Comparative analysis of multimodal medical image fusion using pca and wavelet transforms
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This paper discusses medical image fusion techniques that combine information from multiple imaging modalities to create more informative images for diagnosis. It compares the effectiveness of various fusion methods, including Principal Component Analysis (PCA) and wavelet transforms, concluding that Stationary Wavelet Transform (SWT) outperforms PCA and Discrete Wavelet Transform (DWT) based on evaluated performance metrics. The findings indicate that SWT provides superior quality in fused images, addressing issues like blurring encountered with PCA and the invariance problem found in DWT.
![International Journal of Latest Technology in Engineering, Management & Applied Science (IJLTEMAS)
Volume VI, Issue IV, April 2017 | ISSN 2278-2540
www.ijltemas.in Page 115
Comparative Analysis of Multimodal Medical Image
Fusion using PCA and Wavelet Transforms
Alka Srivastava, Er. Vipul Singhal, Dr. Ashwani Kumar Aggarawal
Sant Longowal Institute of Engineering and Technology, Longowal, Distt. Sangrur, Punjab, India.
Abstract— nowadays, there are a lot of medical images and their
numbers are increasing day by day. These medical images are
stored in large database. To minimize the redundancy and
optimize the storage capacity of images, medical image fusion is
used. The main aim of medical image fusion is to combine
complementary information from multiple imaging modalities
(Eg: CT, MRI, PET etc.) of the same scene. After performing
image fusion, the resultant image is more informative and
suitable for patient diagnosis. There are some fusion techniques
which are described in this paper to obtain fused image. This
paper presents two approaches to image fusion, namely Spatial
Fusion and Transform Fusion. This paper describes Techniques
such as Principal Component Analysis which is spatial domain
technique and Discrete Wavelet Transform, Stationary Wavelet
Transform which are Transform domain techniques.
Performance metrics are implemented to evaluate the
performance of image fusion algorithm. An experimental result
shows that image fusion method based on Stationary Wavelet
Transform is better than Principal Component Analysis and
Discrete Wavelet Transform.
Index Terms: Image Fusion, Discrete Wavelet Transform,
Principal Component Analysis, Stationary Wavelet
Transform
I. INTRODUCTION
mage fusion is the process of combining complementary
information from two or more images, resultant image more
informative than any of source images. These fused images
are help in medical diagnosis, remote sensing, surveillance
system and target tracking. Medical images (such as X-ray
image, CT-scan image, MRI image etc) are increasing day by
day. To optimize the storage capacity and minimize the
redundancy medical image fusion is used. In medical imaging,
X-Ray, Computed Tomography (CT), Magnetic Resonance
Imaging (MRI), Positron Emission Tomography (PET),
Single Photon Emission Computed Tomography (SPECT) and
other modes of medical images show human information from
various angles. CT scan is generally used for visualizing
dense structure and is not suitable for soft tissues and
physiological analysis. It also provides details cross sectional
view. On the other hand MRI provides better visualization of
soft tissues and is generally used for detection of tumors and
other tissue abnormalities. PET gives information about blood
flow, oxygen and glucose metabolism in the tissues of the
brain [1].
II. CLASSIFICATION OF MULTIMODAL IMAGE
FUSION METHODS
Image fusion methods can be classified in three categories:
Pixel level, feature level and decision level. Pixel level image
fusion deals with the information content corresponding to
individual pixels of the input images. This type of image
fusion generates an image in which each pixel is appraised
from pixels in input images. It is also known as signal level
fusion. Advantages of pixel level image fusion are simple and
straight forward and disadvantage is altering the spectral
information of the original image [2].
In feature level image fusion, the source image is
divided into various regions depending upon the features like
texture; edges, boundaries etc, and then fused the images. It is
also known as object level fusion.
In decision level image fusion, image fusion is done
by decision. It is also known as symbol level image fusion.
Decision level represents probabilistic decision information
based on the voting or fuzzy logic, employed on the output of
feature level processing on the images.
As Compared to feature and decision level, pixel level
methods are more suitable for medical imaging as they can
preserve spatial details in fused images.
III. MEDICAL IMAGE FUSION METHODS
There are various medical image fusion methods but pixel
level methods are mostly used for medical image fusion.
Some pixel level methods are Wavelet transforms, Principal
Component Analysis (PCA) as discussed in this paper.
