International Journal of Computer Science and Business Informatics
IJCSBI.ORG
Pixel Level Image Fusion:
A Neuro-Fuzzy Approach
Swathy Nair
Dept. of Electrical and Electronics Engineering
MA College of Engineering
Kothamangalam, Kerala, India
Bindu Elias
Dept. of Electrical and Electronics Engineering
MA College of Engineering
Kothamangalam, Kerala, India
VPS Naidu
Multi Sensor Data Fusion Lab
CSIR – National Aerospace Laboratories
Bangalore-17, India
ABSTRACT
Image fusion is done for integrating images obtained from different sensors, which outputs
a single image containing all relevant data from the source images. Five different image
fusion algorithms, SWT, fuzzy, Neuro-Fuzzy, Fuzzylet and Neuro-Fuzzylet algorithms has
been discussed and tested with two datasets (mono-spectral and multi-spectral). The results
are compared using fusion quality performance evaluation metrics. It was observed that
Neuro-Fuzzy gives better results than Fuzzy and SWT. Fuzzylet and Neuro-Fuzzylet were
obtained by combining Fuzzy and Neuro-Fuzzy respectively with SWT. It was observed
that Fuzzylet gives better results for mono-spectral images and on the other hand, NeuroFuzzylet had given better results for multi-spectral images at the cost of execution time.
Keywords
Image fusion, Fuzzy logic, image processing, Nero-fuzzy.
1. INTRODUCTION
For Intelligent systems, integration of information from different sensors
plays a great role. Image fusion is done for integrating images obtained from
different sensors, which outputs a single image containing all relevant data
from the source images and provides a human/machine perceivable result
with more useful complete information. Image Fusion has got great
importance in many applications such as object detection, automatic target
recognition, remote sensing, computer vision, flight vision, robotics etc.
This paper deals with a comparison of certain pixel level image fusion
techniques based on SWT, Fuzzy and Neuro-Fuzzy.
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Many methods have been proposed and implemented for image fusion [1].
Wavelet transform based image fusion has the merits of multi-scale and
multi-resolution. In [2], an approach of multi-sensor image fusion using
wavelet transform and principal component analysis (PCA) was proposed
and comparison of image fusion with different techniques based on fusion
quality performance metrics is done. Wavelets have a disadvantage of shift
variance which results in loss of edge information in fused image [3].
Stationary Wavelet Transform (SWT) solves this problem which is shift
invariant [4]. Since the concept of image fusion is not that certain and crisp,
Fuzzy logic and Neuro- Fuzzy logic are implemented for image fusion in
order to incorporate uncertainty to the images [5]. The help of Neuro-fuzzy
of fuzzy systems can achieve sensor fusion. The major difference between
neuro-fuzzy and fuzzy systems is that a neuro-fuzzy system can be trained
using the input data obtained from the sensors. The basic concept is to
associate the given sensory inputs with some decision outputs. After
developing the system, another group of input data is used to evaluate the
performance of the system. Algorithms for image fusion using Fuzzy and
Neuro-Fuzzy approaches are introduced in [6]. In [7], SWT with higher
level of decomposition is introduced and Fuzzy logic is incorporated into it
to form a novel algorithm called Fuzzylet.
This work is done as an extension to the work done in [7]. In this paper
Neuro-fuzzy based image fusion is tested and compared with SWT and
Fuzzy logic. An algorithm is formed in which Neuro-fuzzy is incorporated
into SWT which is named as Neuro-Fuzzylet and compared with Fuzzylet.
All the comparisons are done by evaluating Fusion Quality Performance
Metrics and results are verified with different sets of images. In this paper, it
is assumed that images to be fused are already registered.
2. IMAGE FUSION TECHNIQUES
Pixel level image fusion technique using SWT, Fuzzy and Fuzzylet are
explained in [7]. Matlab code for SWT based image fusion is given in [8].
In [7] it is proved that SWT with higher decomposition levels and Fuzzy
logic with greater number of membership functions gives the better result.
