Post on 11-Mar-2020
International Journal of Electronics Engineering Research.
ISSN 0975-6450 Volume 9, Number 5 (2017) pp. 677-693
© Research India Publications
http://www.ripublication.com
Arnold transform based Security Enhancement using
Digital Image Watermarking with Complex Wavelet
Transform
Sukhwinder Kaur,1,* and Dr. Rajneesh Talwar2, *
1 PhD Research Scholar, IKJPTU Jalandhar, India.
2 Principal, CGC Group of Colleges, Janjheri, Punjab, India.
Abstract
Digital image security is of utmost importance in today’s scenario. This paper
proposes a novel type of image security method involving Arnold
transformation and frequency domain transformation i.e. Dual Tree Complex
wavelet transform (DTCWT) .The main idea here is to decompose the cover
image into sub-bands using dual tree complex wavelet transform and then
applying Arnold Transform to the watermark image and again DTCWT is
applied to encrypted image. Finally watermarking rule is applied and
watermarked image is obtained. Here we are aiming at comparing the
performance of extracting the watermark from different sub planes of complex
wavelet transform which has not been done so far. A detailed analysis is
carried out to compare the performances against attacks in various subplanes.
The experimental results clearly show a better visual imperceptibility and an
excellent resiliency of the proposed watermarking scheme against various
types of attacks. The security is evaluated using a correlation coefficient and
PSNR values.
Keywords: Dual Tree Complex Wavelet Transform,Arnold Transform.
1. INTRODUCTION
Digital watermarking has gained a lot of importance in recent years as protection of
data i.e. may be images audio or videos . A robust watermark can resist all types of
attacks, while a fragile watermark gets destroyed even after the smallest
unintentional manipulation.
678 Sukhwinder Kaur and Dr. Rajneesh Talwar
Most of the image watermarking methods use Discrete Cosine Transform[2] (DCT)
or wavelet domain for detecting the tampered regions in the image. The original
image is partitioned into blocks, and selected block is embedded with its own
watermark using a secret key [5]. In [9] ridgelet transform as an efficient transform
for representing images with line singularities was proposed. Our proposed algorithm
aims on eliminating the drawbacks of such schemes, using a Dual Tree Complex
Wavelet Transform (CWT) based approach and Arnold Transformation. The DTCWT
is used to increase the robustness while encryption increases the security of the
watermark. From the simulation results it can be seen that our algorithm gives better
results in terms of PSNR ratio and along with that security of watermark is also
covered effectively. Proposed algorithm improves the quality of the watermarked
image, unlike conventional block-based methods.[7] The algorithm can work
effectively against geometrical attacks like rotation, Gaussian noise, salt and pepper
noise etc. The remainder of this paper is organized as follows. In Section 2 we present
the proposed complex wavelet transform scheme in the wavelet domain, and the basic
concept of Arnold Transformation. Section 3 contains the proposed block diagram for
watermark embedding and extraction .The results and performances of the proposed
scheme and conclusions are given in Section 4.
2. BACKGROUND
2.1 Basics of Wavelet Transform
Whenever DTCWT is applied to 2-D signals or images, it exhibits the following
features it is performed separably, using 2 trees for the rows of the image and 2 trees
for the columns of the image yielding a Quad-Tree structure with a 4:1 redundancy
[16].These 4 quad-tree components of each coefficient are combined by simple sum
and difference operations to yield a pair of complex coefficients. These are part of
two separate sub bands in adjacent quadrants of the 2-D spectrum. This produces 6
directionally selective sub bands at each level of the 2-D DT CWT. The DT CWT is
directionally selective because the complex filters can separate positive and negative
frequency components in 1-D, and hence separate adjacent quadrants of the 2-D
spectrum. Real separable filters are not able to implement this [16].That is why we get
better result for watermarking using DTCWT.Typical features of the Dual Tree
Complex Wavelet Transform (DT CWT) include good shift invariance that means
negligible aliasing. [1].Hence transfer function through each sub band is independent
of shift, and wavelet coefficients can be interpolated within each sub band,
independent of all other sub bands. Good directional selectivity in 2-D, 3-D etc. –
derives from analyticity in 1-D (ability to separate positive from negative
frequencies).Perfect reconstruction with short support filters is possible which is also
proved through the quality of the retrieved watermark [16].