Principal Component Analysis falls under spatial domain
where as discrete wavelet transform (DWT) and Stationary
Wavelet Transform (SWT) fall under transform domain
technique.
PRINCIPAL COMPONENT ANALYSIS (PCA):
PCA is a mathematical tool which transforms a number of
correlated variables into a number of uncorrelated variables.
The PCA is used widely in image compression and image
classification. The PCA involves a mathematical procedure
that transforms a number of correlated variables into a number
of uncorrelated variables called principal components. It
computes a compact and optimal description of the data set.
I](https://image.slidesharecdn.com/comparativeanalysisofmultimodalmedicalimagefusionusingpcaandwavelettransforms-170505073651/85/Comparative-analysis-of-multimodal-medical-image-fusion-using-pca-and-wavelet-transforms-1-320.jpg)
![International Journal of Latest Technology in Engineering, Management & Applied Science (IJLTEMAS)
Volume VI, Issue IV, April 2017 | ISSN 2278-2540
www.ijltemas.in Page 116
The first principal component accounts for as much of the
variance in the data as possible and each succeeding
component accounts for as much of the remaining variance as
possible. First principal component is taken to be along the
direction with the maximum variance. The second principal
component is constrained to lie in the subspace perpendicular
of the first. Within this Subspace, this component points the
direction of maximum variance. The third principal
component is taken in the maximum variance direction in the
subspace perpendicular to the first two and so on. The PCA is
also known as Karhunen-Loève transform or the Hotelling
transform. The PCA does not have a fixed set of basis vectors
like FFT, DCT and wavelet etc. and its basis vectors depend
on the data set [3].
Algorithm:
The basic steps involve in principal component analysis
algorithm is discussed below.
Let the source images (images to be fused) be arranged in
two-column vectors. The steps followed to project this data
into two dimensional subspaces are:
1. Organize the data into column vectors. The resultant
matrix Z is of dimension 2 × n.
2. Compute the empirical mean along each column. The
empirical mean vector Me has a dimension of 1 × 2.
3. Subtract the empirical mean vector Me from each
column of the data matrix Z. The resultant matrix X
is of dimension 2 × n.
4. Find the covariance matrix C of X i.e. C=XXT
mean
of expectation = cov(X).
5. Compute the eigenvectors V and eigen value D of C
and sort them by decreasing eigen value. Both V and
D are of dimension 2 × 2.
6. Consider the first column of V which corresponds to
larger eigen value for computation of P1 and P2 as:
P1
∑
and P2 = ∑
….(1.1)
where V (1) and V (2) are the first and second element
of that column which corresponds to larger eigen value and
∑ is summation of eigen vector matrix.
Image Fusion using PCA
The information flow diagram of PCA-based image fusion
algorithm is shown in Fig. 1.1. The input images to be fused
I1(x, y) and I2 (x, y) are arranged in two column vectors and
their empirical means are subtracted. The resultant vector has
a dimension of n x 2, where n is length of each image vector.
Compute the eigenvector and eigen values for this resultant
vector and then find the eigenvectors corresponding to the
larger eigen value. The normalized components P1 and P2 (i.e.,
P1 + P2 = 1) using Eq. are computed from the obtained
eigenvector. The fused image (If) is given by:
If = P1I1(x, y) + P2I2(x, y) ……(1.2)
Fig.1.1: Information flow diagram employing PCA
Wavelet Transform
The most common transform type medical image fusion
algorithms are the wavelet transform. It is very simple and
ability to preserve time and frequency related content of the
images to be fused. In this method, first input images are
decomposed into lower sub-bands and higher sub-bands.
Then, lower sub-bands (LL, LH) are combining by particular
fusion rule and higher sub-bands (HL, HH) are also
combining by particular fusion rule. Finally, the fused image
is reconstructed by inverse wavelet transform. The two
dimensional DWT is very useful for image processing
because the image data are discrete and spatial and spectral
resolution is dependent on the frequency. The DWT (Discrete
Wavelet Transform) has property that the spatial resolution is
smaller in lower-frequency bands but larger in higher
frequency bands.
Fig. 1.2: General representation of fusion process in wavelet transforms
DWT suffers from certain disadvantages like loss of
edge information due to down-sampling, blurring effect and
high storage cost etc. In order to eliminate these
disadvantages, stationary wavelet transform (SWT) technique
is used.
