An Improved PCA Based Algorithm for Image

Fusion & Its Output Analysis and Comparision with

Output of Image Fusion Technique of Wavelet

Toolbox

Sunil Kr. Sharma1, Sanjay Gurjar

2

1M. Tech. Scholar,

2Assistant Professor,

Department of Electronics & Communication Engineering,

Institute of Engineering & Technology, Bhagwant

University, Ajmer, India 1sunilsharma96@gmail.com,

2ersanjay86@yahoo.in

Divyanshu Varma3, Y.P. Mathur

4

3M. Tech. Scholar,

4Assistant Professor,

Department of Electronics & Communication Engineering,

Institute of Engineering & Technology, Bhagwant

University, Ajmer, India 3maildivyanshu@yahoo.com

Abstract— A tool which helps to combine multi sensors

images of same scene by means of progressive image processing

and analysis methods consider as Image fusion technique.

Basically, it is nothing just a proposal to first extracts the proper

data from a set of different images of same scene and then

combines them by means of appropriate method and form a new

composite image which have all the properties of images which

are combined. In more general way image fusion is a need to get

extended statistical content in order to overwhelm the restriction

of the nature, kind, resolution and determination of the hardware

instruments capturing images. This tool can be functional to

number of fields dealing with images such as medical image

characteristic analysis, remote sensing, military surveillance,

computer-aided quality control etc. In this research paper a novel

and improved Principal Component Analysis (PCA) based image

fusion method has been proposed. Here, first the different output

based on PCA image fusion method is introduced then the main

output which provides complete statistical information about the

scene is developed. This developed output is compared with

output of fusion technique of the wavelet toolbox of MATLAB. To measure the effect of this technique on output image

histogram of each image, their retained energy levels, No. of

zeroes, Peak Signal-to-Noise Ratio (PSNR), Mean Square Error

(MSE) and Bits Per Pixel (BPP) also announced.

Keywords—Image fusion, PCA, wavelet toolbox, PSNR, MSE.

I. INTRODUCTION

Image fusion is the procedure that gets information from number of images of the similar sight and then combines them. The outcome of image fusion is a fresh image that holds the greatest needed material and features of each & every input image. The chief submission of image fusion is merging the gray-level high-resolution panchromatic image and the colored low-resolution multispectral image. These images may be taken from different instruments, picked up at different instants, or having different dimensional, spatial and spectral features. The main goal of the image fusion is to recollect the greatest appropriate features of all images. By the accessibility of multi-sensor facts in no. of areas, image fusion has been

getting growing consideration in the studies for a wide range of submissions and applications. The basic algorithm to fuse two different images of same site can be represented by Fig. 1 [1].

Fig. 1. General image fusion analogy for two different images of same sight.

On the basis of kind approach or rule used in the image fusion there are numerous approaches that have been established to achieve image fusion some of them are shown in following list [2]:

(1) Intensity-hue-saturation (IHS) transform based fusion

(2) PCA based fusion

(3) Mathematical arrangements

(a) Brovey transform

(b) Artificial flexible coefficient ratio method

(c) Proportion development procedure

(4) Multi-scale transform based fusion

(a) High pass filter analysis technique

(b) Pyramid technique

(i) Gaussian based pyramid

(ii) Laplacian based pyramid

(iii) Gradient based pyramid

(iv) Morphological based pyramid

(v) low pass ratio based pyramid

(vi) Contrast based pyramid

(vii) Filter subtract and decimation based pyramid

(c) Wavelet transform based

(i) Discrete wavelet transform (DWT)

(ii) Stationary wavelet transform (SWT)

(iii) Dual tree discrete wavelet transform (DTDCT)

(iv) Lifting wavelet transform (LWT)

(v) Multi-wavelet transform (MWT)

(d) Curvelet transform based

(5) complete probability density based fusion

(6) Biologically motivated information based fusion

Here, first basic image fusion arrangements are introduced which are standard, modest and possibly the most common and prevalent. Then rest of the broadsheet is prepared as following. Section II briefly argues about the associated mechanism and what other investigators did in this region of image fusion. In Section III, discussion on the elementary system plan, the improved PCA based image fusion and the change due to change in components and the basic process of image fusion toolbox of wavelet toolbox of MATLAB. Next, in Section IV examination of all images is planned by comparing them on the source of various parameters like MSE, PSNR, and Histograms etc. Then, Section V finalizes the paper by conclusion.

II. ASSOCIATED EFFORTS

As the above consideration there are various rule for the

fusion are available which provides a great boom in the field

of image fusion. All research in the field of image fusion has a

great need and uniqueness. Some of these rules and algorithms

has introduce here to show the research done up to here.