Arnold transform based Security Enhancement using Digital Image Watermarking.. 679
2.2 DWT
Wavelets are the basis functions of a relatively new type of mathematical transform
that occupies a space between the spatial domain of image pixels, and the frequency
(Fourier) domain of spatial frequency components. Wavelet functions are scaled and
shifted versions of a common mother wavelet shape. In that sense they are simpler
than Fourier functions. Usually wavelets are scaled in generations: each parent having
4 children in 2-D, and each child being half the size (in length) of its parent.[3]The
main reason for using this transform is that we do not loose information[12] .
Wavelets are used mainly for analysis and synthesis of signals specially image
signals. As a signal consists of many frequencies wavelets can be applied for either
1D, 2D & 3D signals. [4]The main advantage being that it is a separable transform i.e.
it can be applied row wise and column wise, also called mathematical microscope as
more details are visible , by changing the scale of the picture so we can zoom to any
frequency with wavelets .In standard wavelet like DWT,only 3 directions i.e.
LL,LH,HH are available ,so to overcome this complex wavelet transform is used as in
complex wavelets, we have two trees one for real and another for imaginary .Each one
of them gives information in 3 directions ,so we get information in 6 directions.
If f(t) is the original signal ,then transform is given as
dt
Here the kernel function changes according to transform
dt
)
standard wavelet we are having one scaling function and and one wavelet
function Ψ(t) but in complex wavelets we are having two scaling functions and a pair
of wavelet functions [4]
This is called Hilbert pair [14] since they are having phase shift of 90°.Because of so
many directions characterization is done more efficiently in all the directions. So
complex wavelets are of great importance in watermarking as we need to preserve
680 Sukhwinder Kaur and Dr. Rajneesh Talwar
information in all the directions effectively in applications like watermarking.As the
watermarked image [4]goes through the communication channel ,it can be affected
by attacks of various types of attacks during this process. So in order to retrieve the
original image or the watermark effectively DTCWT proves out to be quite beneficial.
As the DTCWT is an extension to standard wavelet & uses two separate trees of real
DWT filters that operate in parallel to generate real and imaginary parts of a complex
filter so we have double number of coefficients in DTCWT so more features can be
extracted. [11]When we implement watermarking using DTCWT ,the quality of the
watermarked image is much better than DWT which is visible through the value of
PSNR .When the watermarked image travels through the communication channel ,the
watermark can be retrieved back efficiently as compared to standard wavelet .To add
to security feature we have encoded watermark image using Arnold transformation
and then inserted it as a watermark to the cover image .To ensure level of security a
key is used while insertion and at the receiver side same key has to be given in order
to retrieve the watermark or the cover image.The results of this are much better as
compared to wavelet i.e. DWT in terms of PSNR and security .[8] So when we apply
DTCWT to image watermarking also we get six directionally selective subbands at
each level of the 2D DTCWT which provide us more information and hence during
watermarking when the image goes through the communication channel and has to be
retrieved again at the receiver end DTCWT gives better result as compared to
standard wavelets like DWT,DCT etc[4][17].
The Arnold transform has been used for encrypting the watermark image to provide a
feature of additional security.
Scrambling of the watermark ensures that the watermark cannot be extracted at the
receiver without the particular key which was used at the time of encryption.[10] This
adds more level of security to our algorithm Image scrambling technology depends on
data hiding technology which provides non-password security algorithm for
information hiding. The image after scrambling encryption algorithms is chaotic, so
attacker cannot decipher it [20].
