a new robust adjustable logo watermarking scheme

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A new robust adjustable logo watermarking scheme

Gaurav Bhatnagar a,*, Q.M. Jonathan Wua, Balasubramanian Raman b

aDepartment of Electrical and Computer Engineering, University of Windsor, Windsor, ON N9B 3P4, CanadabDepartment of Mathematics, Indian Institute of Technology Roorkee, Roorkee 247 667, India

a r t i c l e i n f o

Article history:

Received 4 June 2011

Received in revised form

6 October 2011

Accepted 10 November 2011

Keywords:

Digital watermarking

Fractional wavelet packet transform

Singular value decomposition

Quadratic residues

* Corresponding author. University of WindWindsor, ON N9B 3P4, Canada. Tel.: þ1 5195

E-mail addresses: [email protected] (G0167-4048/$ e see front matter ª 2011 Elsevdoi:10.1016/j.cose.2011.11.003

a b s t r a c t

In this paper, a novel, yet simple, watermarking algorithm for image authentication is

proposed using fractional wavelet packet transform (FRWPT) via singular value decom-

position (SVD). Unlike the traditional watermarking schemes where the watermark is

added to the transform coefficients, the proposed algorithm is based on embedding in the

singular values (luminance) of the host image. To improve the fidelity, the perceptual

quality of the watermarked image and to enhance the security of watermarking, we model

an adjustable watermarking algorithm. The meaning of the word adjustable is that the

watermark is embedded into the host image by taking two watermark embedding

strengths, according to owner and some cryptographic conditions. Finally, a reliable

watermark extraction algorithm is developed for the extraction of watermark from the

distorted image. The feasibility of this method and its robustness against different kind of

attacks are verified by computer simulations and comparison with the existing work.

ª 2011 Elsevier Ltd. All rights reserved.

1. Introduction The spatial domain approaches work on a simple logic of

The phenomenal increase in the generation, transmission,

rapid use of internet andmultimedia inmany applications has

placed some very crucial issues for multimedia such as illegal

copying, distribution, editing, copyright protection etc. This

has led to an obsession with creating a technological barrier or

standard solution to protect the multimedia. Recently, to ach-

ieve the desired goal, digital watermarking has drawn much

attention as a standard solution to resolve these issues. Digital

watermarking is a technique for inserting one or more secret

information, called watermarks, into digital data (an image,

audio or a video), which can be later extracted or detected for

variety of purposes including identification and authentication

purposes. The embedding is done in suchaway that itmust not

cause serious degradation to the original digital media.

There are many ways to classify and analyze digital

watermarking techniques. Among these, the most common

taxonomies are embedding in spatial and frequency domains.

sor, Department of Elect637462.. Bhatnagar), jwu@uwindier Ltd. All rights reserve

modifying the intensity of image pixels to embed a water-

mark. The earlier watermarking techniques were almost

spatial-based approaches. The simplest example is to modify

the least significant bits (LSBs) of image pixels for embedding

the watermark. Such methods are fast but usually susceptible

to attacks (Schyndle et al., 1994; Hwang et al., 1999). On the

contrary, frequency domain approaches such as discrete

cosine transform (DCT) (Cox et al., 1997; Patra et al., 2010),

discrete wavelet transform (DWT) (Dawei et al., 2004; Kundur

and Hatzinakos, 2004; Reddy and Chatterjii, 2005; Rahman

et al., 2009; Lin and Lin, 2009; Peng et al., 2010; Al-Otum and

Samara, 2010; Wang et al., 2010; Run et al., 2011) and

wavelet packet transform (WPT) (Vehel and Manoury, 2000;

Reddy and Chatterji, 2004; Bhatnagar and Raman, 2009a,b)

transform the original data into the frequency domain and

modulate frequency coefficients to embed the watermark.

Frequency domain watermarking is more popular since it

provides more advantages and better performances than

rical and Computer Engineering, 401 Sunset Avenue, Essex Hall,

sor.ca (Q.M.J. Wu), [email protected] (B. Raman).d.

mailto:[email protected]



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c om p u t e r s & s e c u r i t y 3 1 ( 2 0 1 2 ) 4 0e5 8 41

those in the spatial domain. One well-known DCT-based

method proposed in Cox et al. (1997) is a spread spectrum

watermarking scheme which embeds a set of randomly

generated real numbers with Gaussian distribution into the

most significant magnitude DCT coefficients. The wavelet

based methods decompose an image into several sub-bands.

Each sub-band keeps some spatial localization and

frequency spread information. A watermark can be inserted

into certain or all sub-bands. Usually, these methods provide

more robustness against various attacks due to their excellent

spatial localization, frequency spread and multiresolution

characteristics. The wavelet based watermarking schemes

have one limitation. This limitation is the use of watermark

which is either Gaussian noise type sequence or binary image/

sequence. Only one or two schemes use a gray-scale mean-

ingful image as watermark. Particularly, a gray-scale water-

mark has more chance to survive than a binary or Gaussian

noise one because it carries tremendously continuous image

contents to preserve a certain degree of contextual relation-

ship effect even under a variety of attacks.

In order to embed a gray-scale watermark, a new trans-

form namely singular value decomposition (SVD) is explored

for watermarking. Until now,many researchers have come up

with a variety of SVD basedwatermarking techniques, and the

techniques proposed so far have been highly effective when

compared to the coeval techniques (Liu and Tan, 2002;

Chandra, 2002; Chang et al., 2005). These approaches work on

the simple concept of finding the SVD of a cover image or the

SVD of each block of the cover image and then modifying the

singular values to embed the watermark. Further, some

researchers have presented hybrid watermarking schemes in

which they have combined SVD with the other existing

transforms (Ganic and Eskicioglu, 2005; Li et al., 2007;

Bhatnagar and Raman, 2009a,b, 2010, 2011). The main reason

behind the hybridization is the fact that SVD based scheme

withstands a variety of attacks but it is not resistant to

geometric attacks like rotation, cropping etc. Hence, for

improving the performance hybridization is needed.

The main stressed motive of this work is to develop and

implement a new concept in SVD based hybrid adjustable

watermarking scheme for enhanced security. The meaning of

the word adjustable is that the watermark is embedded into

the host image by taking two watermark embedding

strengths, according to owner and some cryptographic

conditions. For this purpose, the concept of quadratic residues

is used. Further, a key concept is also introduced such that if

someone has the knowledge of full embedding process except

these keys then he/she can never extract the watermark

properly. Here, the key concept is introduced by the fractional

wavelet packet transform (FRWPT). Therefore, the develop-

ment of an adjustable watermarking system is proposed in

this work which will use the FRWPT as an actuating factor to

strengthen the security. The FRWPT is the combination of

time and frequency domains and this combination is decided

by an arbitrary angle called transform order. FRWPT essen-

tially exhibits the multiresolution property describing the

spatial as well as the frequency information. The transform

orders of the FRWPT act as the key in the proposed work.

