
2017. And his specialization
filed is digital electronics. And
during his course in the
masters he has done his
internship in V V Technologies
Tumakur.

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