Stationary Wavelet Transform:
Stationary Wavelet Transform (SWT) is similar to Discrete
Wavelet Transform (DWT), the only difference is that in](https://image.slidesharecdn.com/comparativeanalysisofmultimodalmedicalimagefusionusingpcaandwavelettransforms-170505073651/85/Comparative-analysis-of-multimodal-medical-image-fusion-using-pca-and-wavelet-transforms-2-320.jpg)
![International Journal of Latest Technology in Engineering, Management & Applied Science (IJLTEMAS)
Volume VI, Issue IV, April 2017 | ISSN 2278-2540
www.ijltemas.in Page 117
SWT process of down-sampling is suppressed which means it
is translation-invariant [4].
Fig. 1.3: SWT decomposition scheme
where Ii , Gi , Hi represent source images, low-pass filter and
high-pass filter, respectively.
The 2D Stationary Wavelet Transform (SWT) is based on the
idea of no decimation. It applies the Discrete Wavelet
Transform (DWT) and omits both down-sampling in the
forward and up-sampling in the inverse transform. More
precisely, it applies the transform at each point of the image
and saves the detail coefficients and uses the low frequency
information at each level. The Stationary Wavelet Transform
decomposition scheme is illustrated in fig. 1.3.
SWT Algorithm
The basic algorithm of stationary wavelet transform is
explained below [5].
1. Decompose the two source images using SWT at one level
resulting in three detail sub bands and one approximation sub
band (HL, LH, HH and LL bands).
2. Compute the average of approximate parts of images.
3. Find the absolute values of horizontal parts of the image by
subtracting second part of image from first.
D = |H1L2 |- |H2L2 | >= 0 .…. (1.3)
where D denotes the difference and H1L2, H2L2 are the
horizontal part of image.
4. Make element wise multiplication of D and horizontal part
of first image and then subtract another horizontal part of
second image multiplied by logical not of D from first for the
fusion of horizontal part.
5. Find D for vertical and diagonal parts and obtain the fused
vertical and details of image.
6. Obtain the fused image by taking inverse stationary wavelet
transform.
Performance Parameters
Performance evaluation is necessary for qualitative and
quantitative analysis of the image fusion techniques. The
performance parameters or the quality metrics namely
entropy, standard deviation, root means square error and peak
signal to noise ratio are explained in the following section [6-
9].
Entropy:
Entropy is one of the most important quantitative measures in
image fusion. Higher entropy indicates more informative
image. For an image consisting of L gray levels, the entropy
of an image is defined as.
∑
where p (i) is the probability of each gray scale level.
Standard Deviation:
Standard deviation reflects discrete case of the image grey
intensity relative to the average. It represents the contrast of
an image. If the standard deviation is large, then the image
grey scale distribution is scattered and the image’s contrast is
high then it means more information in the image. It can be
defined as given in eq 1.3.
√
∑ ∑ ( ̅ )
where F (i, j) is the grey value of fused image at point (i,
j) ̅ is the mean value of grey-scale image fusion and M×N is
the size of image.
Root Mean Square Error (RMSE):
Root Mean Square Error presents the error between the
reconstructed image and the original image as a percentage of
the mean intensity of the original image. The RMSE is
calculated by.
√ ∑ ∑[ ]
where Itrue(x, y) represents the reference image, Ifused(x, y)
represents the fusion image and M, N are the dimensions of
the images.
Peak Signal to Noise Ratio (PSNR):
Peak signal to noise ratio is commonly used to measure of
quality of reconstruction of loss compression codec’s (e.g., for
image compression). In this case, the signal is the original
data of the image, and the noise is the error introduced by
compression. When comparing compression codes it is used
as an approximation to human perception of reconstruction
quality, therefore in some cases, one reconstruction may
appear to be closer to the original than another, even though it
has a lower PSNR. A higher PSNR will generally indicate that
the reconstruction is of higher quality.](https://image.slidesharecdn.com/comparativeanalysisofmultimodalmedicalimagefusionusingpcaandwavelettransforms-170505073651/85/Comparative-analysis-of-multimodal-medical-image-fusion-using-pca-and-wavelet-transforms-3-320.jpg)
![International Journal of Latest Technology in Engineering, Management & Applied Science (IJLTEMAS)
Volume VI, Issue IV, April 2017 | ISSN 2278-2540
www.ijltemas.in Page 118
The PSNR is calculated by using the following formula.
