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8/6/2019 Modified PCA based Image Fusion and its Quality Measure
http://slidepdf.com/reader/full/modified-pca-based-image-fusion-and-its-quality-measure 1/7
JOURNAL OF COMPUTING, VOLUME 3, ISSUE 4, APRIL 2011, ISSN 2151‐9617
HTTPS://SITES.GOOGLE.COM/SITE/JOURNALOFCOMPUTING/
WWW.JOURNALOFCOMPUTING.ORG 170
Modified PCA based Image Fusion and its
Quality Measure
Amit Kumar Sen , Subhadip Mukherjee and Amlan Chakrabarti
Abstract – Image Fusion is an emerging area of research in image processing and computer vision. This paper proposes an
algorithm which is based on the revised version of the traditional principal component analysis (PCA) technique and it overcomes
the shortcomings of the traditional PCA based algorithm. This algorithm is applied for fusing benchmark images and then the results
are compared with the results of traditional PCA based fusion in terms of image quality. The results shows that the quality of the
fused image by the proposed algorithm produces better result than the traditional PCA based technique.
Index Item – Image Fusion, Principal Component Analysis, Wavelet Transform, Luminance, Contrast, Correlation
Coefficient, Entropy, Mutual Information.
1. INTRODUCTION
Image Fusion is the process of combining
relevant information from two or more images into a
single image. The resulting image happens to be
more informative than each of the individual images.
Image Fusion is utilized in various applications like
medical imaging, aerial and satellite imaging, robot
vision, digital camera etc...
Image fusion techniques fall into two groups ‐ i. Discrete wavelet transform based and ii. Statistical
based. In Statistical based image fusion techniques
there are various techniques such as principal
component analysis (PCA) based and histogram
(HIS) transform based. There are also other image
fusion methods like Laplacian Pyramid Method.
This paper is organized in the following way: In
Section 2 we discuss the fundamentals of the PCA
algorithm. Section 3 briefs our proposed algorithm
which is the modified version of the traditional PCA
algorithm. In Section 4 we brief on the quality
measures that we have performed to find the
performance of our proposed technique. Section 5
discuses the experimental results. In Section 6 we
have compared our results with that obtained
through discrete wavelet technique (DWT).
Concluding remarks are presented in Section 7.
2. PRINCIPAL COMPONENT ANALYSIS
PCA is mathematically defined as an orthogonal
linear transformation that transforms the data to a
new coordinate system such that the greatest variance
by any projection of the data comes to lie on the first
coordinate (called the first principal component), the
second greatest variance on the second coordinate,
and so on. PCA is theoretically the optimum
transform for a given data in least square terms.
For a data matrix, XT
, with zero empirical mean (the empirical mean of the distribution has been
subtracted from the data set), where each row
represents a different repetition of the experiment,
and each column gives the results from a particular
probe, the PCA transformation is given by:
———————————————— Amit Kumar Sen Assistant Professor, Information Technology
Department, IMPS College of Engineering & Technology. Subhadip Mukherjee. Amlan Chakrabarti Assistant Professor, A.K.Choudhury, School of
Information Technology, University of Calcutta.
8/6/2019 Modified PCA based Image Fusion and its Quality Measure
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JOURNAL OF COMPUTING, VOLUME 3, ISSUE 4, APRIL 2011, ISSN 2151‐9617
HTTPS://SITES.GOOGLE.COM/SITE/JOURNALOFCOMPUTING/
WWW.JOURNALOFCOMPUTING.ORG 171
Where the matrix Σ is an m‐ by‐n diagonal matrix
with nonnegative
real
numbers
on
the
diagonal
and
W Σ VT is the singular value decomposition (svd) of
X.
3. MODIFIED PCA BASED IMAGE FUSION
ALGORITHM
PCA is a way of identifying patterns in data, and
expressing the data in such a way as to highlight their
similarities and dissimilarities. PCA fusion rule is, to
find the principal axis Eigen value of the
approximation images, calculate the corresponding
eigenvector, and the perform fusion on these
approximation images according to the principal
eigenvector. But there is a disadvantage in these
traditional PCA based image fusion. In traditional
PCA based algorithm [1] it may happen that all the
principal components are selected from the same
region of the image.
