 Open Access
 Total Downloads : 1050
 Authors : Mrs.S.V.More, Prof.Dr.Mrs.S.D.Apte
 Paper ID : IJERTV1IS5285
 Volume & Issue : Volume 01, Issue 05 (July 2012)
 Published (First Online): 02082012
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
PixelLevel Image Fusion Using Wavelet Transform
Mrs.S.V.More1, Prof.Dr.Mrs.S.D.Apte2
Rajarshri Shahu College of Engineering, E&TC Department, Tathawade, Pune, India
Abstract
Image fusion is a process to combine information from multiple images of the same scene. The result of image fusion will be a new image which is more suitable for human and machine perception or further tasks of image processing such as image segmentation, feature extraction and object recognition. In this paper we present a waveletbased image fusion algorithm. The images to be fused are firstly decomposed into high frequency and low frequency bands. Then, the low frequency components are combined by maximum energy rule and high frequency components are combined by variance rule. Finally, the fused image is constructed by inverse wavelet transform. We select four groups of images to simulate, and compare our simulation results with the pixel averaging method and most common wavelet method based on meanmax fusion rule.

Introduction
Due to the limitation of depth of focus all the objects in a sensor image are not clear, so multiple images of the same scene with focus on different objects are required each of these images has some important information about the scene but none of them is sufficient in terms of its information content. To understand and acquire the complete information, view the series of images is not an easy task for humans as well as for machine perception.so all these images should be fused to form a single image in such a way that the fused image has better focus on all objects and complete information[1]. Image fusion can be divided into three levels, which are pixellevel fusion, feature level fusion and decisionlevel fusion. Almost all image fusion algorithms, from the simplest weighted averaging to more advanced multiscale methods, belong to pixellevel fusion [2].
In pixellevel image fusion, some general requirements are imposed on the fused results: 1) The fusion process should preserve (as far as possible) all salient information in the source images; 2) The fusion
process should not introduce any artefacts; 3) The fusion process should be shiftinvariant performed [3]. In the field of image fusion, pixellevel fusion becomes the primary method since it can preserve original information of source images as much as possible, and the algorithms are computationally efficient and easy to implement, the most image fusion applications employ pixel level based method[4]. There are three commonly used methods of pixellevel image fusion, including simple image fusion (such as linear weighted average, HPF (highpassfilter), HIS (intensity huesaturation), PCA (principal component analysis), etc.), pyramidbased decomposition image fusion (such as Laplace pyramid decomposition, ratio pyramid, etc.) and wavelet transform image fusion, etc. [5]. Recently, wavelet transform becomes an important aspect of image fusion research with the merits of
multiscale and multiresolution.
This paper is organized as follows: In section 2, the proposed waveletbased image fusion is introduced. In section 3, experiments on different focus images with the proposed method performed and compared. Finally, conclusion is provided.

Proposed wavelet based image fusion technique

General Procedure of Wavelet Based Image Fusion
The information flow diagram of waveletbased image fusion algorithm is shown in figure 1. In wavelet image fusion scheme, the source images I1(x, y) and I2(x, y) are decomposed into approximation and detailed coefficients at required level using DWT. The approximation and detailed coefficients of both Images are combined using fusion rule . The fused image If(x, y) could be obtained by taking the inverse wavelet transform (IDWT) as:
If (x, y) =
IDWT [ {DWT (I1(x, y), DWT (I2(x, y)))}] (1)
The fusion rule used is vary from simple rule i.e. averages the approximation coefficients and picks the detailed coefficient in each sub band with the largest magnitude to very advance rule described below[6].
2
The high frequency bands contain the detail coefficients of an image, which usually have large absolute values correspond to sharp intensity changes and preserve salient information in the image. On the other hand, according to characteristic of HVS it is easy to know that for the high resolution region the human visual interest is concentrated on the detection of changes in contrast between regions on the edges separate these regions. Therefore, a good method for the high frequency bands should produce large coefficients on those edges. Based on the above analysis, we propose a scheme by computing the variance in a neighbourhood to select the high frequency coefficients. The variance of an image is defined as follows
Figure.1 information flow diagram in image fusion
scheme using wavelet transforms
I ( p)
1
S T s
S / 2
S / 2 t
T / 2
f i
T / 2
s, j t
meanI p
(4)