PSNR = 10 * log10 ) …..(1.7)
where M, N are the dimensions of the image. PSNR is
generally expressed in decibel i.e. db.
Results and Discussion:
Input image 1 (CT-scan) Input image 2 (MRI-scan)
(a) DWT-Avg. (b) DWT-Avg.-Max
(c) SWT (d) PCA
Fig 1.5 Fused images for dataset
Table 1.1 Results for tested dataset for Different Techniques
Performance
Parameters
Techniques
Entropy Standard
deviation
Peak
Signal to
Noise
Ratio
(PSNR)
db
Root
Mean
Square
Error
(RMSE)
PCA 4.5752 44.4132 28.3416 96.02
DWT(avg.) 4.8530 47.1878 30.3299 60.74
DWT(avg.-
max)
5.0567 47.4620 30.3147 60.96
SWT 4.9882 48.0827 37.6482 11.2632
IV. CONCLUSION
In this paper medical image fusion using pixel level methods
are implemented. In spatial domain, Principal component
analysis is implemented and in transform domain discrete
wavelet transform and stationary wavelet transform are
implemented. Principal component analysis has blurring
problem. The discrete wavelet transform method provides a
high quality spectral content. But DWT in transform domain
is time invariant, this problem is overcome by using SWT. It
can be concluded from Entropy, Standard deviation, RMSE
and PSNR values that SWT is better image fusion technique
compared to PCA and DWT.
REFERENCES
[1]. Nemir Al-Azzawi and Wan Ahmed K. Wan Abdullah, “Medical
Image Fusion Schemes using Contourlet Transform and PCA
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[2]. R. Redondo, F. Sroubek, S. Fischer and G. Cristobal, “Multifocus
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[3]. F. Belhloul, M. Janier, P. Croisille, C. Poirier, and A. Boudraa,
“Automatic assessment of myocardial viability based on PET-MRI
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[4]. Mirajkar Pradnya P. and Sachin D. Ruikar Mirajkar, “Image
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[5]. Q. Gao, Y. Zhao and Y. Lu, “ Despecking SAR image using
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[7]. Jionghua Teng, Xue Wang, Jingzhou Zhang and Suhuan Wang
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[10]. http://www.med.harvard.edu/aanlib/home.html
[11]. https://www.imagefusion.org](https://image.slidesharecdn.com/comparativeanalysisofmultimodalmedicalimagefusionusingpcaandwavelettransforms-170505073651/85/Comparative-analysis-of-multimodal-medical-image-fusion-using-pca-and-wavelet-transforms-4-320.jpg)
Comparative analysis of multimodal medical image fusion using pca and wavelet transforms
- 1. International Journal of Latest Technology in Engineering, Management & Applied Science (IJLTEMAS) Volume VI, Issue IV, April 2017 | ISSN 2278-2540 www.ijltemas.in Page 115 Comparative Analysis of Multimodal Medical Image Fusion using PCA and Wavelet Transforms Alka Srivastava, Er. Vipul Singhal, Dr. Ashwani Kumar Aggarawal Sant Longowal Institute of Engineering and Technology, Longowal, Distt. Sangrur, Punjab, India. Abstract— nowadays, there are a lot of medical images and their numbers are increasing day by day. These medical images are stored in large database. To minimize the redundancy and optimize the storage capacity of images, medical image fusion is used. The main aim of medical image fusion is to combine complementary information from multiple imaging modalities (Eg: CT, MRI, PET etc.) of the same scene. After performing image fusion, the resultant image is more informative and suitable for patient diagnosis. There are some fusion techniques which are described in this paper to obtain fused image. This paper presents two approaches to image fusion, namely Spatial Fusion and Transform Fusion. This paper describes Techniques such as Principal Component Analysis which is spatial domain technique and Discrete Wavelet Transform, Stationary Wavelet Transform which are Transform domain techniques. Performance metrics are implemented to evaluate the performance of image fusion algorithm. An experimental result shows that image fusion method based on Stationary Wavelet Transform is better than Principal Component Analysis and Discrete Wavelet Transform. Index Terms: Image Fusion, Discrete Wavelet Transform, Principal Component Analysis, Stationary Wavelet Transform I. INTRODUCTION mage fusion is the process of combining complementary information from two or more images, resultant image more informative than any of source images. These fused images are help in medical diagnosis, remote sensing, surveillance system and target tracking. Medical images (such as X-ray image, CT-scan image, MRI image etc) are increasing day by day. To optimize the storage capacity and minimize the redundancy medical image fusion is used. In medical imaging, X-Ray, Computed Tomography (CT), Magnetic Resonance Imaging (MRI), Positron Emission Tomography (PET), Single Photon Emission Computed Tomography (SPECT) and other modes of medical images show human information from various angles. CT scan is generally used for visualizing dense structure and is not suitable for soft tissues and physiological analysis. It also provides details cross sectional view. On the other hand MRI provides