The core idea is to decompose host image using FRWPT with

the used transform orders as potential keys followed by

modifying each sub-band singular values based on random

series (which is generated by a seed) and quadratic residues.

After embedding, inverse fractional wavelet packet transform

is performed to construct the watermarked image. Further,

a reliable watermark extraction scheme is developed for the

extraction of watermark from the distorted image. The

experimental results demonstrate better visual impercepti-

bility, resiliency and robustness of the proposed scheme

against intentional or un-intentional variety of attacks

whereas the superiority is carried out by the comparison

made by us with the existing methods.

The remaining paper is organized as follows. Section 2

briefly describes the associated watermarking schemes fol-

lowed by themathematical preliminaries in Section 3. Section

4 introduces the proposed adjustablewatermarking technique

in detail followed by experimental set-up in Section 5. Section

6 discusses the proposedmethod and comparisons with some

existing methods. Finally, conclusions are given in Section 7.

2. Previous works

Generally speaking, current watermarking techniques are not

strongly robust to all possible attacks, so their use is limited

(Licks and Jordan, 2005). We shall begin by introducing several

famous works which use gray-scale images or logos as

watermarks. These techniques are as follows.

2.1. Gray-scale watermark image based techniques

Kundur and Hatzinakos (2004) proposed the use of gray-scale

logo as watermark. They addressed a multiresolution fusion

based watermarking method for embedding gray-scale logos

into wavelet transformed images via salience factor. This

technique is not robust to geometric attacks. This is due to the

features of the fusion i.e. registration. Geometric attacks

generally disturb the registration between two images.

Therefore, this technique fails to give accurate watermark

estimation for geometric attacks. Reddy and Chatterjii (2005)

have proposed a method in which a gray-scale logo is

embedded in the significant wavelet coefficients selected on

the basis of Human Visual System (HVS) characteristics. They

extracted watermark from the distorted image by considering

the distortion caused by the attacks. This technique shows

very good robustness to image compression attacks but it is

sensitive to common attacks like noise addition, rotation and

sharpening. These are the only schemes which embeds gray-

scale watermarks without using SVD.

Liu and Tan (2002) have proposed the use of SVD in

watermarking. In their technique, authors find the singular

values of the host image and then modify them by adding the

watermark. SVD transform is again applied on the resultant

matrix to find the modified singular values. These singular

values are combined with the known component for getting

watermarked image. This technique shows better robustness

against geometric attacks when compared to wavelet based

techniques. Ganic and Eskicioglu (2005) proposed the water-

marking scheme in which the authors find the wavelet

transform of the host image and then apply SVD transform on

all sub-bands and watermark image. In order to find the




modified singular values, the singular values of watermark

and sub parts of the image are summed up. This technique

enhances the performance when compared to technique in

Liu and Tan (2002) but it is again not significantly robust to

geometric attacks especially cropping and resizing.

Li et al. (2007) have proposed a scheme similar to Ganic and

Eskicioglu (2005). The only difference between these two

schemes is that the watermark strength is randomly selected

in Ganic and Eskicioglu (2005) whereas here watermark

strength is determined by the human visual model by which

this scheme shows the excellent robustness against general

image processing attacks except cropping and rotation.

Bhatnagar and Raman (2010) have proposed a new transform

namely, distributed multiresolution discrete Fourier trans-

form (D-MR-DFT) with its application in watermarking. The

basic idea is to decompose host image by D-MR-DFT rather

thanDWT inGanic and Eskicioglu (2005). The use of D-MR-DFT

makes the scheme robust to geometric attacks to some extent

but makes it sensitive to most common attacks like filtering,

compression and sharpening. Another common drawback of

all these schemes is that there is no key concept in the process.

Therefore, if any intruder has the full knowledge of embedding

process then he/she can extract the watermark properly. Due

to this fact, the use of all these schemes are somewhat limited.

2.2. Performance analysis

Somegeneral requirements ofwatermarking technique are: (1)

it must not introduce artifacts or inconsistencies to the

watermarked image. In other words, the perceptual difference

between the host and watermarked image should be unno-

ticeable. Generally, this requirement is known as the imper-

ceptibility of the watermarking technique. (2) it should be

robust to different kind of attacks. In other words, robustness

refers to the ability of thewatermark to be preserved evenafter

distortions which may be introduced either intentionally or

un-intentionally. In the proposedwork, the adoptedmeasures

for imperceptibility and robustness are described as follows.

� Evaluation of Imperceptibility: The imperceptibility is

measured using peak signal to noise ratio based on human

visual system (PSNRHVS) (Egiazarian et al., 2006). Mathe-

matically, the PSNRHVS between two images f and g is given

by

PSNRHVS ¼ 10�log

�2552

MSEHVS

�(1)

where MSEHVS is the mean-square error, which is calculated

taking into account HVS and given by

MSEHVS ¼ 164ðM� 7ÞðN� 7Þ

XM�7

i1¼1

XN�7

j1¼1

X8

i¼1

X8

j¼1

��Fði; jÞi1 ;j1

� Gði; jÞi1 ;j1�Tcði; jÞ

�2(2)

where Fði; jÞi1 ;j1 and Gði; jÞi1 ;j1 are the DCT coefficients of 8 � 8

block for which the coordinates of its left upper corner are

equal to i1 and j1 for f and g respectively. Further, Tc(i,j ) is the

matrix of correcting factors such that 1=64P8i¼1

P8j¼1

ðTcði; jÞÞ2 ¼ 1.

Basically, the higher the PSNRHVS is, the better imperceptibility

of the watermarking technique is Egiazarian et al. (2006).

� Evaluation of Robustness: Robustness is judged by the

similarity between original and extracted watermarks. To

verify the robustness, the correlation coefficient is used and

given as

rðS;SÞ ¼Pri¼1

ðSðiÞ � SmeanÞðSðiÞ � SmeanÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffis ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffis (3)
Pri¼1
ðSðiÞ � SmeanÞ2Pri¼1

ðSðiÞ � SmeanÞ2

where S, S, Smean and Smean are the original, extracted singular

values, mean of original and extracted singular values and

r ¼ min(m,n) for original and extracted watermarks respec-

tively. The value of r lies between [�1, 1]. If it is equal to 1 then

the extracted singular values are just equal to the original

ones and if it is �1 then the difference is negative for the

largest singular values. In this case, the lighter parts of the

image become darker and darker parts become lighter, i.e.,

constructed watermark looks like negative thin film.

3. Mathematical preliminaries

This section gives the basic background, primarily the theory

of fractional wavelet packet transform, singular value

decomposition and quadratic residue on which the proposed

technique is based. These are as follows.

