modified pca based image fusion and its quality measure

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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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.






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.






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






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






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.






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






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.

modified pca based image fusion and its quality measure

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