Fuzzylet algorithm is formed by combining SWT with 4 levels of
decomposition and Fuzzy with 5 membership functions. In this paper,
Neuro-Fuzzy logic is also tested and compared with the results obtained in
[7].
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2.1 Neuro-Fuzzy Approach to Image Fusion
Neural Network (NN) is a network which stores the experimental
knowledge and uses it for test data. Neuro- Fuzzy is a combination of
Artificial Neural Network (ANN) and Fuzzy logic. Using this method we
can train the system with input dataset and desired output. After training the
system, this system can be used for any other set of input data. A Neurofuzzy system is a fuzzy system which is trained by any of neural network
learning algorithms and according to the training data system parameters are
modified automatically. Implementation of Neuro-Fuzzy system is done
using ANFIS. ANFIS stands for Adaptive Neural Fuzzy Inference System.
The Fuzzy Inference System (FIS) is a model that does the following
mappings:
A set of input characteristics to input membership functions
Input membership functions to rules
Rules to a set of output characteristics
Output characteristics to output membership functions and
The output membership function to a single-valued output
A FIS has the following limitations:
Membership functions are fixed and somewhat arbitrarily chosen
Fuzzy Inference is applied for modeling systems in which the rules
are predetermined strictly based on the viewpoint of user to the
model.
The shape of the membership functions can be changed by changing the
membership function parameters as it is dependent on these parameters. In
an ordinary FIS, these parameters are selected arbitrarily in a trial and error
basis just looking into the available data. For applying fuzzy logic to a
system in which a collection of input-output data is available, a
predetermined parameter set will not be available. In some situations
arbitrary selection of parameters will not be sufficient to model a system in
a desired way. Instead of choosing member ship function parameters
arbitrarily, it would be more effective if the parameters are adjusting
themselves based upon the input data variation. In such cases, Neuroadaptive learning techniques can be incorporated into the FIS.
Using the input-output data given, ANFIS constructs a FIS whose
membership function parameters are tuned using any neural network
algorithm. This allows the FIS to learn from the data that are given as the
test data. There is an ANFIS editor toolbox in Matlab which does all this
learning. A Neuro-Fuzzy system can be schematically represented as in Fig
1.
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I1
Fuzzy
Inference
System
If
Fused image
I2
Registered input images
ANFIS
Figure 1. Schematic Diagram of Neuro-Fuzzy system
The ANFIS training structure obtained from Matlab ANFIS editor toolbox
for two inputs and three membership functions is as shown in Fig. 2.
Figure 2. ANFIS training structure obtained for two inputs and three membership
functions
In the ANFIS training structure shown in Fig.2. The leftmost nodes
represent the inputs and the rightmost node represents the output. The
branches are coded using different colors to indicate the logical operations
used in rule formation, that is, it indicates whether and, or or not is used to
combine antecedences to consequences.
For image fusion, the pixel values of input images and reference (desired)
image are given to the ANFIS for training the FIS, so that the system will
produce a fused image which is closer to the reference image from the input
images. Algorithm for image fusion using Neuro-Fuzzy logic (abbreviated
as NF(I 1 ,I 2 ) ) is as follows:
Step 1: Read the images ( I1 & I 2 ) to be fused into two variables
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Step 2: Obtain a training data, which is a matrix with three columns (2
columns of input data and one column of output data)
Step3: Obtain a check data, which is a matrix of pixel values of two
input images in column format
Step 4: Decide number and type of membership functions for both
the input images
Step5: Generate a FIS structure from the train data and train the FIS
Step 6: Provide check data to the FIS structure for processing and obtain
the output image in column format
Step 7: Convert the column form into matrix form to get the fused
image I f
In the case of dataset without a reference output, the 3rd column (output) of
the training data is given as the maximum of absolute pixel values of the
input images.
2.2 Neuro-Fuzzylet Algorithm for Image Fusion
In [7], Fuzzylet Image Fusion algorithm has been developed. In Fuzzylet
algorithm, Fuzzy logic is used to find out the approximate and detail
coefficients of SWT of input images. In Neuro-Fuzzylet, instead of Fuzzy
Neuro-fuzzy algorithm discussed in section 2.A is used to calculate the
SWT coefficients. The information flow diagram of image fusion using
Fuzzylet is shown in Fig. 3.