3.1. Fractional wavelet packet transform

Fractional Wavelet Packet Transform (FRWPT) is a realization

of the wavelet packet transform in the fractional Fourier

domain (Huang and Suter, 1998). The fractional Fourier

transformhas a unique property of describing the information

of spatial and frequency domain due to the rotation of

timeefrequency plane over an arbitrary angle. In contrast,

wavelet packet transform has a multiresolution property. A

combination of these two domains results into FRWPT that

exhibits multiresolution property, describing the spatial as

well as frequency domain information. The arbitrary angle is

called transform order/fractional order associated with the

transform. The mathematical representation of the FRWPT of

1D function f(t), having the transform order a is written as

Waðu; s; sÞ ¼ZN�N

ZN�N

fðtÞKaðt; xÞe�juxjs;sðxÞdtdx (4)

where s and s are the dilation (scale) and translation (position)

parameters respectively. Further, Ka(t,x) is the transform

kernel and is given by

Kaðt; xÞ ¼

8>><>>:

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� icot a

pei

t2þx2

2 cot a�ixtcsca asnpdðt� xÞ; a ¼ 2npdðtþ xÞ; a ¼ 2np� p

(5)

where n is a given integer. Like fractional Fourier transform,

FRWPT is also a combination of time and frequency domains.




The main property of FRWPT is that the signal obtained is in

purely time (wavelet packet) domain if transform order (a) is

0 and in purely frequency (fourier-wavelet packet) domain if

transform order (a) is p/2. Another important property of

FRWPT is the separable nature i.e. the two or higher dimen-

sion FRWPT is obtained by successively taking one dimen-

sional transform along all the axis.

3.2. Singular value decomposition

In linear algebra, the singular value decomposition (SVD)

(Golub and Reinsch, 1970) is an important factorization of

a rectangular real or complex matrix with many applications

in signal/image processing and statistics. Let A be a general

real (complex) matrix of order m � n. The singular value

decomposition (SVD) of A is the factorization

A ¼ U � S � VT (6)

where U and V are orthogonal (unitary) matrices and S is

a diagonal matrix given by S ¼ {diag(s1,s2,.,sr):r ¼ min(m,n)},

where si are in non-increasing fashion and are called the

singular values of the matrix A. On the contrary, the columns

of U are called left singular vectors whereas the columns of V

are called right singular vectors. The SVD and its characters

can efficiently reveal essential property of image matrix and

are possess algebraic and geometric invariance to some

extent. Therefore, it is necessary and doable to utilize singular

values of images as embedding coefficients in watermarking.

3.3. Quadratic residue

Quadratic residue (QR) (Burgess, 1997; Witno, 2008) is an

abstract mathematical concept from the branch of number

theory, which is now used in applications ranging from

acoustical engineering to cryptography and for the factoriza-

tion of large numbers. Mathematically, If there is an integer

0 < x < p such that

x2hqðmod pÞ (7)

i.e., the congruence (7) has a solution, then q is said to be

a quadratic residue (mod p). The trivial case q ¼ 0 is generally

excluded from the list of quadratic residues so that the

number of quadratic residues (mod p) is taken to be one less

than the number of squares (mod p). If the congruence (7) does

not have a solution, then q is said to be a quadratic non-

residue (mod p). The shorthand notations to indicate that q is

a quadratic residue (non-residue) is given as qRp (qNp). When p

is odd prime then the best way to determine whether q is

a quadratic residue or not, is Legendre symbol. The detailed

information on Legendre symbol can be found inWitno (2008).

4. Proposed watermarking technique

In this section, some of themotivating factors in design of our

approach to watermarking are discussed. The proposed algo-

rithm relies on FRWPT, quadratic residues and SVD. The core

idea is to transform host image using FRWPT followed by the

embedding of watermark in selected or all sub-bands. Due to

the fact of describing the spatial as well as frequency domain

information, FRWPT sub-bands provide richer representations

of details among all other existing transforms which further

leads to more flexible watermarking techniques. In the next

step, the SVD is applied to FRWPT sub-bands and a gray-scale

watermark is embedded by modifying the singular values.

While embedding the watermark, the adjustability factor is

introduced based on some owner’s and cryptographic condi-

tions. These cryptographic conditions are posed by consid-

ering the quadratic residue properties. For this purpose, two

odd prime numbers are selected followed by the generation of

two random series using these primes as initial seeds. Now,

the adjustability is given to the process by using two water-

mark strengths and the decision which watermark strength is

used at a particular position and is achieved by the two

random series and quadratic residues. Finally, inverse FRWPT

is performed to construct the watermarked image.

Without loss of generality, assume that the sizes of the

original gray-scale image F and gray-scalewatermark imageW

are of sizeM�N andm� n (M�m andN� n), respectively, i.e.

F ¼ ffði; jÞ : 0 � fði; jÞ � 255g (8)

W ¼ fwði; jÞ : 0 � wði; jÞ � 255g (9)

4.1. Watermark embedding

The goal of this phase is to embed watermark in the host

image. The detailed embedding procedure is depicted in Fig. 1

and is formulated as follows.

1. Perform l-level fractional wavelet packet transform with

transform orders (ax,ay) on the host image, which is deno-

ted by f qi;j, where q˛{A,H,V,D} and j ¼ 1, 2, 3,., 2l�1�2l�1.

2. Perform SVD transform on the watermark,

W ¼ UW SW VTW (10)

3. Perform SVD transform on all frequency sub-bands,

f ql;j ¼ Ufql;jSf q

l;jVT

f ql;j

(11)

4. Create a random series of length r ¼ min(m,n), as follows

xi ¼ ððpþ qÞxi�1 þ cÞmod s (12)

where p and q are two odd prime numbers, s ¼ pq, x0 is initial

seed to generate the random series and c is such that

GCD(s,c) ¼ 1 i.e., s and c are relatively prime.

5. Modify the singular values of all sub-bands with the

singular values of the watermark as follows

8>>>>>>>>sf q

l;jðiÞ þ m sW; ðxi þ iÞRp and ðxi þ iÞRq;

sf ql;jðiÞ þ m sW; ðxi þ iÞNp and ðxi þ iÞNq;

snewf ql;j

ðiÞ ¼>>><>>>>>>>>>>>:

sf ql;jðiÞ þ hsW; ðxi þ iÞRp and ðxi þ iÞNq;

sf ql;jðiÞ þ h sW; ðxi þ iÞNp and ðxi þ iÞRq;

sf ql;jðiÞ þ m sW; ðxi þ iÞ ¼ 0mod p and ðxi þ iÞRq

sf ql;jðiÞ þ m sW; ðxi þ iÞRp andðxi þ iÞ ¼ 0mod q

sf ql;jðiÞ þ h sW; otherwise;

(13)



Fig. 1 e Block diagram of the proposed embedding algorithm.


where m and h are the watermark strengths.