A. IHS Based Approach for Image fusion

This approach of fusion is an IHS transform based rule in

which effectually transforms an image from low resolution

Red-Green-Blue (RGB) dominion into spatial (I) and spectral

(H, S) statistics. The strength element (I) of the IHS domain is

then substituted by the high-resolution panchromatic image and

altered back into the main RGB domain by means of earlier H

and S statistical components [3].

B. PCA Based Approach for Image Fusion

A statistical analysis which provides the dimension reduction was introduced as Principal component analysis approach. In PCA generally, the statistical facts is projected from its original domain to its Eigen domain to raise the variance and decrease the covariance by recalling the statistical components equivalent to the largest Eigen values and neglect other components. PCA reduces the terminated statistical component and high spot the components with major influence consequently to raise the signal-to-noise ratio (SNR). PCA also

have linear transformation properties that is familiar to be executed for submission & applications in which enormous amount of statistical facts is to be analyzed. Most common & wide application of PCA are in the field of data compression and pattern recognition by showing the data in a way to highly spot the matches and dissimilarities with tiny or short loss of statistical facts and data [3]. Here, just an improved version of this approach with comparison of outputs introduced due to change in Eigen values is presented.

C. Wavelet Transform Based Image Fusion

The algorithm flow diagram of wavelet transform based image fusion approach is same as shown in Fig. 1. Only the difference is that source transform is wavelet transform and fused transform will be inverse wavelet transform. In this approach two different images of same scene & site I1(u, v) and I2(u, v), are disintegrated into estimated and detailed coefficients at essential level using discrete wavelet transform (DWT). These estimated and detailed coefficients of both images are then combined using fusion rule F. Then the synthesized image (IF(u, v)) obtained by applying the inverse discrete wavelet transform (IDWT) as given by equation (1)[1].

IF(u, v)= IDWT [F{DWT(I1(u, v)), DWT(I2(u, v))}] (1)

III. PLANNED METHODOLOGY

Here the main base of work is PCA which includes a statistical process that converts number of correlated coefficients into number of uncorrelated coefficients consider as principal components (PC). In PCA a squeezed and optimum explanation of set of data is computed.

The first principal coefficients define for as high of the variance in the information as possible and each subsequent coefficient corresponds for as much as of the left behind discrepancy as probable. First PC is taken to be beside in the way with the extreme variance. The second principal component is forced to fit in the subspace which should be at right angles of the first PC. In the subspace, these components give the direction of extreme variance. Now, the third principal component is find in the extreme variance path in the subspace at right angles to the first two PC’s and so on. PCA is also considering as Hotelling transform (HT) or Karhunen-Loève transform (KLT). In PCA there is no stationary set of base vectors like other transforms Fast Fourier, Discrete Cosine and Wavelet etc. and generally PCA’s base vectors defines by the statistical set of data so, if data can alter then the base vector can also.

A. Proposed Algorithm

In this research work the propped algorithm is very similar to the [1] but here by interchanging the values of eigenvectors V and PC’s P a quite big and attractive approach has been developed and also provides the difference with all other related research approaches. Let the two different source images I1(u, v) and I2(u, v) captured from same scene & site are to be fused bye PCA method is arranged in two column vector and then the following steps must require to achieve the fusion with the optimum information of the site:

1. Arrange the array of each image into double precision array. If any image already contains the double precision array then no change will generate.

2. Calculate the covariance matrix C. which gives the difference coefficient of both images.

3. Now, figure out the eigenvectors V and eigenvalue D of covariance matrix C and arrange them reducing value of eigenvalues D. Both V and D are in 2 x 2 dimensions.

4. By considering the eigenvectors V to find the extreme eigenvalue to calculate the PC’s Pn given by following equations (2).

Pn = V(m) / ∑ V(l) (2)

Where n = 1, 2 m = 1, 2 and l= 1, 2

5. Now by multiply the computed PC’s with the image array and then combine them the main output is achieved. But here the other changes can be generated by interchanging the PC’s as given by the following equations:

IF1 = (I1 X P1) + (I2 X P2) (3)

IF2 = (I1 X P1) + (I1 X P1) (4)

IF3 = (I2 X P2) + (I2 X P2) (5)

IF4 = (I1 X P2) + (I2 X P1) (6)

B. Information Flow Diagram

The approach which shows how that fusion can achieved

based on PCA image fusion algorithm is shown in Fig. 2 [1].

Pn P’n

(I1 Pn + I2 P’n)

Fig. 2. Information flow algorithm in proposed image fusion scheme.

As mentioned in the algorithm both input images (which are to be fused) I1 (u, v) and I2 (u, v) are organized in two column vectors and their experiential means are subtracted. The consequential vector has (a x 2) dimension, where a defines size of the each image vector. For this resultant vector compute the eigenvector and eigenvalues and the eigenvectors consistent to the greater eigenvalue obtained. The normalized components of PC’s are P1 and P2 (i.e., P1 + P2 = 1) using basic approach of covariance are computed from the achieved eigenvector. The fused image is given by equation (7).