3. PROPOSED WATERMARKING METHOD
In DWT one of the main limitations is that whenever the watermarked image
undergoes rotation ,watermark gets destroyed and cannot be retrieved at all but with
complex wavelet transform this problem is overcome & the watermark is effectively
retrieved. The DTCWT coefficients obtained from the first filter bank are called the
real part and the coefficients obtained from the other filter are called the imaginary
part. The real part of the image contains less important data compared to the
imaginary part which contains more information. Our algorithm embeds the
watermark into the whole image, that is, both the real and imaginary parts. This is
preferable because if an attack occurs while transmitting, it can be easily identified
While retrieving we can retrieve with the help of one of the subplanes. In other words,
if only the real part is used for watermark embedding and an unauthorized person tries
Arnold transform based Security Enhancement using Digital Image Watermarking.. 681
to extract the watermark, it can be done with much ease because the real part contains
less information and the sender would not even come to know about it. In the case of
using both real and imaginary parts, an attack can be easily identified as the imaginary
part contains more important information. If the filters in the upper and lower DWTs
are the same, then no advantage is gained. However, if the filters are designed is such
a way that the subband signals of the upper DWT can be interpreted as the real part of
a complex wavelet transform, and subband signals of the lower DWT can be
interpreted as the imaginary part. Equivalently, for specially designed sets of filters,
the wavelet associated with the upper DWT can be an approximate Hilbert transform
of the wavelet associated with the lower DWT. When designed in this way, the dual-
tree complex DWT is nearly shift-invariant, in contrast with the critically-sampled
DWT. Moreover, the dual-tree complex DWT can be used to implement 2D wavelet
transforms where each wavelet is oriented, which is especially useful for image
processing.The proposed watermarking scheme is based on Dual Tree Complex
Wavelet Transform approach. The watermark embedding and extraction algorithms
are described below.
3.1 Block Diagram
3.1.1 Watermark embedding algorithm:
In order to ensure both imperceptibility and the security of watermark Arnold
transformation is used for encrypting the watermark by providing a private key. This
will ensure that the watermark can only be retrieved on the other end by putting that
very key which was used during encryption.
(1) Take cover image C of size m*n and apply DTCWT to it to give the wavelet
coefficients.
(2) After that Arnold transformation is applied to the watermark image W ,to encrypt
the image with the help of a particular key.
=
Where N is the order of the digital image
(3)Now again Dual Tree Complex Wavelet transform is applied to the encrypted
image to get the relevant wavelet coefficients.
(4)In the next step watermarking rule can be applied to the two images namely cover
image and watermark image.
(5) Finally Inverse Dual Tree Complex Wavelet transform is applied to get the final
the final watermarked image WI.
682 Sukhwinder Kaur and Dr. Rajneesh Talwar
DTCWT
Watermark
Image
Arnold Transform
DTCWT
Inverse DTCWTWatermarked
Image
Key
2nd Subplane
12th Subplane
1st Subplane
Cover Image
2nd Subplane
12th Subplane
1st Subplane
Apply watermarking rule
to the subabnd cofficients
Fig 1 Watermarking embedding algorithm using DTCWT with Arnold Transform
3.1.2 Watermark extraction algorithm
(1) Decompose the watermarked image WI into sub-bands using Dual Tree Complex
Wavelet Transform.
(2) From the coefficients obtained subtract the coefficients of cover image C ,we will
get the coefficients of the watermark image W’. This step is carried out for every
subplane separately.
(3) Apply inverse DTCWT to obtain the watermark image.
(4) Now apply inverse Arnold transform along with suitable key to get back get back
the decrypted watermark.
Arnold transform based Security Enhancement using Digital Image Watermarking.. 683
Watermarked Image DTCWT
Cover ImageDTCWT
Subtraction of cofficients
Inverse CWTEncrypted Water mark Inverse Arnold
TransformWatermark
Key
Selection of coff.
Of a particular
subabnd
Selection of coff.
Of a particular
subabnd
Fig 2 Watermark Extraction algorithm using DTCWT with Arnold Transform
4. EXPERIMENTAL RESULTS
When DWT is used for watermarking, it has many limitations.DWT replaces
infinitely oscillating basis functions of the fourier transform with a set of locally
oscillating basis function called wavelet. Any finite energy analog signal x(t) can be
decomposed in terms of wavelet & scaling functions. They provide a time frequency
analysis of the input signal by measuring the frequency content controlled by scale
factor, j at various times which is controlled by time shift n scaling coefficients c(n) &
wavelet coefficients d(j, n) are computed via inner products .Wavelets especially
Discrete Wavelet Transform based techniques are used in watermarking but the
results have not been up to the mark. The problems faced are that of oscillations ,shift
variance, lack of directionality etc. Wavelets especially discrete wavelet transform
have been employed in watermarking lately, As a result of extensive experimentation
we observe that watermarking with DTCWT gives much better results as compared to
discrete wavelet transform and because of addition of Arnold Transform the main
feature of security which is needed in watermarking also gets enhanced.DWT shows
limitations in case of complex signals such as radar, music, or geophysics &
imaging.CWT presents much more efficient representation for many types of
signals.More number of complex coefficients are obtained at various angles in case of
complex wavelet transform, which gives it an edge over DWT in case of
watermarking applications.[19] For this reason watermark can be embedded more
effectively with the help of complex wavelet transform. Wavelet coefficients are
widely spaced so it results in aliasing in DWT. Any wavelet coefficient processing
disturbs the delicate balance between forward and inverse transforms leading to
artifacts.