6. Obtain modified sub-bands as

f ql;j

new¼ Uf q

l;jSnewf ql;j

VTf ql;j

(14)


transform orders (�ax,�ay) to get the watermarked image.

4.2. Watermark extraction

The objective of the watermark extraction is to obtain an

estimate of the watermark from the watermarked image

(possibly distorted). The extraction process is depicted in Fig. 2

and is formulated as follows.


transform orders (ax,ay) on the host and watermarked

images denoted by f ql;j and~fq

l;j, where q˛{A,H,V,D} and j¼ 1, 2,

3,., 2l�1�2l�1.

2. Perform SVD transform on all frequency sub-bands of both

the host and watermarked images,

Fig. 2 e Block diagram of the pro

f ql;j ¼ Uf ql;jSf q

l;jVT

f ql;j

~fq

l;j ¼ U~fq

l;jS~f

q

l;jVT

~fq

l;j

(15)

3. Extract the singular values of watermark as

sextWq

l;jðiÞ ¼

8>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>:

s~fq

l;jðiÞ � sf q

l;jðiÞ

m; ðxi þ iÞRp and ðxi þ iÞRq;

s~fq

l;jðiÞ � sf q

l;jðiÞ

m; ðxi þ iÞNp and ðxi þ iÞNq;

s~fq

l;jðiÞ � sf q

l;jðiÞ

h; ðxi þ iÞRp and ðxi þ iÞNq;

s~fq

l;jðiÞ � sf q

l;jðiÞ

h; ðxi þ iÞNp and ðxi þ iÞRq;

s~fq

l;jðiÞ � sf q

l;jðiÞ

m; ðxi þ iÞ ¼ 0 modp and ðxi þ iÞRq

s~fq

l;jðiÞ � sf q

l;jðiÞ

m; ðxi þ iÞRp and ðxi þ iÞ ¼ 0 modq

s~fq

l;jðiÞ � sf q

l;jðiÞ

h; otherwise;

(16)

posed extraction algorithm.



Table 1 e PSNRHVS values for all experimental images.

Image Lady Lena Barbara Goldhill Fruit Pepper

PSNRHVS 41.0695 39.2562 37.5734 38.1355 37.3208 37.9624


4. Perform inverse SVD to construct the estimate of

watermark,

ðWql;jÞext¼ UW Sext

Wql;jVT

W (17)

5. Experimental set-up

In order to explore the performance of introduced water-

marking algorithm,MATLAB platform is used and a number of

experiments are performed on different gray-scale images of

size 512 � 512, namely Lady, Lena, Barbara, Goldhill, Fruit and

Pepper. Six different gray-scale logos of size 128� 128, namely

CVGIP LAB, IEEE, IEEE CS, Ducky, Pecock and IIT are used as

watermarked images. Logos CVGIP LAB, IEEE, IEEE CS, Ducky,

Pecock and IIT are embedded into Lady, Lena, Barbara, Gold-

hill, Fruit and Pepper images respectively. For embedding

watermark into the host image, 2-level of decomposition of

FRWPT is used and embedding is done in all frequency sub-

bands. Hence, watermark is embedded 16 times in the host

image. In the extraction process, we only select an image

whose correlation coefficient is the greatest among all, as the

extracted watermark. The watermarked image quality or

imperceptibility is measured using peak signal to noise ratio

based on human visual system (PSNRHVS). Fig. 3(b) shows the

resultant watermarked images and the corresponding

PSNRHVS values are given in Table 1.

No perceptual degradation is observed between the orig-

inal and watermarked images according to human perception

(Fig. 3). For further analysis, Fruit and Lady images are used,

since they have the lowest and the highest PSNRHVS values

among all the experimental images (the results for other

images can be seen on our web-site https://sites.google.com/

site/goravdma/Home/adjust_water). In Fig. 4, all original and

extracted watermark images are shown whereas Fig. 5 shows

the correlation coefficients of all extracted 16 patterns of

watermarks for all the experimental images. It is clear from

the figure that the correlation coefficient lies in the range

[0.9982e1].

Fig. 3 e a) Experimental host ima

5.1. Determination of transform orders

In the proposed algorithm, transform orders are used as the

keys in extraction process. Hence, the process of determining

the transform orders is a very important issue. To enhance the

security and for improving the results, transform orders are

needed to be calculated very carefully and securely. For this

purpose, original signal/image is transformed via FRWPT for

any arbitrary value of a followed by the reconstruction of

original signal using inverse FRWPTand thenerror is calculated

using Eqn. (18) between the original and reconstructed signal,

˛ ¼ZN�N

jfðtÞ � ~fðtÞj2dt (18)

where f(t) and ~fðtÞ are the original and reconstructed signal

respectively. From Eqn. (18), it is clear that the value of a is

determined in such a way that the mean-square error

between the original and the reconstructed signal should be

minimal. Hence, the value of a is chosen as the optimized

transform order which gives the minimum error between the

original and reconstructed signals. If theMSE between original

input and reconstructed input is zero then the perfect recon-

struction occurs. Hence, minimumMSE value is considered in

order to get perfect reconstruction and if perfect reconstruc-

tion occurs, the probability of watermark extraction is also

increased. Nevertheless, it is also possible that the MSE values

(˛) are equal for more than one transform orders. In this case,

the owner can choose any of the transform orders among

all the obtained values. In the proposed algorithm, transform

orders come out to be ax ¼ �1/7 ¼ �0.1428 and ay ¼ �2/7 ¼�0.2857 for both the Fruits and Lady images.

The proposed algorithm is highly sensitive to the trans-

form orders becausewithout knowing correct set of transform

ges b) Watermarked images.

http://https://sites.google.com/site/goravdma/Home/adjust_water

http://https://sites.google.com/site/goravdma/Home/adjust_water



Fig. 4 e a) Original watermark images b) Extracted watermark images.

Fig. 5 e Correlation coefficients of all extracted watermark

images from the experimental images.


order no one can obtain correct transformed domain in which

the watermark is embedded and hence cannot extract the

watermark from the watermarked image. This makes FRWPT

a best and suitable candidate for watermarking. Fig. 6 gives

the visual assessment of transform order sensitivity. It is clear

from the figure that different set of transform orders produce

different FRWPT coefficients. Since, the watermark is

embedded in the singular values of FRWPT coefficients

therefore the variation of singular values is also analyzedwith

respect to the transform orders.

For this purpose, the Fruits image is decomposed via 2-

level of FRWPT with different set of transform orders fol-

lowed by the largest singular value comparison of each sub-

band obtained from each set of transform orders.

P ¼ 10�log

0BBBBB@

2552

164ðM� 7ÞðN� 7Þ

XM�7

i1¼1

XN�7

j1¼1

X8

i¼1

X8

j¼1

hWði; jÞi1 ;j1 � Wði; jÞi1 ;j1

Comparison of the largest singular values (chosen because it

contains most of the signal/image energy) of each sub-band

for different set of transform orders are depicted in Fig. 7.