This drawback is taken care in our proposed
modification of the PCA algorithm. Our technique is
a window
based
approach
over
the
existing
PCA.
Here first we divide the images into some static
window blocks. Then we find the principal
eigenvector for each window block and perform
fusion on two corresponding window blocks of the
two images to be fused. This assures that the
principal component will be selected from each of the
window blocks.
The modified PCA Algorithm for image fusion is
discussed as below:
Step 1: Creation Window block for the images.
Each of the images is split into n window blocks
and the number of blocks for both images must be
same.
Step 2: Generation of data vectors for window
blocks:
The row and the column of every window block
is arranged to create data vector, i.e. for n window
block for first image creates the data vector X1 , X2 ,…, Xn and for second image creates the data vector Y1 ,
Y2 ,…, Yn.
Step 3: Finding the covariance matrix for the
window blocks.
The covariance between the two images is
calculated by means of covariance matrix matrix (C)
from the image data vectors of Step2. For the ith
window block of both the images the covariance is
calculated as follows:
C =
Step 4: Determining the eigenvectors and the
principal eigenvector.
The Eigen value of all the Eigen vectors are
calculated from the covariance matrix. The
eigenvector that has the maximum value for each of
the window blocks is called the principal Eigen
vector. i.e. the principal Eigen vector for all window
blocks are (x1 ,y1)T , (x2 ,y2)T … (xn ,yn)T.
Step 5: Calculation of the approximate weight
for every window block.
The approximate weight of every window blocks
is calculated by the following formula as given below.
For the ith window blocks
W (Ai) = xi/( xi + yi) and W (Bi) = yi/( xi + yi);
here Ai and Bi represents the ith window block of
the two images and (xi , yi) are the corresponding
principal Eigen vectors.
Step 6: Summing two corresponding window
block of images.
8/6/2019 Modified PCA based Image Fusion and its Quality Measure
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JOURNAL OF COMPUTING, VOLUME 3, ISSUE 4, APRIL 2011, ISSN 2151‐9617
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Adding of the approximation weight of two
corresponding window blocks and generating a new
fused window block. i.e. ith fused window block
F= A*W (Ai) + B*W (Bi).
Step 7: Aggregation of all fused window blocks.
Arranging all the fused window blocks and
getting the final fused image.
Figure 1 shows the sequence of steps for the
fusion process
.
Figure 1: Flow Chart of Modified PCA based
Algorithm
4. IMAGE QUALITY MEASURE
To check the quality of fused image we have chosen
eleven quality criteria. The image qualities are
being defined as follows:
Correlation Coefficient: It measures the degree of
correlation between the fused and the reference
images.
Cross Entropy: It reflect the information difference
between the fused and the reference image.
Entropy: It measures the richness of information in the fused image.
Mutual Information: It measures the information
shared between the fused image and the reference
image using histograms.
Mean Square Error: It measures the spatial
distortion introduced by fusion process.
Normalized least square Error: It indicates the
normalized difference between the fused and
reference image.
Relative Sift Mean: It indicates the amount of
information added or lost during fusion. Standard Deviation: It reflects the contrast of
image.
Spatial Frequency: It measures the clarity of fused
image.
Signal to noise ratio: It measures the ratio between
information and noise of fused image.
Warping Degree: It measures the level of optical
spectral distortion.
Contrast: It measures how similar contrasts of
images are.
Luminance: It measures how close the mean
luminance is between the images.
Now, quality of the fused image is measured
by some standard quality index. Among the
above mentioned quality factors; correlation
coefficient, contrast and luminance are used as
standard quality index. Standard quality index
is represented
by
a combination
of the
above
three.[4]
Q = (1)
Where is the correlation coefficient,
is the luminance and is the
contrast.
Creation of Window block for the
Generation of data vectors for window
Summing of two corresponding window block of images.
Calculation of the approximate weight of every window
Determining the eigenvector and then determine principal
Finding the covariance matrix for window blocks.
Aggregation of all fused window blocks
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JOURNAL OF COMPUTING, VOLUME 3, ISSUE 4, APRIL 2011, ISSN 2151‐9617
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Here x and y are the pixel values, and are
the contrast of X and Y images. This quality is
measured by breaking the image into 8×8 pixel.