684 Sukhwinder Kaur and Dr. Rajneesh Talwar
In reconstructed signal, DWT is lacking directional selectivity which greatly
complicates processing of edges etc. And causes severe limitations in case of
watermarking when it suffers attacks. If the watermarked image undergoes attacks
like rotation DWT would not be able to identify it as it cannot distinguish between
+45 &-45.[18]The basis of complex wavelets is the fourier transform ,as the
magnitude of fourier transform does not oscillate between positive and negative but
gives a smooth envelope in the fourier domain that is why we are able to retrieve
watermark effectively .Several experiments are carried out to measurethe performance
of the proposed watermarking in terms of imperceptibility and robustness against
attacks. A variety of images were tested for watermarking.Image quality is measured
using peak signal to noise ratio (PSNR) and mean square error (MSE). Lower the
value of MSE lower the error and better picture quality.
4.1 Peak Signal to Noise Ratio (PSNR)
For measuring image quality peak signal to noise ratio (PSNR) and mean square error
(MSE) are used. A low value of MSE indicates lower error and better picture quality.
Mean Square Error between original image and watermarked image is calculated as
follows:
𝑋 𝑖,𝑗 : Original image,
𝑋′ 𝑖,𝑗 : Watermarked image, and
𝑁𝑡 : Size of image
PSNR is calculated between the original and the watermarked image. The larger the
PSNR value, more similar is watermarked image to the original image. This image
quality metric is defined in decibels as:
The watermarked cameraman image with size 256×256 undergoing attacks are
shown in Fig. 3(a) These watermarked images are tested for various attacks namely
speckle noise, poisson noise,rotation ,salt and pepper noise and watermark is
extracted from the attacked images. The NC values are calculated for original
watermark and extracted watermark .Fig 3 below shows the proposed watermarking
rule applied to three images ,and the extracted watermarks.
Arnold transform based Security Enhancement using Digital Image Watermarking.. 685
Fig. 3. Watermarked images a Rice having PSNR=58.2384 and extracted watermark
in (d) with NC=1 (b) Cameraman having PSNR =58.2384 and extracted watermark in
(e) with NC=1 (c) Woman Blonde having PSNR=56.2135 dB and extracted
watermark in (f) with NC=1
Fig 4 below shows the proposed watermarking rule applied to three images and then
gaussian noise attack applied and the extracted watermarks in each case.
686 Sukhwinder Kaur and Dr. Rajneesh Talwar
Fig. 4 Watermarked images with Gaussian noise Rice having PSNR=39.930 and
extracted watermark in (d) with NC=0.9998 (b) Cameraman having PSNR =40.0530
and extracted watermark in (e) with NC=0.9998 (c) Woman Blonde having
PSNR=39.9527 dB and extracted watermark in (f) with NC=0.9998.
Experiments were carried out to evaluate the performance of the proposed
watermarking method against different types of attacks like rotation, salt and pepper
noise, speckle noise ,Gaussian noise etc and the extracted watermark in each case.
(a)
Poisson Noise
(b)
Rotation 60
(c)
Salt
and pepper Noise
(d)
Gaussian Noise
0.01
PSNR =
40.1714
NC = 0.9998
PSNR
=29.7454
NC = 0.9981
PSNR =42.5652
NC = 0.9992
PSNR =
36.5953
NC = 0.9981
Fig 5 Cameraman image(256*256) under attacks i.e. Speckle, Poisson, Rotation,
Salt & Pepper & Gaussian noise & corresponding retrieved watermarks
Arnold transform based Security Enhancement using Digital Image Watermarking.. 687
While carrying out the experimentation , comparison is made as to how the results are
effected in case of using only a particular sub plane for retrieving the watermark and
using the reconstruction filter for the same. The values of Normalised correlation &
PSNR are compared for all the sub planes of DTCWT in order to see how close the
retrieved watermark is to the original watermark.