better visualization of soft tissues and is generally used for detection of tumors and other tissue abnormalities. PET gives information about blood flow, oxygen and glucose metabolism in the tissues of the brain [1]. II. CLASSIFICATION OF MULTIMODAL IMAGE FUSION METHODS Image fusion methods can be classified in three categories: Pixel level, feature level and decision level. Pixel level image fusion deals with the information content corresponding to individual pixels of the input images. This type of image fusion generates an image in which each pixel is appraised from pixels in input images. It is also known as signal level fusion. Advantages of pixel level image fusion are simple and straight forward and disadvantage is altering the spectral information of the original image [2]. In feature level image fusion, the source image is divided into various regions depending upon the features like texture; edges, boundaries etc, and then fused the images. It is also known as object level fusion. In decision level image fusion, image fusion is done by decision. It is also known as symbol level image fusion. Decision level represents probabilistic decision information based on the voting or fuzzy logic, employed on the output of feature level processing on the images. As Compared to feature and decision level, pixel level methods are more suitable for medical imaging as they can preserve spatial details in fused images. III. MEDICAL IMAGE FUSION METHODS There are various medical image fusion methods but pixel level methods are mostly used for medical image fusion. Some pixel level methods are Wavelet transforms, Principal Component Analysis (PCA) as discussed in this paper. Principal Component Analysis falls under spatial domain where as discrete wavelet transform (DWT) and Stationary Wavelet Transform (SWT) fall under transform domain technique. PRINCIPAL COMPONENT ANALYSIS (PCA): PCA is a mathematical tool which transforms a number of correlated variables into a number of uncorrelated variables. The PCA is used widely in image compression and image classification. The PCA involves a mathematical procedure that transforms a number of correlated variables into a number of uncorrelated variables called principal components. It computes a compact and optimal description of the data set. I
- 2. International Journal of Latest Technology in Engineering, Management & Applied Science (IJLTEMAS) Volume VI, Issue IV, April 2017 | ISSN 2278-2540 www.ijltemas.in Page 116 The first principal component accounts for as much of the variance in the data as possible and each succeeding component accounts for as much of the remaining variance as possible. First principal component is taken to be along the direction with the maximum variance. The second principal component is constrained to lie in the subspace perpendicular of the first. Within this Subspace, this component points the direction of maximum variance. The third principal component is taken in the maximum variance direction in the subspace perpendicular to the first two and so on. The PCA is also known as Karhunen-Loève transform or the Hotelling transform. The PCA does not have a fixed set of basis vectors like FFT, DCT and wavelet etc. and its basis vectors depend on the data set [3]. Algorithm: The basic steps involve in principal component analysis algorithm is discussed below. Let the source images (images to be fused) be arranged in two-column vectors. The steps followed to project this data into two dimensional subspaces are: 1. Organize the data into column vectors. The resultant matrix Z is of dimension 2 × n. 2. Compute the empirical mean along each column. The empirical mean vector Me has a dimension of 1 × 2. 3. Subtract the empirical mean vector Me from each column of the data matrix Z. The resultant matrix X is of dimension 2 × n. 4. Find the covariance matrix C of X i.e. C=XXT mean of expectation = cov(X). 5. Compute the eigenvectors V and eigen value D of C and sort them by decreasing eigen value. Both V and D are of dimension 2 × 2. 6. Consider the first column of V which corresponds to larger eigen value for computation of P1 and P2 as: P1 ∑ and P2 = ∑ ….(1.1) where V (1) and V (2) are the first and second element of that column which corresponds to larger eigen value and ∑ is summation of eigen vector matrix. Image Fusion using PCA The information flow diagram of PCA-based image fusion algorithm is shown in Fig. 1.1. The input images to be fused I1(x, y) and I2 (x, y) are arranged in two column vectors and their empirical means are subtracted. The resultant vector has a dimension of n x 2, where n is length of each image vector. Compute the eigenvector and eigen values for this resultant vector and then find the eigenvectors corresponding to the larger eigen value. The normalized components P1 and P2 (i.e., P1 + P2 = 1) using Eq. are computed from the obtained eigenvector. The fused image (If) is given by: If = P1I1(x, y) + P2I2(x, y) ……(1.2) Fig.1.1: Information flow diagram employing PCA Wavelet Transform The most common transform