We have also compared the Peak Signal Noise Ratio and Mutual Information of the fused
image. The results are also compared with the
wavelet based fusion results.
5. EXPERIMENTAL RESULTS AND
ANALYSIS
The principle essence of fused image is that it
gives better information than the individual input
images. To prove this statement we apply our
algorithm on the following images as shown in
Figure 2 and Figure 3. The fused image is shown in Figure 4. The fused image is compared with the input
images and for this comparison; entropy has been
taken as a standard parameter [2]. To calculate the
entropy, histogram of the images has been used.
Table 1 shows the entropy measure of the images.
Figure 2: Input Image A
Figure 3: Input Image B
Figure 4: Fused Image by Modified PCA
Figure 5: Fused Image by traditional PCA
Table 1: Entropy Measure Comparison
The results show that the entropy of the fused
image is better than input images A and B.
Now we measure the eleven quality parameters
as shown in Table 2, for both the images obtained
through our modified PCA (Figure 4) and by
traditional PCA as shown in Figure 5.
Image Entropy
Input Image A 0.54
Input Image B 0.56
Fused 0.94
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JOURNAL OF COMPUTING, VOLUME 3, ISSUE 4, APRIL 2011, ISSN 2151‐9617
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Table 2: Comparison of the quality parameters
between our modified PCA approach and traditional
PCA
Image Quality Traditiona
l PCA based Fusion
Modifie
d PCA based
Fusion
Correlation
Coefficient
1 1
Cross Entropy 0.42 0.47
Entropy 0.88 0.94
Mutual
Information
0.74 0.71
Mean Square
Error
0.88 0.84
Normalized
Least square Error
0.38 0.35
Relative Sift
in Mean
0.56 0.52
Standard Deviation
0.001 0.001
Warping
degree
0.35 0.37
Contrast 0.87 0.88
Luminance 0.91 0.92
Figure 6: Comparison chart of Quality of PCA
based and Revised PCA based image.
From the experimental results as shown in Table
2 it can be observed that the values of entropy, mutual information and wrapping degree of the
fused image generated by our modified PCA
algorithm are greater than values for the fused image
generated by the traditional PCA algorithm. The
error parameters like the Mean Square Error,
Normalized Least square Error and Relative Sift in
Mean have lesser values for our algorithm than the
traditional PCA algorithm. These results clearly show
that our modified PCA based image fusion produces
better result than traditional PCA.
6. COMPARISION WITH WAVELET
TRANSFORM
One of the traditional image fusion techniques is
Wavelet Transform. Popular wavelet based approach
is to find the decomposition coefficient for image
fusion. The wavelet based method is available as
image fusion tool in wavelet toolbox which is used
for fusing various registered images of the same size.
The principal of image fusion using wavelet is to
merge the wavelet decompositions of two original
images using fusion methods.
Now we measure the standard quality index of
fused image for our modified PCA algorithm and
they are compared with the fused image results
obtained through wavelet transform method.
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JOURNAL OF COMPUTING, VOLUME 3, ISSUE 4, APRIL 2011, ISSN 2151‐9617
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For this measurement we select some standard
images as shown in Figure 7, which represent the first
input image C and Figure 8 represents the second
input image D. Figure 9 represents the fused image
by our modified PCA and Figure10 represents the
fused image by traditional PCA and Figure 12
represents the fused image by Wavelet Transform.
Figure 7: Input image C
Figure 8: Input image D
Figure 9: Fused image by our algorithm
Figure 10: Fused image by traditional PCA
Figure 11: Fused image by Discrete Wavelet
Transform
Table 3: Quality comparison of PCA based fused
image and our modified PCA based fused image and
the Wavelet Transform
It is clear from Table 3 that our modified PCA is
better than the traditional PCA based results and
very close in quality as compared to the wavelet
based technique. The wavelet based technique has more complexity than our technique so it can be
inferred that our modified PCA based technique can
be useful technique in terms of good quality as well
as reduced complexity.
Quality
Metric
Modified
PCA
PCA Wavelet
Transform
Q 0.79 0.78 0.87
MI 0.3 0.31 0.28
PSNR 29 28 32
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7. CONCLUSION
This paper presents an algorithm on image
fusion which shows much better performance than
the traditional PCA. The proposed algorithm is based
on
statistical
measure
techniques.