Performance under attacks
Experiments were carried out to evaluate the performance of the watermarking
method against different types of attacks like rotation, salt and pepper noise, speckle
noise ,Gaussian noise etc. Table 1 shows the comparison of watermark extraction
from different subplanes ,the PSNR & NC in each case and the embedding capacity
of the watermarking channel.A comparison chart of Normalised correlation wrt
different subplanes is shown in Fig 7.It is clear that watermark is effectively
recovered in each case.
Table 1. Comparison of PSNR values under attack of speckle noise (0.002)
Speckle Noise Image Cameraman
MSE RMSE PSNR(dB) NC Embedding
capacity
1 w1{j}{1}{1}{1} 0.0884 0.2973 42.7375 0.9997 5.4508
2 w1{j}{1}{2}{1} 0.3096 0.5565 42.7368 0.9998 5.4508
3 w1{j}{1}{2}{2} 0.0986 0.3410 42.7372 0.9997 5.4508
4 w1{j}{1}{2}{3} 0.0407 0.2018 42.7319 0.9997 5.4501
5 w1{j}{1}{1}{3} 0.0160 0.1266 42.7163 0.9997 5.4501
6 w1{j}{1}{1}{2} 0.0549 0.2344 42.7195 0.9997 5.4502
7 w1{j}{2}{1}{2} 0.0913 0.3022 42.7081 1 5.4498
8 w1{j}{2}{2}{2} 0.0922 0.3036 42.7375 1 5.4508
9 w1{j}{2}{2}{3} 0.2706 8.7683 42.7368 1 5.4508
10 w1{j}{2}{2}{1} 0.2707 0.5203 42.7372 1 5.4508
11 w1{j}{2}{1}{1} 0.2354 0.4852 42.7319 1 5.4506
12 w1{j}{2}{1}{3} 0.2351 0.489 42.7163 1 5.4501
688 Sukhwinder Kaur and Dr. Rajneesh Talwar
Fig 7. Variation of NC in different subplanes of DTCWT.
It is observed that the value of PSNR is higher in case of w1{j}{2}{2}{2}&
w1{j}{1}{1}{1} and lowest in case of w1{j}{2}{1}{2} as is evident from the graph
but even then in all such cases it is seen the the value of Normalised correlation
varies within the range of 0.997 to 1 in all cases thus depicting that the retrieved
watermark is similar to the embedded watermark. Embedding capacity is better as
compared to the technique employed in [29].
Table 2. Comparison of PSNR ,MSE,RMSE & NC values under attack of poison
noise
Poisson noise Image Cameraman
MSE RMSE PSNR NC Embedding
Capacity
1 w1{j}{1}{1}{1} 39.8972 6.3164 40.1261 0.9977 5.3620
2 w1{j}{1}{2}{1} 39.4634 6.2820 40.1498 0.9974 5.3628
3 w1{j}{1}{2}{2} 39.2974 6.288 40.1590 0.9982 5.3631
4 w1{j}{1}{2}{3} 39.4986 6.2848 40.1479 0.9978 5.3627
5 w1{j}{1}{1}{3} 39.7964 6.3084 40.1316 0.9977 5.3622
6 w1{j}{1}{1}{2} 39.5199 6.2865 40.1467 0.9981 5.3627
7 w1{j}{2}{1}{2} 39.3027 6.2692 40.1587 0.9997 5.3631
8 w1{j}{2}{2}{2} 39.4156 6.2782 40.1525 0.9997 5.3629
9 w1{j}{2}{2}{3} 39.7160 6.3021 40.1360 0.9996 5.3623
10 w1{j}{2}{2}{1} 39.6134 6.2939 40.1416 0.9997 5.3625
11 w1{j}{2}{1}{1} 39.1881 6.2600 40.1650 0.9998 5.3633
12 w1{j}{2}{1}{3} 39.3654 6.2742 40.1552 0.9998 5.3630
Arnold transform based Security Enhancement using Digital Image Watermarking.. 689
A comparison chart of Normalised correlation wrt different subplanes is shown in Fig
8.It is clear that watermark is effectively recovered in each case.
Fig 8. Variation of PSNR in different subplanes of DTCWT.