type medical image fusion algorithms are the wavelet transform. It is very simple and ability to preserve time and frequency related content of the images to be fused. In this method, first input images are decomposed into lower sub-bands and higher sub-bands. Then, lower sub-bands (LL, LH) are combining by particular fusion rule and higher sub-bands (HL, HH) are also combining by particular fusion rule. Finally, the fused image is reconstructed by inverse wavelet transform. The two dimensional DWT is very useful for image processing because the image data are discrete and spatial and spectral resolution is dependent on the frequency. The DWT (Discrete Wavelet Transform) has property that the spatial resolution is smaller in lower-frequency bands but larger in higher frequency bands. Fig. 1.2: General representation of fusion process in wavelet transforms DWT suffers from certain disadvantages like loss of edge information due to down-sampling, blurring effect and high storage cost etc. In order to eliminate these disadvantages, stationary wavelet transform (SWT) technique is used. Stationary Wavelet Transform: Stationary Wavelet Transform (SWT) is similar to Discrete Wavelet Transform (DWT), the only difference is that in
- 3. International Journal of Latest Technology in Engineering, Management & Applied Science (IJLTEMAS) Volume VI, Issue IV, April 2017 | ISSN 2278-2540 www.ijltemas.in Page 117 SWT process of down-sampling is suppressed which means it is translation-invariant [4]. Fig. 1.3: SWT decomposition scheme where Ii , Gi , Hi represent source images, low-pass filter and high-pass filter, respectively. The 2D Stationary Wavelet Transform (SWT) is based on the idea of no decimation. It applies the Discrete Wavelet Transform (DWT) and omits both down-sampling in the forward and up-sampling in the inverse transform. More precisely, it applies the transform at each point of the image and saves the detail coefficients and uses the low frequency information at each level. The Stationary Wavelet Transform decomposition scheme is illustrated in fig. 1.3. SWT Algorithm The basic algorithm of stationary wavelet transform is explained below [5]. 1. Decompose the two source images using SWT at one level resulting in three detail sub bands and one approximation sub band (HL, LH, HH and LL bands). 2. Compute the average of approximate parts of images. 3. Find the absolute values of horizontal parts of the image by subtracting second part of image from first. D = |H1L2 |- |H2L2 | >= 0 .…. (1.3) where D denotes the difference and H1L2, H2L2 are the horizontal part of image. 4. Make element wise multiplication of D and horizontal part of first image and then subtract another horizontal part of second image multiplied by logical not of D from first for the fusion of horizontal part. 5. Find D for vertical and diagonal parts and obtain the fused vertical and details of image. 6. Obtain the fused image by taking inverse stationary wavelet transform. Performance Parameters Performance evaluation is necessary for qualitative and quantitative analysis of the image fusion techniques. The performance parameters or the quality metrics namely entropy, standard deviation, root means square error and peak signal to noise ratio are explained in the following section [6- 9]. Entropy: Entropy is one of the most important quantitative measures in image fusion. Higher entropy indicates more informative image. For an image consisting of L gray levels, the entropy of an image is defined as. ∑ where p (i) is the probability of each gray scale level. Standard Deviation: Standard deviation reflects discrete case of the image grey intensity relative to the average. It represents the contrast of an image. If the standard deviation is large, then the image grey scale distribution is scattered and the image’s contrast is high then it means more information in the image. It can be defined as given in eq 1.3. √ ∑ ∑ ( ̅ ) where F (i, j) is the grey value of fused image at point (i, j) ̅ is the mean value of grey-scale image fusion and M×N is the size of image. Root Mean Square Error (RMSE): Root Mean Square Error presents the error between the reconstructed image and the original image as a percentage of the mean intensity of the original image. The RMSE is calculated by. √ ∑ ∑[ ] where Itrue(x, y) represents the reference image, Ifused(x, y) represents the fusion image and M, N are the dimensions of the images. Peak Signal to Noise Ratio (PSNR): Peak signal to noise ratio is commonly used to measure of quality of reconstruction of loss compression codec’s (e.g., for image compression). In this case, the signal is the original data of the image, and the noise is the error introduced by compression. When comparing compression codes it is used as an approximation to human perception of reconstruction quality, therefore in some cases, one reconstruction may appear to be closer to the original than another, even though it has a lower PSNR. A higher PSNR will generally indicate that the reconstruction is of higher quality.