IF(u, v) = (I1 (u, v)X P1) + (I2(u, v) X P2) (7)

C. Image Fusion Based on Wavelet Toolbox of MATLAB

The second part of the paper contains the basic approach of image fusion using wavelet toolbox of MATLAB. This approach follows the wavelet transform based algorithm. This technique shows in Fig. 3 with maximum fusion rule selection.

Fig. 3. Wavelet toolbox based image fusion approach.

By Fig. 3 It easily observed that the both different images of same site are load in toolbox window then the wavelet transform has been found. This transformation provides the decomposition of both images. Now, by applying the fusion rule like maximum, minimum or average value of coefficient the fusion decomposition is achieved. Here the maximum fusion selection rule is applied which provides the selection of maximum coefficient of decomposed images. This fused decomposition is now applied on inverse wavelet tool to get back the image. The obtained synthesized image contained the properties of both applied images.

IV. ANALYSIS OF OUTPUT IMAGES AND COMPARISION

The comparative opinion of all output images of both PCA coding based and Wavelet toolbox based are shown in following figures. Here the all output generated due to interchange of PC’s and eigenvectors values are also shown. These figures also contain the histogram, cumulative histograms and energy levels of main outputs. The Fig. 4 and 5 gives the applied two different but same site images which have to be fused. Fig. 6 gives the PCA based output when both

P1 & P2 are same value V(1) / ∑ V(1) and applied fusion by equation (3) and in other figures with some changes also generated to give the difference with other images.

I1(u, v) I2(u, v)

PCA

Fused Image

IF

Fig. 4. Applied source image I1(u, v).

Fig. 5. Applied source image I2(u, v).

Fig. 6. PCA based fused image output when both PC’s are same and fusion based on equation (3).

Fig. 7. PCA based fused image output when P1 based on eigenvector V(1) while P2 based on eigenvector V(1) as well as V(1) and fusion based on equation (3).

Fig. 8. PCA based fused image output when P2 based on eigenvector V(2)/∑V(1) while P1 based on eigenvector V(1)) only and fusion based on equation (3).

Fig. 9. PCA based fused image output when P1 based on eigenvector V(1)/∑V(1) P2 based on eigenvector V(2)/∑V(2) and fusion based on equation (4).

Fig. 10. PCA based fused image output when P1 based on eigenvector V(1)/∑V(1) P2 based on eigenvector V(2)/∑V(2) and fusion based on equation (5).

Fig. 11. PCA based fused image output when P1 based on eigenvector V(1)/∑V(1) P2 based on eigenvector V(2)/∑V(2) and fusion based on equation (6).

Fig. 12. PCA based fused image output when P1 based on eigenvector V(1)/∑V(1) P2 based on eigenvector V(2)/∑V(2) and fusion based on equation (3).

From the all output of PCA based approach we may easily observed that the Fig. 12 provides the appropriate required information. Fig. 13 describes the histogram & cumulative histogram for the Fig12. Fig.14 gives the output of wavelet toolbox which is very close to the Fig. 12. And Fig. 15 provides its histogram & cumulative histogram.

Fig. 13. Histogram analysis of output image Fig. 12.

Fig. 14. Wavelet toolbox based image fusion output image for applied image Fig. 4 Fig. 5 with maximum selection of fusion rule.

Fig. 15. Histogram analysis of output image Fig. 14.

The Fig. 16 and 17 gives the information about the energy level of the PCA based output and wavelet toolbox based output. These figures also contain the information about the global threshold and the percentage of the retained energy and No. of zeros.

Fig. 16. Energy level of PCA based output image.

Fig. 17. Energy level of wavelet toolbox based output image.

By looking on the other parameter of these two output images that the MSE PSNR and BPP also obtained. So, the other view of comparison of these two output images has been observed by Table I.

V. CONCLUSION AND FUTURE SCOPE

In this research article, improved version of PCA based

image fusion approach has been introduced with the analysis

of all output images. Then by comparison with the output

images of both PCA based and wavelet based images it is

observed that the both techniques have their advantages but it

is obtain that the PCA based output of fusion has low MSE

and BPP and high PSNR which is the main advantage of this

approach. The proposal for the future scope about this

approach to how can PCA and wavelet based approach

provides better accuracy. Some additional exploration is also

needed to resolve this technique in various fields of

applications. Furthermore a review can produce by comparing

this approach with the all other methods like mathematical

transformation based, IHS based transformation, Curvelet

transform, PDF based etc.

TABLE I.

COMPARISON TABLE

PARAMETER

OUTPUT IMAGES

PCA BASED OUTPUT

IMAGE WAVELET TOOLBOX BASED

OUTPUT IMAGE

PSNR 0.881 0.851

MSE

5.309e+004 5.345e+004

BPP 0.0020447 0.0020752

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