Table 4 gives a comparison of proposed method in terms of rotation noise, speckle
noise, salt & pepper noise, gaussian noise and resizing with latest methods. In case of
rotation attack NC is 0.9988 and in other methods it is 0.7351[17'] &0.6841 in [14].In
case of speckle noise also NC is 0.9994 as compared to 0.9867 in [22]] .In case of salt
& pepper noise NC is 0.9963 as compared to 0.6573 in[17'].In case of gausian noise
NC is 0.9989 as compared to 0.9376 in[22] .Even in case of resizing attack NC is
equal to 1as compared to 0.9851 in [22].The performance of proposed method against
geometric attacks namely rotation and resizing is better in this case.
Table 3. Comparison of PSNR ,MSE,RMSE & NC values under mentioned attacks
and its comparison with latest methods
Image Proposed
Method
Ansari &
Pant[22]
Shishir
Kumar[26]
Bhatnagar &
Raman [28]
Bhatnagar&
Raman [27]
Rotation(60)* 0.9988 ---- 0.7351 0.6841 -----
Speckle Noise(0.01) 0.9994 0.9867 0.6743 0.6743 0.6644
Salt & Pepper
Noise(0.001)
0.9963 ---- 0.6573 0.6512 0.3557
Gaussian
Noise(0.01)
0.9989 0.9376 0.6684 0.6644 0.2575
Resizing
( 256->512->256)*
1 0.9851 0.8728 0.7619 ----
Note:* Indicates geometric attacks
690 Sukhwinder Kaur and Dr. Rajneesh Talwar
The above experiments have been carried on a set of 9 images namely Rice(PSNR
51.8dB), Cameraman (PSNR = 51.8494 dB) , Woman Blonde (PSNR = 51.6284 dB) ,
Khairnar ( PSNR 51.6138 dB) , Pirate (PSNR 51.6101 dB) ,Mandrill (PSNR
51.6091 dB), Living Room( PSNR 51.6237 dB),Boat( PSNR = 51.6121 dB) ,Lena
(PSNR 51.6243 dB) .
CONCLUSION
We have presented an algorithm for increasing the security using Digital Image
Watermarking by Complex Wavelet Transform with Arnold Transform. And we have
basically compared the performances of different sub planes of DTCWT in terms of
RMSE, PSNR & NC. A detailed analysis is done for all the sub planes .It is found that
the value of PSNR obtained in all the sub planes is approximately 50dB,and the value
of NC is nearly equal to 1 which indicates that the retrieved watermark is nearly same
as embedded watermark. So with improved PSNR we have also added feature of
security. The algorithm shows robustness against some common signal attacks like,
salt and pepper noise, speckle noise, Gaussian noise, rotation etc. The watermark
survives even when the image undergoes attacks.
ACKNOWLEDGEMENTS
We would like to acknowledge the support offered by IK Gujral Punjab Technical
University, Jalandhar, Punjab ,India by means of providing access to the latest
journals and making available the resources.
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692 Sukhwinder Kaur and Dr. Rajneesh Talwar
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AUTHORS DETAILS:
Sukhwinder Kaur is working as an Assistant Professor in JSPM’s
Imperial College of Engineering & Research ,Pune since 2008 and is
presently pursuing PhD from IKGPTU Jalandhar. She is having an
experience of more than 14 years in Teaching . She received
M.Tech. in Electronics and Communication Engineering from Guru
Nanak Dev Engineering College in 2008 and B.Tech. Degree in
Electronics Engineering from Giani Zail Singh College of Engineering & Technology
in 2002. Her research interests are Digital Image watermarking, Image Denoising, She
has more than 10 research publications in various national and international journals
and conferences to his credit and has guided 12 M.Tech. students.
Dr. Rajneesh Talwar is presently working as Professor and
Principal, CGC- College of Engineering at Chandigarh group of
colleges,Jhanjeri, Punjab India. He has a Professional experience of
more than 15 years in teaching and research. He has a U.S patent
“FIBER OPTIC POINT TEMPERATURE SENSOR” to his credit,
six international Journal Publications, presented six papers at
International conferences and many national level conference participations. He is
Editorial board member of International Journal of Engg. Science and Technology,
Nigeria, Reviewer of MAEJO International Journal of Engineering Science and
Technology, Thailand and “Materials and Design”, a ELSEVIER International
Journal. `Already guided one M.Tech thesis and two more students are pursuing
M.Tech thesis under him. Presently guiding five candidates for their Phd.
work..Recently he has been conferred with Bharat Vidya Shiromani Award by
International Business Council.
694 Sukhwinder Kaur and Dr. Rajneesh Talwar