- 4. International Journal of Latest Technology in Engineering, Management & Applied Science (IJLTEMAS) Volume VI, Issue IV, April 2017 | ISSN 2278-2540 www.ijltemas.in Page 118 The PSNR is calculated by using the following formula. PSNR = 10 * log10 ) …..(1.7) where M, N are the dimensions of the image. PSNR is generally expressed in decibel i.e. db. Results and Discussion: Input image 1 (CT-scan) Input image 2 (MRI-scan) (a) DWT-Avg. (b) DWT-Avg.-Max (c) SWT (d) PCA Fig 1.5 Fused images for dataset Table 1.1 Results for tested dataset for Different Techniques Performance Parameters Techniques Entropy Standard deviation Peak Signal to Noise Ratio (PSNR) db Root Mean Square Error (RMSE) PCA 4.5752 44.4132 28.3416 96.02 DWT(avg.) 4.8530 47.1878 30.3299 60.74 DWT(avg.- max) 5.0567 47.4620 30.3147 60.96 SWT 4.9882 48.0827 37.6482 11.2632 IV. CONCLUSION In this paper medical image fusion using pixel level methods are implemented. In spatial domain, Principal component analysis is implemented and in transform domain discrete wavelet transform and stationary wavelet transform are implemented. Principal component analysis has blurring problem. The discrete wavelet transform method provides a high quality spectral content. But DWT in transform domain is time invariant, this problem is overcome by using SWT. It can be concluded from Entropy, Standard deviation, RMSE and PSNR values that SWT is better image fusion technique compared to PCA and DWT. REFERENCES [1]. Nemir Al-Azzawi and Wan Ahmed K. Wan Abdullah, “Medical Image Fusion Schemes using Contourlet Transform and PCA Based”, Annual International Conference of the IEEE, Engineering in Medicine and Biology Society, pp.5813-5816, 2009. [2]. R. Redondo, F. Sroubek, S. Fischer and G. Cristobal, “Multifocus image fusion using the log-Gabor transform and a Multisize Windows technique”, Information Fusion, vol. 10, no. 2, pp. 163– 171, 2009. [3]. F. Belhloul, M. Janier, P. Croisille, C. Poirier, and A. Boudraa, “Automatic assessment of myocardial viability based on PET-MRI data fusion”, in Proc. of 20th International Conference of the IEEE Engineering in Medicine and Biology Society, Hong Kong, China, Nov. 1998. [4]. Mirajkar Pradnya P. and Sachin D. Ruikar Mirajkar, “Image Fusion Based on Stationary Wavelet Transform”, International Journal of Advanced Engineering Research and Studies, ISSN: 2249–8974, July 2013 [5]. Q. Gao, Y. Zhao and Y. Lu, “ Despecking SAR image using stationary wavelet transform combining with directional filter banks”, Appiled Mathematics and Computation, vol. 205, pp. 517–524, 2008 [6]. M.A. Mohamed, R.M EI-Den, “Implementation of Image Fusion Techniques for Multi-Focus Images Using FPGA”, 28th National radio science conference, 2011. [7]. Jionghua Teng, Xue Wang, Jingzhou Zhang and Suhuan Wang International Congress on Image and Signal Processing (CISP2010). [8]. Zhiming Cui, Guangming Zhang, Jian Wu, “Medical Image Fusion Based on Wavelet Transform and Independent Component Analysis”, International Joint Conference on Artificial Intelligence (JCAI ’09), Hainan Island, April 2009, pp 480-483, April 2009. [9]. De-gan Zhang, Chao Li, Dong Wang, Xiao-li Zhang, “A New Method of Image Data Fusion Based on FNN”, IEEE, 2010. [10]. http://www.med.harvard.edu/aanlib/home.html [11]. https://www.imagefusion.org