For analysis, the different set of transform orders are taken

which are ax ¼ �1/7,ay ¼ �2/7; ax ¼ 0.5,ay ¼ 0.0007;

ax ¼ 0.5,ay ¼ 0.1 and ax ¼ p/4,ay ¼ p/4. From figure, it is clear

that the change in transform orders leads to the significant

change in the singular values too. Hence, the transform orders

play the vital role of keys for watermark extraction process

and enhance the image security when combined with SVD.

5.2. Determination of watermark strength

For the imperceptible watermark embedding, watermark

strength should be computed in such a way that the

watermark embedding leads to imperceptible visual degra-

dation of the image. Desired goal is achieved by taking

human visual system (HVS) in consideration. The PSNRHVS is

considered in this work to find watermark embedding

strength. First, perform SVD on watermark image

W:W ¼ UWSWVW followed by the construction of W such that

W ¼ UWðgSWÞVWzgW. The PSNRHVS is then estimated

between W and W using Eqn. (1). From literature, if the value

of PSNR � 28 then the visual quality of image is unnotice-

able. The core idea is to calculate the values of g for a given

value of PSNRHVS and then the required watermark strength

for the proposed algorithm is 1�g. The whole process can be

summarized as follows.

Step 1: Select a value of PSNRHVS, say P, corresponding to

which the watermark strength must be calculated.

Step 2: Solve Eqn. (1) for g considering P, W and W i.e.

Tcði; jÞi2

1CCCCCA (19)



Fig. 6 e a) Original Image, 2-level FRWPT when b) ax [ L1/7 & ay [ L2/7 c) ax [ 0.05 & ay [ 0.0007 d) ax [ 0.5 & ay [ 0.1 e)

ax [ p/4 & ay [ p/4 f) ax [ p/2 & ay [ p/2.


where Wði; jÞi1 ;j1 and Wði; jÞi1 ;j1 are the DCT coefficients of 8 � 8

block for which the coordinates of its left upper corner are

(i1,j1) for W and W respectively.

Step 3:The watermark strength corresponding to P is given

by 1�g.

The proposed technique uses two values of PSNRHVS in

order to compute two watermark strengths m and h. These

Fig. 7 e Comparison of largest singular values of each sub-

bands for different set of transform orders.

values of PSNRHVS are P1 and P2 and the corresponding solution

of Eqn. (19) are gP1 and gP1 respectively. Finally, the two

watermark strengths are given as m ¼ 1� gP1 and h ¼ 1� gP2 .

Further analysis and experiments is done by considering

P1 ¼ 28 and P2 ¼ 45.

6. Security analysis

A highly key sensitive watermarking technique protects the

data against various attacks because slight change in the keys

never gives the perfect extraction which further increases the

security. Therefore, keys play the vital role to enhance the

security. Hence, the key sensitivity of the proposed technique

is validated. For this purpose, it is assumed that an intruder

knows the complete embedding and extraction structure but

not the used key. In the proposed technique, six keys p,q,x0,c,

ax and ay are used. Among these keys, first four keys are used

for generating a random series which is further used to give

adjustability to the proposed technique whereas the last two

keys are used as the transform orders for FRWPT. All of these

keys are private keys and only available at embedding and

extraction ends. Here c is such that GCD(c,pq) ¼ 1. Therefore, c

is always dependent on p and q i.e. if either p or q is changed, c

will also be changed.

The sensitivity of proposed technique is checked by

extractingwatermarks using thewrong keys. For this purpose,

the watermark is extracted with the wrong keys in two cases

1) when all individual keys are slightly changed 2) when all the



Fig. 8 e Security analysis of the proposed watermarking

technique (E1 [ p is wrong, E2 [ q is wrong, E3 [ x0 is

wrong,E4[ax iswrong,E5[ay iswrong,E6[p,qandx0 are

wrong, E7 [ ax and ay are wrong, E8 [ all keys are wrong).


keys are simultaneously slightly changed. In the experiments,

the values of p,q,x0,c, ax and ay are used to be 99,119, 4013,

12,546, 357,714, �0.1428 and �0.2857 respectively. On the

other hand, the modified values of p,q,x0, ax and ay are 99,109,

4007, 12,545, �0.142799999 and �0.285711111 respectively

whereas the value of c is determined with respect to the

changed values of p and q. Due to the fact that p and q are

prime numbers, the nearest prime numbers are selected as

the modified values of p and q. For other keys, the slight

change is made in such a way that the original and modified

keys are approximately same. Fig. 8 shows the correlation

coefficients for extracted watermarks when themodified keys

are used. From figure, it is clear that the value of correlation

coefficients is in the vicinity of 0 which further demonstrates

that there is no/diminutive similarity between the extracted

and original watermarks. All keys have same impact on the

extraction since a single modified key leads to the imperfect

extraction. Hence, the proposed technique is highly sensitive

to the keys and all correct keys are necessary for perfect

extraction.

Fig. 9 e Results for average filtering 13 3 13 a) Attacked Fruit b

watermark images.

7. Results and discussions

7.1. Results

To investigate the robustness of the proposed algorithm, the

watermarked image is attacked by Average and Median

Filtering, Gaussian and Salt & Pepper noise addition, JPEG

compression, Row and Column deletion, Resizing, Cropping,

Rotation, Histogram Equalization, Wrapping, Pixelation and

motion blur attacks. After all these attacks on the water-

marked image, the extracted watermark is compared with the

original one.

The most common manipulation in digital image is

filtering. The extracted watermarks, after applying 13 � 13

averaging andmedian filtering are shown in the Figs. 9 and 10.

Addition of noise is another method to estimate the robust-

ness of the watermark. Generally, addition of noise is not only

responsible for the degradation and distortion in the image

but also for degrading the watermark information, which

results in difficulty in the watermark extraction. Robustness

against additive noise is estimated by degrading the water-

mark image by randomly adding 100% Gaussian and salt and

pepper noise. From the Figs. 11 and 12 it can be observed that

after adding the noise, images are verymuch degraded and lot

of data is lost but the extracted watermarks are still recog-

nizable. Another most commonmanipulation in digital image

is image compression. To check the robustness against image

compression, the watermarked image is tested with JPEG

compression attacks. The extracted watermark from 100:1

compressed images are shown in Fig. 13.