We
have
also
compared the quality of our technique with that of
traditional PCA based fusion and wavelet based
fusion. From the experimental results it is observed
that the result image have better qualities in terms of
information content as well as lower values of error
measure compared to the traditional PCA. In future
we would like to investigate our algorithm for video
fusion applications.
REFERENCES
[1] Y. Zheng, X. Hou, T. Bian, Z. Qin ‐ Effective Image Fusion
Rules Of Multi‐scale Image Decomposition , Procedings of the
5th International Symposium on image and signal Processing
and Analysis(2007) pp362‐366.
[2] S. Gupta, K. P. Ramesh, E. P. Blasch – “Mutual Information
Metric Evaluation for PET/MRI Image” Fusion. IEEE NAECON
Conf., July 2008, pp 305 – 311.
[3]S. Li, Z. Li, J. Gong – “Multivariate statistical analysis of
measures for assessing the quality of image fusion . International Journal of Image and Data Fusion”, Volume 1,
Issue 1 March 2010 , pp 47 – 66.
[4] N. Cvejic, A. Łoza, D. Bull, and N. Canagarajah – “A Novel
Metric for Performance Evaluation of Image Fusion
Algorithms” World Academy of Science, Engineering and
Technology 7 2005 pp 80 ‐85.
[5] Y. Zhu, P. K. Varshney and H.Chen – “Evaluation of ICA
Based Fusion of Hyperspectral Images for Color Display” .
World Academy of Science, Engineering and Technology 7 2005
[6] A. Haq, A. M. Mirza and S. Qamar – “An Optimized Image
Fusion Algorithm for Night‐time Surveillance and Navigation”
Proceedings of IEEE symposium , sept2005 , pp 138 – 143
[7]M. F. Yakhdani and A. Azizi – “Quality assessment of image
fusion techniques for multisensory High resolution satellite
images” (case study: irs‐p5 and irs‐p6 Satellite images) .
[8] Y. Zheng ‐ “Pyramid, DWT and Iterative DWT ‐ Multi‐scale
Fusion Algorithm Comparisons.” 12th international conference
on image fusion , 2009 pp 1260 –1267.
[9] S. G. Nikolov, D. R. Bull, C. N. Canagarajah, M. Halliwell, P.
N. T. Wells ‐ “Image fusion using a 3‐d wavelet transform.”
Image Processing and its Applications, Conference Publication
No. 465 0 IEE 1999 pp 235‐239. [10] L. I Smit – “A tutorial on Principal Component Analysis”,
2002, pp 1 ‐27.
Mr. Amit Kumar Sen is at present an Assistant Professor in the
Information Technology Depertment, IMPS College of Engg. &
Technology, Malda, India. He has done B.Tech in Information
Technology from Bengal Institute of Technology, India (2002‐
2006) and M.Tech in Multimedia and Software System from
NITTTR, Kolkata ( 2006‐2008). His present research area is
Computer Vision and Image Processing.
Mr. Subhadip Mukherjee is at present working with
CMC.Ltd. , India. Prior to this he was an Assistant Professor in
the Information Technology Depertment, IMPS College of
Engg. & Technology, Malda, India.He is done B.Tech in
Information Technology from Bengal College of Engineering
&Technology, India (2002‐2006) and M.Tech in Multimedia and
Software System from NITTTR, Kolkata ( 2007‐2009). His
present research interest is Computer Vision and Image
Processing.
Dr. Amlan Chakrabarti is at present an Assistant Professor
(Reader) , in the A.K.Choudhury School of Information Technology, University of Calcutta, India. Prior to this he was a
faculty in the Department of Computer Science and
Engineering, West Bengal University of Technology, Meghnad
Saha Institute of Technology, Kolkata and IIIT Calcutta. He is
an M.Tech. from the University of Calcutta (2001) and has done
his Doctoral research on Quantum Computing at Indian
Statistical Institute, India Kolkata, 2004‐2008. He was also a
VLSI Design Engineer from 1998‐2000. He is a Fellow of
Association of Computer Electronics and Electrical Engineers
(ACEEE), Senior member of the International Association of
Computer Science and Information Technology (IACSIT),
Singapore. His present research interests are Quantum
Computing, VLSI design, Embedded System Design and Video
and Image Processing Algorithms.