Research Journal of Applied Sciences, Engineering and Technology 4(24): 5548-5551, 2012
ISSN: 2040-7467
© Maxwell Scientific Organization, 2012
Submitted: April 07, 2012
Accepted: April 25, 2012
Published: December 15, 2012
Comparative performance of image fusion methodologies in eddy current testing
S. Thirunavukkarasu, B.P.C. Rao, Anil Kumar Soni, S. Shuaib Ahmed and T. Jayakumar
Nondestructive Evaluation Division, Indira Gandhi Centre for Atomic Research, Kalpakkam,
TN 603 102, India
Abstract: Image fusion methodologies have been studied for improving the detectability of eddy current
Nondestructive Testing (NDT). Pixel level image fusion has been performed on C-scan eddy current
images of a sub-surface defect at two different frequencies. Multi-resolution analysis based Laplacian
pyramid and wavelet fusion methodologies, statistical inference based Bayesian fusion and Principal
Component Analysis (PCA) based fusion methodologies have been studied towards improving the
detectability of defects. The performance of the fusion methodologies has been compared using image
metrics such as SNR and entropy. Bayesian based fusion methodology has shown better performance as
compared to other methodologies with 33.75 dB improvement in the SNR and an improvement of 3.22 in
the entropy.
Keywords: Bayesian fusion, eddy current testing, laplacian pyramid, nondestructive evaluation, principal
component analysis, wavelet transform
INTRODUCTION
Eddy current testing is one of the most popular
techniques for nondestructive evaluation of engineering
components and structures (Rao, 2007). Some of the
important applications of this technique include
detection of defects in tubes, rods and bars. Depth of
penetration of eddy currents in a metallic material
obeys the classical skin effect phenomenon. As a result,
defects which are open to surface are readily detected.
Use of lower excitation frequencies enhances
penetration of eddy currents enabling the detection of
sub-surface defects, however with an associated
decrease in resolution and Signal-to-Noise Ratio
(SNR). In this regard, combining the EC data (image)
obtained from different frequencies is beneficial and
expected to enhance the defect detection probability.
The process of combining two or more images
containing complementary as well as redundant
information into a single image is called image fusion.
Image fusion maximizes the information content in the
image. Image fusion is gaining importance in NDE and
image fusion based on multi-resolution analysis and
statistical inferences are widely used Gros (1997) and
Prachetaa and Rao (2010). Apart from NDE, image
fusion method has reported to be successfully used in
various applications (Burt and Adelson, 1983; Naidu
and Rao, 2008; Djafari, 2003). In this study, Laplacian
pyramid, Wavelet transform, Bayesian and Principal
Components Analysis (PCA) based pixel level image
fusion methodologies have been implemented for
fusion of eddy current images of subsurface defects
obtained at different frequencies. The study presents the
results of comparison of performance of the four
techniques.
THEORETICAL BACKGROUND
In this section, brief details of the principles of four
fusion methodologies namely Laplacian pyramid,
wavelet transform, Bayesian and PCA are given.
Laplacian pyramid based fusion: Laplacian pyramid
sub-samples the image into different resolution levels
(Burt and Adelson, 1983). With an increase in the level,
there is a decrease in resolution and increasing in
scaling level of the image. Each level of the image Ii is
constructed by low pass filter and decimation by 2 with
i = 0 as the original image. Higher level image Ii can be
constructed using Ii-1 as:
Ii= Reduce(Ii-1)
(1)
and residual at that stage using:
Residuali-1=Ii-1– Expand(Ii)
(2)
Lower level image can be reconstructed by
interpolating it by 2 along with its residual using:
Ii = Expand (Ii+1) + Residuali
(3)
Corresponding Author: B.P.C. Rao, NDE Division, Indira Gandhi Centre for Atomic Research, Kalpakkam 603 102, TN, India
5548
Res. J. Appl. Sci. Eng. Technol., 4(24): 5548-5551, 2012
Wavelet transform based fusion: Wavelet transform
decomposes an image into four coefficients namely,
LL, LH, HL and HH using high-pass and low-pass
filters (Naidu and Rao, 2008). LL coefficient contains
less redundant information, while LH, HL and HH
contain directional information of the image.
Decomposition of an image Ii is performed by:
I
W
I
W
(4)
is the input image, W is the twiddle factor
where, I
matrix given by; W Fusion of source images is performed in wavelet
transformed domain. Coefficients of the images after
transformation are fused together and inverse wavelet
transform is used for reconstruction of the fused image.