The proposed algorithm has also been tested for row-

ecolumn deletion attack. In rowecolumn deletion, we

randomly delete some rows and columns of the water-

marked image and then extract watermark. The results of

randomly deleted 5 rows and 5 columns are shown in Fig. 14

whereas Fig. 15 shows the results for randomly deleted 20

rows and 20 columns. To fit the image into the desired size,

enlargement or reduction is commonly performed and this

results in information loss of the image including the

embedded watermark. For this attack, the size of the

watermarked image is reduced to 64 � 64 and then again

) Extracted watermark c) Attacked Lady d) Extracted



Fig. 10 e Results for median filtering 13 3 13 a) Attacked Fruit b) Extracted watermark c) Attacked Lady d) Extracted

watermark images.

Fig. 11 e Results for additive Gaussian noise 100% a) Attacked Fruit b) Extracted watermark c) Attacked Lady d) Extracted

watermark images.


brought to its original size 512 � 512. Extracted watermark is

shown in Fig. 16. Image cropping is very frequently used in

real life. Cropping is the process of selecting and removing

a portion of an image to create focus or strengthen its

composition. Cropping of an image is done by either hiding

Fig. 12 e Results for salt and pepper noise 100% a) Attacked Fru

watermark images.

or deleting rows or columns. This is a lossy operation. For

this attack, 75% area of the watermarked image is cropped

and then watermark is extracted (Fig. 17). Fig. 18 shows the

results of rotation, where the watermarks are extracted from

30 rotated watermarked image.

it b) Extracted watermark c) Attacked Lady d) Extracted



Fig. 13 e Results for JPEG compression (CR [ 100) a) Attacked Fruit b) Extracted watermark c) Attacked Lady d) Extracted

watermark images.

Fig. 14 e Results for row and column deletion (5 rows, 5 columns) a) Attacked Fruit b) Extracted watermark c) Attacked Lady

d) Extracted watermark images.


We have also tested our proposed watermarking algorithm

for histogram equalization, pixelation, wrapping, blur and

shearing attacks. In Figs. 19 and 20, results for Histogram

Equalization and wrapping are shown. Wrapping is the

process of giving 3D effect to an object by distorting the image

Fig. 15 e Results for row and column deletion (20 rows, 20 colu

Lady d) Extracted watermark images.

and stretching it to fit the selected curve. Robustness against

wrapping is estimated by giving the 3D effect to watermark

image around a spherical shape (Fig. 20). Pixelation is the

process of displaying a digitized image where the individual

pixels are apparent to the viewer. These kind of situations

mns) a) Attacked Fruit b) Extracted watermark c) Attacked



Fig. 16 e Results for resizing (512 / 64 / 512) a) Attacked Fruit b) Extracted watermark c) Attacked Lady d) Extracted

watermark images.

Fig. 17 e Results for cropping (75% area cropped) a) Attacked Fruit b) Extracted watermark c) Attacked Lady d) Extracted

watermark images.


occur un-intensionally in real life when a low-resolution

image designed for an ordinary computer display is pro-

jected on a large screen (Fig. 21). Blurring is the process by

which an image becomes unfocused. There are two main

blurring methods viz Gaussian blur and motion blur. Fig. 22

shows the results of Gaussian blurring considering 13 � 13

Fig. 18 e Results for rotation (30) a) Attacked Fruit b) Extracted w

window whereas Fig. 23 shows the results of motion blurring.

For motion blurring, linear motion of camera by 20 pixels with

an angle of 45 in a counter clockwise direction is considered.

Proposed method is somewhat resilient against Histogram

Equalization and wrapping as observed by the obtained

results. For shearing attack, watermarked image is sheared

atermark c) Attacked Lady d) Extracted watermark images.



Fig. 19 e Results for histogram equalization a) Attacked Fruit b) Extracted watermark c) Attacked Lady d) Extracted

watermark images.

Fig. 20 e Results for wrapping a) Attacked Fruit b) Extracted watermark c) Attacked Lady d) Extracted watermark images.


along x-axis and filled in the area followed by the watermark

extraction. The concerned results are depicted in Fig. 24. For

contrast adjustment and sharpen, the contrast is decreased by

55% whereas sharpness is increased by 90% followed by the

watermark extraction. The respective results are depicted in

Figs. 25 and 26. The correlation coefficients for all extracted

watermarks after all attacks are given in Table 2.

Fig. 21 e Results for pixelation a) Attacked Fruit b) Extracted w

The proposed algorithm shows very good performance

against JPEG compression attack. To prove our claim, JPEG

compression attack with decreasing quality is also tested.

Generally, JPEG compression process consists of two stages,

quantization and entropy coding. Between these two stages

the most of the information loss occurs in quantization

stage and hence watermark loss is also occurs. To test the

atermark c) Attacked Lady d) Extracted watermark images.



Fig. 22 e Results for Gaussian blur (13 3 13) a) Attacked Fruit b) Extracted watermark c) Attacked Lady d) Extracted

watermark images.

Fig. 23 e Results for motion blur a) Attacked Fruit b) Extracted watermark c) Attacked Lady d) Extracted watermark images.


robustness of the proposed algorithm, the watermarked

image is compressed by varying the compression ratio from

50 to 100. In Figs. 27 and 28, the correlation coefficients of

all extracted watermark pattern from compressed water-

mark image with compression ratio 50, 60, 70, 80, 90 and

100 respectively are given. In most of the cases, the

watermark is extracted even for the compression ratio 100

Fig. 24 e Results for shearing attack (along x-axis by factor 0.5) a

Extracted watermark images.

resulting in a 0.7483 and 0.7608 for Fruits and Lady images

respectively.

7.2. Comparative analysis

In order to demonstrate the significant performance of the

proposed scheme, the more elaborated performance

) Attacked Fruit b) Extracted watermark c) Attacked Lady d)



Fig. 25 e Results for contrast adjustment (60% decreased) a) Attacked Fruit b) Extracted watermark c) Attacked Lady d)

Extracted watermark images.

Fig. 26 e Results for sharpen (90% increased) a) Attacked Fruit b) Extracted watermark c) Attacked Lady d) Extracted

watermark images.

Table 2 e Correlation coefficient of extracted watermarks.