SWT
I1
Fuzzy
Inference
System
Registered input
images
Wavelet coefficient
maps
If
Fused image
Fused Wavelet
Coefficient map
SWT
I2
ISWT
ANFIS
Figure 3. Schematic diagram of Neuro-Fuzzylet Image Fusion Algorithm
The images to be fused I 1 and I 2 are decomposed into K ( k 1,2,..., K ) levels
using SWT. The resultant approximation and detail coefficients from I 1 are
I 1 1 AK ,
H
1
approximation
k
, 1Vk , 1Dk
and
k 1 ,2 ,...,K
.
Similarly
detail
from I 2 the
resultant
coefficients
are
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I2
A
2
K
,
H
2
k
, 2 V k , 2 Dk
using SWT as:
. The fused image I can be obtained
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A
k 1 ,2 ,...,K
If
f
K
Where
f
AK
f
1
,
f
f
H k , f V k , f Dk
k 1 ,2 ,...,K
AK 2 AK
2
(1)
(2)
H k NF ( 1 H k ,2 H k ), k 1,2 ,..., K
(3)
f
Vk NF ( 1Vk ,2 Vk ), k 1,2 ,..., K
(4)
f
Dk NF ( 1 Dk ,2 Dk ), k 1,2 ,..., K
(5)
Where, the function NF ( a , b ) is a Neuro-Fuzzy logic based image fusion
algorithm described in section 2.A.
3. IMAGE FUSION QUALITY EVALUATION INDICES
The quality of fused images obtained from different algorithms (SWT,
Fuzzy, Neuro-Fuzzy, Fuzzylet and Neuro-Fuzzylet) is compared using
Fusion Quality Performance Evaluation Indices. In this paper, two datasets
are used for the evaluation of algorithms. One among the datasets has a
reference image to which the fused image is compared while the other is not
having a reference image. So for the two datasets different evaluation
indices are used. Evaluation indices are calculated for all algorithms and
compared to find out the best algorithm.
A. With Reference Image
For datasets having reference image, fusion quality could be evaluated using
the following evaluation indices:
1. Root Mean Square Error(RMSE)
RMSE is computed as the root mean square error of the
corresponding pixels in the reference image I r and the fused image
I f . The RMSE between a reference image and the fused image is
given by:
RMSE
1
MN
I
M
N
i 1 j 1
r
( i, j ) I f ( i, j )
(6)
Where I f (i, j ) and I r (i, j ) are the gray value of fused image and
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reference image respectively at index (i, j ) . For better quality
images, the root mean square error should be less.
2. Peak Signal to Noise Ratio (PSNR)
Peak signal to noise ratio (PSNR) value will be high when the fused
and the ground truth images are comparable. Higher value implies
better fusion. PSNR can be calculated as:
L2
PSNR 20 log10
RMSE
(7)
Where, RMSE is the root mean square error and L is the number of
gray levels in the image.
3. Relative dimensionless global error in synthesis(ERGAS)
Relative dimensionless global error in synthesis (ERGAS) calculates
the amount of spectral distortion in the image it is given by:
ERGAS 100
h
l
1
B
RMSE ( b )
m( b )
b 1
B
2
(8)
Where, h is the resolution ratio, m(b) is the mean of bth band and B is
l
the number of bands.
4. Structural Content (SC)
Structural content can be calculated by using the equation:
I
M
SC
N
i 1 j 1
M N
f
i 1 j 1
r
( i, j )
I ( i , j )
(9)
Structural content should be 1 for fused image identical to the
reference image.
5. Error Image (EI)
The error image is computed as the difference between
corresponding pixels of reference and fused image. Image of better
fusion quality would have less error and an ideal fusion results in a
complete black error image.
EI I r I f
(10)
B. Without Reference Image
Evaluation indices that are used for datasets without reference image
are:
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1. Entropy (H)
Entropy is used to measure the information content of an image.
Entropy is sensitive to noise and other unwanted rapid fluctuations.
An image with high information content would have high entropy.