Selection Scheme for Low Frequency Bands
meanI ( p)
1 S / 2
S T
T / 2
f i
s, j t
(5)
s S / 2 t T / 2
The low frequency band is the original image at the coarser resolution level, which can be considered as a smoothed and subsampled version of the original image. Therefore, most information of the source images is kept in the low frequency band. When the image has more obvious texture features (information) in a certain frequency bands or direction, the
Where S Ã—T is the neighboring size and in this paper it is considered as 4Ã—4, meanI(p), 1(p) denote the mean value and variance value of the coefficients centered at (i, j) in the window of SÃ—T respectively. Then the fusion rule for the high frequency bands can be illustrated as following:
corresponding wavelet channel output has larger energy. The bigger energy of corresponding pixel gives the clearer texture feature. Therefore, an energybased
fH i, j
A H i, j , BH i, j
if A
B
else
(6)
scheme is adopted for low frequency coefficients. The energy of image is described as follows:
fH(i,j), AH(i,j), BH(i,j) respectively represents high frequency (HL,LH,HH) coefficient pixel value of fused
M N
f
E i 1 j 1
M
i, j
N
(2)
image, image A, image B at point (i, j). A and B respectively represent variance of high frequency coefficient of pixel value of image A and image B at point (i, j).
Where f (i, j) represents pixel grey value of point (i, j). M*N is the size of image.
Then the fusion scheme for low frequency bands can be illustrated as the following:
2.4. Procedure of Proposed DWT Based Image Fusion
To implement twodimension discrete wavelet decomposition (DWT) to each source image
fL i, j
AL i, j , BL i, j
if EA
EB
else
(3)
on the level of N, and obtain 3N+1 subimage. Decompose source image A and Bs low frequency part LLA(i,j)and LLB(i,j) into 4Ã—4
fL(i,j), AL(i,j), BL(i,j) respectively represents low frequency coefficient pixel value of fused image, image A, image B at point (i, j). EA and EB respectively represent energy of low frequency coefficient of pixel value of image A and image B at point (i, j).
2.3. Selection Scheme for High Frequency Bands
sub images and calculate energy using equation (2) and using equation (3) obtain low frequency part of fused image LLF(i,j).
A A
B B B
Decompose source imae A and Bs high frequency part LH K(i,j), HL K(i,j), HHAK(i,j),LH K(i,j),HL K(i,j), HH K(i,j) into 4Ã—4 sub images and calculate variance of all 4Ã—4 sub images using equation (4) & (5) and using equation(6) obtain high frequency part
F F F
of fused image LH K(i,j), HL K(i,j), HH K(i,j) respectively.
distribution is scattered and the images contrast is large that more information can be seen. It can be
K represents decomposition level (K=1,2,3.).
Finally, using LLF(i,j), LH K(i,j), HL K(i,j),
defined as Ref. [7]
M
N 2
K F F F (i, j) f
HHF (i,j), obtain fused image by inverse
i 1 j 1
(9)
discrete wavelet transform (IDWT). M N


RESULTS
The proposed method has been tested on several pairs of multifocus images. Four examples are given here to illustrate the performance of the fusion process. And proposed method is evaluated by comparing with most common pixel averaging method and wavelet based method in which weighted averaging rule used for low frequency coefficient and the rule of selection of maximum value for high frequency coefficient .In all
cases the grey value of pixel are scaled between 0 to
F (i, j) is the grey value of fused image at point (i, j). is the mean value of greyscale image fusion. MÃ—N
is the size of image.
3.1.3. Root mean square error (RMSE): Root mean square error (RMSE) indicates how much error the fused image conveys about the reference image. Hence, lower the RMSE, the better the fused result. The RMSE is defined as ref. [7]
1/ 2
255. The source images are assumed to be registered
RMSE
1 M N
R i, j
F i, j 2
(10)
and no preprocessing is performed.

Objective Evaluation of an Image
In addition to visual analysis, we conducted some quantitive analysis of fused image and three objective criteria are used to compare the fusion results are entropy, standard deviation and root mean square error.

Entropy: Image entropy is an important indicator for measuring the image information richness. The image entropys value represents the average amount of information which is included by the image. The calculated information entropy can objectively evaluate the amount of information changes. According to principal of Shannon information theory, entropy of an image is defined as Ref. [7]
M N i 1 j 1
R (i, j) is ideal reference image, F (i, j) is the fused image, MÃ—N is the size of image


Visual Analysis of an Image
Experiment is performed on a popular widely used standard image Lena of size 256Ã—256 as shown in Fig.2 (a), which served as ideal reference image here. Then the two other source images are obtained with a Gaussian blurring method as reference [9].Fig.2 (b) is the image blurred on the lower horizontal, Fig.2(c) is the image blurred on upper.
M N
H
i 1 j 1
M
Pij log 2 Pij
N
(7)
pij f
i, j
f
i 1 j 1
i, j
(8)
Where HPixel Entropy, LImage total grayscale Pi The i Pixels rate to the images total ones N i.e.=Ni/N
3.1.2. Standard deviation (): Standard deviation reflects discrete case of the image grey intensity relative to the average. The standard deviation represents the contrast of an image. If the standard deviation is large, then the image grey scale
(a)
TABLE 1
ENTROPY
STANDARD
DEVIATION
RMSE
Reference image
Lena
7.5784
52.3689
–
Horizontally blurred Lena 1
7.5035
48.2143
5.4776
Horizontally
blurred Lena 2
7.5246
49.4620
4.9028
Pixel averaging
5.6372
35.4814
8.3216
Wavelet based Mean max fusion rule
db1
7.4509
48.0642
5.3936
Sym1
7.4509
48.0462
5.3936
Coif1
7.4469
47.9500
5.3418
Bior3.3
7.4466
47.8966
5.3601
Dmey
7.4466
47.9093
5.3688
haar
7.4509
48.0642
5.3936s
Proposed method
Db1
7.6071
52.4130
3.4991
Sym1
7.6071
52.4130
3.4991
coif1
7.5979
52.1534
3.3547
Bior3.3
7.6228
52.8679
3.8543
Dmey
7.5900
52.0523
3.1029
haar
7.6071
52.4130
3.4991
Entropy and Standard Deviation of Fig.2 (Lena image)
(b) (c)
(d) (e)
(f)
Figure 2. Simulation results of Lena images. (a) reference Lena image (b)Lena image blurred on the horizontal lower;(c) Lena image blurred on the horizontal upper; (d) fused image by pixel averaging method; (e) fused image by wavelet based meanmax algorithm; (f) fused image by proposed method using 5 level wavelet decomposition;


CONCLUSION
In this paper, we present a waveletbased image fusion, and show the simulation result and objective evaluation. In the process of fusion we gave fusion rule based on energy and variance, which effectively conserved the energy of source images and avoided the loss of useful information. Comparing with the most common algorithm, proposed fusion method gives improved visual effect of fused image and also improved objective parameter such as, entropy, standard deviation and RMSE.

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International Journal of Engineering Research & Technology (IJERT)
ISSN: 22780181
Vol. 1 Issue 5, July – 2012

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