Attack Correlation coefficient

Lady Lena Barbara Goldhill Fruits Peppers

Average Filtering 0.3881 0.3499 �0.2326 0.2944 �0.5608 0.3792

Median Filtering 0.7025 0.4624 0.2006 0.3858 0.3950 0.7035

Additive Gaussian Noise 0.2108 0.3603 0.3493 0.5092 0.4468 0.3358

Salt and Pepper Noise 0.2244 0.4635 0.4540 0.6650 0.5280 0.4279

JPEG Compression 0.9391 0.9637 0.9245 0.8257 0.8923 0.9275

Row/column Deletion 0.9976 0.9942 0.9947 0.9988 0.9988 0.9891

Row/column Deletion 0.9978 0.9880 0.9905 0.9967 0.9960 0.9988

Resize 0.6691 0.4295 0.2025 0.4099 0.5007 0.5756

Cropping �0.9988 �0.9861 �0.9931 �0.9989 �0.9776 �0.9969

Rotation 0.9340 0.9025 0.6580 0.7788 0.8181 0.9262

Histogram Equalization 0.9651 0.9861 0.9804 0.9870 0.9570 0.9562

Wrapping 0.8438 0.9492 0.8267 0.9955 0.9132 0.8260

Pixelation 0.8156 0.6176 0.4267 0.5364 0.9190 0.8506

Gaussian Blur 0.3912 0.3691 0.3516 0.3817 0.4247 0.3912

Motion Blur 0.4857 0.4416 �0.4658 0.4586 0.5431 0.4168

Shearing 0.9677 0.7834 0.6996 0.6459 0.8283 0.8090

Contrast Adjustment 0.5469 0.5478 0.5246 0.5480 0.5396 0.5481

Sharpen 0.7296 0.8161 0.7737 0.8020 0.8057 0.7428





images from compressed Fruit Image with compression

ratio 50, 60, 70, 80, 90 and 100.


comparison with the existing methods (Kundur and

Hatzinakos, 2004; Reddy and Chatterjii, 2005; Li et al., 2007;

Bhatnagar and Raman, 2010) is given below. Watermarking

techniques in Kundur and Hatzinakos (2004) and Reddy and

Chatterjii (2005) are the only wavelet based techniques

which use gray-scale image as watermark. On the other hand,

Li et al. (2007) and Bhatnagar and Raman (2010) are the recent

watermarking techniques which embed gray-scale water-

marks in the singular values of the host image. In order to

achieve fair comparison, the same host and watermark

images which are used in the proposed technique are

considered. Therefore, comparative analysis uses the host

images of size 512� 512 andwatermark images of size 64� 64.

The detailed comparison study is given in Table 3.

From the table, it is clear that the proposed technique

shows better performance than the existing techniques. For

average and median filtering, existing and the proposed

techniques extract watermark upto 11 � 11 and 13 � 13


images from compressed Lady Image with compression

ratio 50, 60, 70, 80, 90 and 100.

respectively. For noise addition, JPEG compression, Rotation

and Resizing, the proposed method shows excellent results.

Watermark is extracted upto 100% and 75% Gaussian noise

addition whereas upto 100% and 85% salt & paper noise

addition with the proposed and existing techniques respec-

tively. For JPEG compression, proposed method extracts

watermark upto a compression ratio of 100 whereas existing

techniques extract watermark upto a compression ratio

of 80.

The proposed technique performs better against geometric

attacks. For rotation, the proposed method extracts water-

mark upto 30 rotation whereas wavelet based and SVD based

techniques extract watermarks upto 0.5 and 20 respectively.Only for cropping attack wavelet based existing techniques

perform better than the proposed and SVD based technique.

For cropping, the proposed technique extract watermark upto

25% area remaining however wavelet based and SVD based

techniques extract watermark upto 2.5% and 50% area

remaining respectively. For histogram equalization, wrapping

and contrast adjustment attacks, all the five methods are less

effective and perform almost equally. For pixelation and

motion blur, proposed method performs better than existing

methods whereas the proposed technique extracts water-

mark upto 90% whereas existing techniques extract water-

mark upto 60% increased sharpness.

7.3. Computational complexity

In this sub-section, the computation complexity of the

proposed technique is evaluated. For this purpose, Embedding

ratio (ER) and Required information ratio for extraction (RIR)

(Hsia et al., 2002) are important indicators. By these indices the

performance of a watermarking technique is measured effi-

ciently. Embedding ratio is defined as ER ¼ AW/AO, where AW

and AO are the amounts of watermark and original data

respectively. The higher value of ER may lead to less imper-

ceptibility and high robustness. On the other hand, required

information ratio for extraction is defined as RIR ¼ AD/AW,

whereAD is the amount of data required during the extraction

process. The higher value of RIR indicates that the storage

required for extraction is also higher. Hence, for a good

watermarking technique ER must be higher and RIR must be

smaller.

For the proposed method, the major required information

for extraction is watermarked image, host image, left and

right singular vector matrix of the watermark. Since, the

sizes of watermarked and host images are 512 � 512 whereas

the sizes of left and right singular vectors are 128 � 128.

Hence, total amount required for extraction is

2 � 128 � 128 þ 2 � 512 � 512 ¼ 557,056 bytes. The major

required information for extraction of Kundur’s technique is

the host image, watermarked image, optimal weights and

distortion parameters which are of size 512� 512 i.e. required

amount for extraction is 4 � 512 � 512 ¼ 1,048,576 bytes. The

major required information for extraction of Reddy’s tech-

nique is the host image, watermarked image and weight

factors which are of size 512 � 512 i.e. required amount for

extraction is 3 � 512 � 512 ¼ 786,432 bytes.

The major required information for extraction of Li’s

technique is the host image, watermarked image, just-



Table 3 e Comparisons of the proposed and existing gray-scale watermark based techniques.

Existing technique Proposed technique

Kundur andHatzinakos (2004)

Reddy andChatterjii (2005)

Li et al. (2007) Bhatnagar andRaman (2010)

Host image size (in bytes) 512 � 512 512 � 512 512 � 512 512 � 512 512 � 512

Watermark size (in bytes) 128 � 128 128 � 128 128 � 128 128 � 128 128 � 128

Operating Domain DWT DWT DWT þ SVD D-MR-DFT þ SVD FRWPT \ SVD

Embedding Quality Loosy Loosy Loosy Loosy Loosy

Extraction Algorithm Non-Blind Non-Blind Non-Blind Non-Blind Non-Blind

Watermark extracted

Average Filtering up to 9 � 9 up to 11 � 11 up to 13 � 13 up to 11 � 11 up to 13 � 13

Median Filtering up to 9 � 9 up to 9 � 9 up to 11 � 11 up to 11 � 11 up to 13 � 13

Gaussian Noise Addition up to 25% up to 40% up to 75% up to 55% up to 100%

SP Noise Addition up to 30% up to 50% up to 85% up to 70% up to 100%

JPEG Compression up to CR 40:1 up to CR 60:1 up to CR 100:1 up to CR 80:1 up to CR 100:1

RoweColumn Deletion up to 20-R and 20-C up to 10-R and 10-C up to 10-R and 10-C up to 10-R and 10-C up to 20-R and 20-C

Resizing 512 / 64 / 512 512 / 64 / 512 512 / 64 / 512 512 / 32 / 512 512 / 64 / 512

Rotation up to 0.4 up to 0.5 up to 20 up to 30 up to 30

Cropping up to 2.5% AR up to 2.5% AR up to 50% AR up to 30% AR up to 25% AR

Histogram Equalization less effective less effective less effective less effective less effective

Wrapping less effective less effective less effective effective less effective

Pixelation effective effective effective effective less effective

Motion Blur effective less effective less effective effective less effective

Contrast Adjustment up to 60% up to 55% up to 60% up to 40% up to 55% decreased

Sharpen up to 60% up to 50% up to 60% up to 50% up to 90% increased

SP ¼ Salt & Paper, CR ¼ Compression Ratio, AR ¼ Area Remaining.


noticeable distortion matrix and left-right singular vector

matrix of the watermark. The sizes of first three matrices are

512 � 512 whereas the sizes of left and right singular vectors

are 128 � 128. Therefore, total required amount for extraction

is 3 � 512 � 512 þ 2 � 128 � 128 ¼ 819,200 bytes. The major

required information for extraction of Bhatnagar’s technique

is the host image, watermarked image and left-right singular

vector matrix of the watermark which are of size 512 � 512,

512 � 512 and 128 � 128 respectively i.e. required amount for

extraction is 2 � 512 � 512 þ 2 � 128 � 128 ¼ 557,056 bytes.