Entropy is defined as:
H sum p log2 p
(11)
Where, p contains the histogram counts returned from the Matlab
function „imhist‟.
2. Mean (m)
Mean gives the mean pixel value, which is formulated as:
m
1
MN
I
M
N
i 1 j 1
f
( i, j )
(12)
Where, I f (i, j ) is the gray value of fused image at index (i, j ) , MxN
is the size of the image.
3. Standard Deviation (SD)
It is known that standard deviation is composed of the signal and
noise parts. This metric would be more efficient in the absence of
noise. It measures the contrast in the fused image. An image with
high contrast would have a high standard deviation. SD is given by:
SD
1
MN
I
M
N
i 1 j 1
f
( i, j ) m
(13)
Where, m is the mean pixel value of the fused image.
4. Spatial Frequency (SF)
This frequency in spatial domain indicates the overall activity level
in the image. Image with high spatial frequency offers better quality.
It can be calculated as
Row Frequency (RF):
RF
1
MN
I
M 1N 1
i 0 j 1
f
( i , j ) I f ( i , j 1 )2
Column Frequency (CF):
1 N 1 M
CF
I f (i, j ) I f (i 1, j ) 2
MN j 0 i 1
Spatial Frequency (SF):
SF RF 2 CF 2
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(15)
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5. Cross Entropy (CE)
Cross-entropy evaluates the similarity in information content
between input images ( I 1 & I 2 ) and fused image. Better fusion
result would have low cross entropy. Cross entropy can be calculated
as:
CE I 1 , I 2 ; I f
CE I 1 ; I f CE I 2 ; I f
(17)
2
Where, CE I 1 ; I f sum p i log2 p i
pi
CE I 2 ; I
f
1
1
pi
2
sum p i2 log 2
pi
f
f
p i is the normalized histogram of the image I.
6. Fusion Factor(FF)
Fusion factor of two input images ( I 1 & I 2 ) and fused image ( I f ) is
given by:
FF I 1 f I 2 f
(18)
P
Where, I 1 f sum Pi i log i i
Pi Pi
1 f
1 f
Pi2 1i f
I 2 f sum Pi2 i f log
Pi2 Pi f
1
f
Pi1 & Pi f are the probability density functions in the
individual images and
Pi1i f is probability density function of both images
together.
FF indicates the amount information present in fused image from
both the images. Hence, higher value of FF indicates good fusion
quality. But it does not give the indication that the information are
fused symmetrically. For that another metrics called fusion
symmetry is used.
7. Fusion Symmetry(FS)
Fusion symmetry indicates how symmetrically the information from
input images is fused to obtain the fused image. It is given by:
I1 f
0.5
FS abs
I1 f I 2 f
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Since this metric is a symmetry factor, from the equation it is clear
that its value should be as low as possible so that the fused image
would contain the features of both input images. Fusion quality
depends on degree of Fusion symmetry.
8. Fusion Quality Index(FQI)
Fusion Quality Index is given by:
FQI sum c( w ) ( w )QI ( I 1 , I f | w ) ( 1 ( w ))QI ( I 1 , I f | w )
Where,
( w )
i1
(20)
2
i1 i2 2
2
computed
over
a
window;
2
2
c( w ) max( i1 , i2 ) over a window & QI ( I1 , I f | w ) is the
quality index over a window for a given source image and fused
image.
The range of this metric is 0 to 1. One indicates the fused image
contains all the information from the source images. FQI of a better
fusion would have maximum value in between 0 & 1.
9. Execution Time (Et)
It gives the time taken to execute the algorithm.
4. RESULTS AND DISCUSSIONS
The results obtained in [7] are taken and compared with Neuro-Fuzzy and
Neuro-Fuzzylet fusion results. For experimentation, two datasets are taken.
Dataset-1 is of CSIR- NAL indigenously developed SARAS images (monospectral), which consists of a reference image as shown in Fig. 2 and input
images, which are obtained by blurring the reference image as shown in Fig.