Bayesian based fusion: It involves formulating the
fusion problem in probabilities (Djafari, 2003). Input
images are assumed to be independent events with the
likelihood of images I1…IN is given by:
p I , … , I |θ
∏
p I |θ
(5)
where, p (θ) is the prior and known knowledge about
occurrence of defect. The posterior distribution
according to the Bayes principle, is given by:
p θ|I , … , I
∝p θ ∏
p I |θ
Fig. 1: Cross sectional view of the geometry modeled by
CIVA to generate EC images of defects
GENERATION OF EDDY CURRENT IMAGES
As experimental generation of eddy current images
is cumbersome, numerical model has been used to
obtain the images. Numerical modeling of subsurface
defects present in a 5 mm thick stainless steel plate is
carried out using CIVA which is benchmarked software
for NDE techniques (Reboud et al., 2009). Eddy current
images of a defect (5×1×0.5 mm, respectively) located
at a depth of 2.5 mm below the surface of a 3 mm thick
stainless steel plate have been predicted at 125 and 200
kHz for 3 and 5 mm diameter EC coils, respectively.
Modeled geometry is shown in Fig. 1.
The quality of the images has been assessed using
metrics such as SNR and entropy. The entropy (H) is
defined as:
H
∑
P i log P i
(8)
(6)
The prior probability has been formulated as
normal distribution with zero mean and unit standard
deviation. The individual pixel values of the images are
taken as the likelihood.
Principal components analysis based fusion:
Principal Component Analysis is a linear
transformation method (Naidu and Rao, 2008; Rao
et al., 2007; Shuaib et al., 2012). In PCA, the
covariance of an image matrix is computed and a
subspace with larger Eigen values of covariance is
retained. Let:
where, P(i) is the probability of intensity at pixel level
of image. The higher the SNR and entropy, the higher is
the probability of detection of defects. Random noise
has been added to the model simulated images (noise
level is 30% of the maximum amplitude), in order to
represent the practical eddy current testing.
PERFORMING IMAGE FUSION
In order to implement the Laplacian pyramid based
fusion, input images have been transformed into two
levels, to obtain two sub-sampled image with residuals.
Then the image is restored to its original resolution
using inverse Laplacian pyramid transform. For wavelet
∑
(7)
transform based fusion, images are decomposed into
two levels and fused in the transformed domain. For
Bayesian based fusion, it is assumed that the defects are
be the covariance matrix of image with elements of Cx
segmented such that the center of the defect
denoted by cij. The Eigen vectors of this matrix, if
corresponds to the central pixel of the image. Raw
sorted, in descending order of Eigen values, the results
images are normalized using z-score normalization for
will reveal the orthogonal basis with first Eigen vector
PCA based fusion and the images are fused in
having the direction of largest variance of the data.
transformed domain and then reverted using the inverse
Fusion of images is performed in this projected domain
with fewer Eigenvectors.
transform.
5549 Res. J. Appl. Sci. Eng. Technol., 4(24): 5548-5551, 2012
Fig. 2: Raw eddy current images of a subsurface defect with 30% random noise, a) 125 kHz and, b) 200 kHz and images
Fig. 3: Fused images using, a) Laplacian pyramid, b) Wavelet transform, c) Bayesian and, d) PCA based fusion methodologies
5550 Res. J. Appl. Sci. Eng. Technol., 4(24): 5548-5551, 2012
Table 1: Comparative performance of fusion methodologies
S. No:
Image
SNR, dB
Entropy
1
Raw image (125 kHz)
3.25
1.47
2
Raw image (200 kHz)
6.45
2.04
3
Laplacian
6.46
1.95
4
Wavelet
6.74
2.37
5
Bayesian
33.75
3.22
6
PCA
11.75
0.04
ACKNOWLEDGMENT
Authors thank Mr. S.C. Chetal, Director, Indira
Gandhi Centre for Atomic Research, Kalpakkam, India
for encouragement and support.
REFERENCES
RESULTS
Figure 2 shows the raw EC images of the
subsurface defect at 125 and 200 kHz with 30% random
noise and the fused images using different
methodologies is shown in Fig. 3.
As can be seen from Fig. 2, at 125 kHz the defect
is not detected clearly. A good improvement in the
quality of the images is observed after fusion by all the
four fusion methodologies. Table 1 shows the SNR and
entropy values of the raw and images fused by different
methodologies. Laplacian pyramid based fusion
smoothened the effect of noise. However, a decrease in
noise was found after wavelet fusion. A 33.75 dB
improvement in the SNR and an improvement of 3.22
in entropy have been achieved for the Bayesian fusion
methodology. The PCA based fusion methodology
showed significant improvement in the SNR of 11.75
dB, next to Bayesian while only 0.04 improvement in
entropy could be achieved. The performance of multiresolution based Laplacian and Wavelet fusion
methodologies are comparable to each other both in
terms SNR and entropy.
CONCLUSION
Laplacian pyramid, wavelet transform, Bayesian
and PCA based pixel level image fusion methodologies
have been applied to eddy current images of subsurface
defects, towards improving the probability of detection.
The images have been generated using CIVA software
and 30% noise has been added to simulate practical test
conditions. When SNR and entropy are compared, the
Bayesian fusion method showed highest SNR (33 dB)
and entropy (3.22) and found to be superior as
compared to the other fusion methodologies.
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