On the basis of above mentioned information, the ER for

Kundur’s, Reddy’s, Li’s, Bhatnagar’s and proposed techniques

are same (1:16) whereas the RIR are 64:1, 48:1, 50:1, 34:1 and

34:1 respectively. The ER for existing and proposed technique

are same (1:16) but the better performance of the proposed

watermarking technique has the low RIR (34:1). Hence, the

proposed scheme is computationally efficient.

7.4. Time complexity

The time complexity of a technique quantifies the amount of

time taken by a technique to run as a function of the size of the

input to the problem. The complexity of the proposed water-

marking technique is given by the following equation

TðM;NÞ ¼ T1ðM;NÞ þ T2ðM;NÞ þ T3ðM;NÞ þ T4ðM;NÞ þ T5ðM;NÞ(20)

where T1ð+Þ represents the complexity of FRWPT, T2ð+Þ is the

complexity of SVD, T3ð+Þ is the complexity of random

sequence generation, T4ð+Þ is the complexity of getting

watermarked sub-bands using inverse SVD and T5ð+Þ is the

complexity of inverse FRWPT. Each of the mentioned

complexity works on the matrices and if the size of matrix is

M � N, we obtain the following relations.

T1ðM;NÞ ¼ MNlog2NþN2log2NT2ðM;NÞ ¼ minðMN2;M2NÞT3ðM;NÞ ¼ minðM;NÞT4ðM;NÞ ¼ minðM;NÞ þMðminðM;NÞÞ2T5ðM;NÞ ¼ MNlog2NþN2log2N

After putting these values in Eqn. (20), the overall

complexity of proposed watermarking technique is

TðM;NÞ ¼ O�MNlog2NþN2log2N

�þ OðminðMN2;M2NÞÞþOðminðM;NÞÞ þ OðminðM;NÞÞ þ O

MðminðM;NÞÞ2

þO

�MNlog2NþN2log2N

�(21)

In general, the overall complexity of the proposed water-

marking technique is approximated to complexity T4 i.e.,

O(M(min(M,N ))2). Further, it is important to stress that what is

the role of size of matrix in the complexity. Therefore, ifM�N

then the complexities T2 and T4 are dominating and the

overall complexity comes out to beO(MN2). On the other hand,

complexity T2 is dominating when N � M and the overall

complexity comes out to be O(M2N ).

8. Conclusion

Anew robust and efficient adjustablewatermarking scheme is

presented in this paper which uses a visually meaningful

gray-scale logo instead of a noise type Gaussian sequence, as

watermark. Watermark is embedded in fractional wavelet

packet domain via singular values using two embedding

strengths which are computed by taking PSNR value into




consideration, such that the watermark embedding leads to

imperceptible visual degradation of the image. Robustness of

the proposed technique is carried out by a variety of attacks.

The observations regarding the proposed watermarking

technique can be summarized as follows.

1. Proposed technique gives the adjustability to the user, for

making watermarked image in the form of two watermark

embedding strengths and the use of quadratic residues.

2. Main benefit of FRWPT is that without knowing the values

of transform orders (ax,ay) no intruder can extract the

watermark. Hence, transform orders play the vital role of

key in the proposed technique.

3. The values of p,q,x0 and c are used as keys in the proposed

technique. Hence, no intruder can extract the watermark

until he/she knows the values of these keys.

4. Since some attacks are resistant to low frequency, some are

resistant to high frequency and some are resistant tomixed

frequency. In the proposed technique, watermark is

embedded into all the frequencies so it is very difficult to

destroy the watermarks.

5. No intruder can extract the data without accessing the host

image. Hence, the security of the proposed technique lies in

the host image.

6. If any intruder tries to remove the watermark then the

watermark is removed by degrading the image quality.

Hence, the quality of the image degradation is directly

proportional to the quality of the extracted logo.

Acknowledgment

The authors gratefully acknowledges the financial support of

the Canada Research Chair program, the NSERC Discovery

Grant and the Council of Scientific and Industrial Research,

New Delhi, India for this research work.

Last but not least, the authors thank the anonymous

Referees and the Editor for their valuable suggestions and

many constructive comments that resulted in the improve-

ment and readability of this paper.

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Gaurav Bhatnagar is the member of the Computer Vision andSensing Systems Laboratory in the Department of Electrical andComputer Engineering at University ofWindsor, ON, Canada since2009. He received his Ph.D and M.Sc degree in Applied Mathe-matics from Indian Institute of Technology Roorkee, India, in 2010and 2005 respectively. He has coauthored more than 30 journals,conference proceedings and contributed to two books in his areaof interest. His research interests include digital watermarking,encryption techniques, biometrics, image analysis, wavelet anal-ysis and fractional transform theory.

Q.M. Jonathan Wu received the Ph.D. degree in electrical engi-neering from the University of Wales, Wales, U.K., in 1990. From

1995, he has been with the National Research Council of Canada,Ottawa, ON, Canada. He is currently a Full Professor with theDepartment of Electrical and Computer Engineering, University ofWindsor, Windsor, ON. He is a holder of the Canada ResearchChair in automotive sensors and sensing systems and is anAssociate Editor for the IEEE Transaction SMC (part A). He haspublished more than 200 peer-reviewed papers in the areas ofcomputer vision, image processing, security, intelligent systems,robotics and integrated micro-systems.

Balasubramanian Raman is an Assistant Professor in theDepartment of Mathematics at the Indian Institute of Technology,Roorkee since February 2006. He received his Ph.D. in Mathe-matics from the Indian Institute of Technology, Madras, India in2001. He received his B.Sc and M.Sc in Mathematics from theUniversity of Madras in 1994 and 1996 respectively. So far he haspublished in 26 international journals, 41 conference proceedings,4 book chapters and a technical report. His areas of researchinclude Computer Vision, Graphics, Satellite Image Analysis,Scientific Visualization, Imaging Geometry, Reconstruction prob-lems, Biometrics and Watermarking.



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