3. The fusion techniques are further tested using another dataset; Dataset-2
which is a multispectral dataset consists of a Low Light TV (LLTV) image
and a Forward Looking IR (FLIR) as inputs. Reference image is not
available for this dataset. Different fusion techniques are compared using
the fusion quality performance evaluation metrics described in section 3.
A. Dataset-1
As mentioned before, Dataset-1 consists of one reference image ( I r ) and 2
input images ( I 1 and I 2 ) of SARAS as shown in Fig. 4 and 5.
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Fig. 4 Reference image of SARAS ( I r )
Fig. 5 Input images of SARAS ( I 1 and I 2 )
The fusion techniques are tested one by one on Dataset-1 in Matlab. In SWT
algorithm, it is observed that fusion quality increases with the increase in
levels of decomposition at the cost of execution time and it is found out that
fusion results with 4 decomposition levels of SWT gives the better results
[7]. In Fuzzy logic based algorithm, Sugeno FIS with 5 membership
function had given better results. Fuzzylet algorithm is formed by
combining SWT with 4 decomposition levels and Fuzzy with 5 membership
functions [7]. ANFIS training is done to the FIS to get Neuro-fuzzy
algorithm. Here also number of membership functions can be varied.
Performance of image fusion using 3 and 5 membership functions with
ANFIS is tabulated in Table-1. From the table, it is observed that there is no
improvement in evaluation indices by increasing the number of membership
function and execution time increases with increase in membership
functions. So, ANFIS with 3 membership functions is selected for
evaluation. For formulating Neuro-Fuzzylet, the fuzzy function is replaced
with Neuro-fuzzy function in the Fuzzylet algorithm. The performance
metrics obtained for different methods is tabulated in Table-2 for
comparison.
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No:of
MFs
3
5
Entropy
3.578
3.548
Algorithm
SWT
Fuzzy
Neurofuzzy
Fuzzylet
Neurofuzzylet
Table-1 Comparison of the Performance metrics obtained using different
membership functions of ANFIS
Performance evaluation metrics
RMSE PSNR
SD
ERGAS SF
SC
CE
FF
FQI
0.016
66.542 0.199 1.828
0.067 1.003 4.682 3.377 0.816
0.016
65.993 0.198 1.844
0.062 0.986 4.714 3.376 0.814
FS
0.018
0.012
Table-2 Comparison of the Performance metrics obtained from five image fusion
techniques for Dataset-1
Performance evaluation metrics
Entropy RMSE PSNR
SD
ERGAS SF
SC
CE
FF
FQI
3.89
0.007
69.944 0.195 0.744
0.066 1.002 4.215 3.378 0.811
3.578
0.031
63.142 0.195 3.560
0.046 0.981 5.228 3.358 0.771
3.578
0.016
66.542 0.199 1.828
0.067 1.003 4.682 3.376 0.816
4.061
0.005
71.062 0.198 0.224
0.068 1.000 3.255 3.389 0.882
3.912
0.006
70.165
0.066 1.002 3.626 3.379 0.848
0.199 0.771
From the table it is clear that Neuro-Fuzzy gives better results than fuzzy
(see values shown in red). But when it is combined with SWT, fuzzy gives
better results. So out of the five algorithms, Fuzzylet gives best fusion
results (see bold values) for Dataset-1. The fused and error images for all the
algorithms are given from Fig. 6 and 7.
Fig. 6 Fused image using SWT, Fuzzy, Neuro-Fuzzy, Fuzzylet and Neuro-Fuzzylet
respectively for Dataset-1
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Et(sec.)
0.292
0.473
FS
0.016
0.009
0.015
0.013
0.017
Et(sec.)
0.826
0.455
0.292
3.324
3.212
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Fig. 7 Error image using SWT, Fuzzy, Neuro-Fuzzy, Fuzzylet and Neuro-Fuzzylet
respectively for Dataset-1
B. Dataset-2
Dataset-2 is a multispectral data set consists of LLTV ( I1 ) and FLIR ( I 2 )
images as inputs as shown in Fig. 8. Reference image is not available for
this dataset, hence evaluation metrics explained in section 3.B is used for
the comparison.
Human eye is sensitive to a limited range of the electromagnetic spectrum as
well as to low light intensity. To obtain data that cannot be sensed by the
eye, one can use sensor data such as IR sensors or image intensifier night
time sensors. The human observer may use data from multiple sensors. For
example, using the visual channel as well as the IR channel can substantially
improve the ability to detect a target. This can be observed in the input
images shown in Fig.8. In the LLTV image, the bushes, trees etc are more
visible while in FLIR image, the roads are more visible. The fused image
should render the necessary features of both images.
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Fig. 8 Images to be fused (LLTV image and FLIR image)
Fused images using all the five algorithms are shown in Fig. 9. It is
observed that in SWT result, all the features of both input images are visible
but with poor clarity. Rendering of land texture, visual quality of image, etc
are poor. In Fuzzy and Neuro-Fuzzy, it is observed that IR features are
prominent. Its rendering quality is poor with dark texture and over enhanced
view of elements like bushes, trees, etc.
The training data for ANFIS training is selected as mentioned in section
1.A. It is observed that, with the use of Fuzzylet and Neuro-Fuzzylet
algorithm, both Visible and IR features are equally rendered maintaining the
quality of both input image. So visually, Fuzzylet and Neuro-Fuzzylet
provides better result. This can be further evaluated by evaluating fusion
quality metrics tabulated in Table-3 for all the five algorithms.
Table-3 Comparison of the Performance metrics obtained from five image fusion
techniques for Dataset-2
Agorithm
Performance evaluation metrics
Entropy
SD
CE
FF
FS
FQI
Et(sec.)
SWT
7.241
0.187
4.538
2.184
0.023
0.597
0.379
Fuzzy
7.095
0.217
2.185
0.023
0.496
0.428
0.959
Neuro-Fuzzy
7.301
0.283
2.308
2.228
0.033
0.437
0.314
Fuzzylet
7.296
0.288
4.535
2.346
0.043
1.225
0.698
Neuro-Fuzzylet
4.355
0.922
7.321
0.296
2.419
0.045
0.698
From the table it is clear that Neuro-Fuzzy gives better results than Fuzzy
and SWT (see values shown in red).When it is combined with SWT, NeuroFuzzy gives better results. So out of the five algorithms, Neuro-Fuzzylet
gives best fusion results (see bold values) for multispectral images.
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Fig. 9 Fused image using SWT, Fuzzy, Neuro-Fuzzy, Fuzzylet and Neuro-Fuzzylet
respectively for Dataset-2
5. CONCLUSION
Five different image fusion algorithms, SWT, fuzzy, Neuro-Fuzzy, Fuzzylet
and Neuro-Fuzzylet algorithms were discussed and tested with two datasets
(monospectral and multispectral). The results were compared using fusion
quality performance evaluation metrics. It was observed that Neuro-Fuzzy
gives better results than Fuzzy and SWT. Fuzzylet and Neuro-Fuzzylet were
obtained by combining Fuzzy and Neuro-Fuzzy respectively with SWT. It
was observed that Fuzzylet gives better results for monospectral images and
on the other hand, Neuro-Fuzzylet had given better results for multispectral
images at the cost of execution time. It is hoped that the proposed algorithm
can be extended for real time and color images.
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[3] Andrew. P. Bradley, “Shift-invariance in the Discrete Wavelet Transform”, in Proc.
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[4] Pusit Borwonwatanadelok, Wirat Rattanapitakand Somkait Udomhunsakul, “MultiFocus Image Fusion based on Stationary Wavelet Transform and extended Spatial
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[5] R. Maruthi and K. Sankarasubramanian, “Pixel Level Multifocus Image Fusion Based
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[6] Harpreet Singh, Jyoti Raj and Gulsheen Kaur, “Image Fusion using Fuzzy Logic and
Applications”, Budapest Hungary, 25-29 July. 2004.
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21/2/2014.
Accessed
on
This paper may be cited as:
Nair, S., Elias, B. and Naidu V., 2014. Pixel Level Image Fusion: A NeuroFuzzy Approach. International Journal of Computer Science and Business
Informatics, Vol. 12, No. 1, pp. 71-86.
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