Flipping Independent Digital Image Watermarking Using Fourier ...

Flipping Independent Digital Image Watermarking
Using Fourier Transform

Al
-
Hilli Ahmed M. Z.

Technical Collage of Najaf

Abstract:


Digital Watermarking has emerged as a new area of research in an attempt to prevent illegal
copying and duplication and false

representation. In this paper, a proposed algorithm for digital
image
watermarking was presented. This algorithm make use of the
flipping independent

coefficients in Fourier
domain. I
n this algorithm, these coefficients are

used

to produce a watermarking
algorithm robust to
flipping and shifting attacks, in addition to these attacks, this algorithm shows a robustness to JPEG,
JPEG2000, Sample down up attacks.

ةصلاخلا


ليثمتلا و ينوناقلا ريغلا خاسنتسلاا عنمل ةلواحم يف ثحبلل ديدج لاجمك ةيئاملا تاملاعلا ترهظ
مت , ثحبلا هذه يف .ئطاخلا
و بلقلا تايلمعل ةمواقم ةيئاملا تاملاعلا لعجل ةيمزراوخ حارتقا
ةحازلإا
قاطن يف بلقلل ةمواقملا تلاماعملا نم ةدافتسلاا مت ثيح ،
يف تاددرتلا
هليوحت

دق و .ريروف
تتبثأ

و بلقلا تايلمعل ةمواقملا ةحرتقملا ةقيرطلا هذه
ةحازلإا

ةينقتب طغضلا و
JPEG

طغضلاب و
JPEG2000

يولعلا يلفسلا ليلقتلا و


1.
Introduction

The success of the Internet and digital consumer devices has profoundly changed our
society and daily lives by making the capture, transmission, and storage of digital data
extremely easy and
convenient. However, this raises a big concern in how to secure these
data and preventing unauthorized use. This issue has become problematic in many areas.
For example, there are many studies showing that the music and video industry loses
billions of dol
lars per year due to illegal copying and downloading of copyrigh
ted
materials from the Internet (
Tsui
,
et al
, 2008
)
.

As a solution, Digital watermarking is
used very frequently. Hence, digital watermarking becomes very attractive research topic
and many ma
y taxonomies for digital watermarking have been proposed(
Bhatnagarl
,
et
al
, 2009
).

Digital watermarking is a technology that creates and detects invisible
markings, which can be used to trace the origin, authenticity, and legal usage of digital
data. Ideal
ly, they should be hard to notice, difficult to reproduce, and impossible to
remove without dest
roying the medium they protect.(
Saha
,
et al,

2007
)

.
Watermarks also
serve to identify the source of the content and thus aid in investigating abusive
duplicati
on
(
Brannock
,
et al,
2008
)
.

In terms of the embedding domain, watermarking
algorithms are mainly divided into two groups: spatial domain methods which embed the
data by directly modifying the pixel values of the original image and transform domain
methods w
hich embed the data by modulating the transform domain coefficients. The

most commonly used transforms for digital watermarking are DF
T (Discrete Fourier
Transform) (
Chen
, 2007) (
Xiaojun
,
et al,

2007) (
Santi


et al,

2007)
,
DCT (Discrete
Cosine Transform) (
Zhang
,
et al,

2007
)

(
Hsieh
,
et al,

2007) (
Alturki
,
et al,

2007)

and
D
WT (Discrete Wavelet Transform) (
Agreste
,
et al,

2007)
(
Vatsa

,
et al,
2007)

(
Agreste
, et
al,

2007)
.

In general, spatial domain methods have good computing performance and
transform domain
methods have high robustness.
(
Soheili
, 2008
)
.

One of the main challenges of the watermarking problem is to achieve a better
tradeoff between robustness and perceptivity. From an engineering perspective, these are
two conflicting requirements that cannot be

satisfied at the same time. Robustness can be
achieved by increasing the strength of the embedded watermark, but the visible distort
ion
would be increased as well.(
Tsui
,
et al
, 2008
)
.
Robustness means that the watermark is
able to withstand some changes i
n the watermark
-
embedded signal; while
imperceptibility represents the invisibility to human eyes, or for audio clips, the
inaudibility to human ears. A good watermark algorithm should by all means be
simultaneously robust and imperceptible. However, it is

difficult to get the both at the
same time, because watermark embedding is to some extent a tradeoff between strong
robustness and good imperceptibility, namely, minimizing embedding distortion and
maximizing robustness are frequently conflicting with eac
h other. Improving the
robustness in a watermark
-
embedding algorithm is often at the cost of decreasing the
im
perceptibility, and vice versa.(

Tian

,
et al ,
2007)
. In literature, many watermarking
algorithm had been proposed. In

(
Saha
,
et al,

2007
),

the al
gorithm proposed is a
combined cryptographic and steganographic operations so that a violator cannot easily
change the copyright information hidden inside the files. The proposed method is to use
a keyed stream cipher architecture controlled by a key whic
h is the product serial number
to transform the hashed information before hiding. And finally, the use of RSA algorithm
controlled by the private key of the origin to encrypt the cipher stream along with the
product serial number
. In
(
Bhatnagarl
,
et al
, 20
09
)
,
a newer version of Walsh
-
Hadamard
Transform namely multiresolution Walsh
-
Hadamard Transform (MR
-
WHT) is proposed
for images. Further, a robust watermarking

scheme is proposed for copyright protection
using MR
-

WHT and singular value decomposition. The

core idea of the proposed
scheme is to decompose an image using MR
-
WHT and then middle singular values of
high frequency sub
-
band at the coarsest and the finest level are modified with the singular
values

of the watermark.

In (
Pitas
,

et al.,
1995
), (
Bruynd
onckx

,

et al.
, 1995), (
Walton
,
1995)

and (
Bender
,
et al.
, 1995)
,

the watermarks are applied on the spatial domain
.

In
(
Koch
,

et al.
,1995)
, a copyright

code and its random sequence of locations for
embedding

are produced, and then superimposed on the ima
ge based on

a JPEG model.
In (
Cox
,

et al.
, 1995)
, the spread spectrum communication

technique is also used in
multimedia watermarking.

This paper is organized as follow: section 2 discuss the
problem associated with watermarking algorithm section 3 discu
ss the theoretical
concepts of the proposed algorithm, section 4 explain the algorithm for embedding and
extraction of the watermark, section 5 reviews the experimental results for the proposed
algorithm.

2.
Problem

S
tate:

Watermark algorithms may not work

properly if there is out of synchronization
between the original image and the watermarked image. So, there are many different
attack algorithms result in out of synchronization with little degradation between the
watermarked image and the attacked image
such as Stirmark. But the most effective
attack which produce an image with no degradation is flipping. In addition to this, the
observer can not recognize that this image has been flipped without knowing the original
image. In addition, the flipping opera
tion is
a

simple

image processing

algorithm.

So,
there are three properties of flipping attack:

1.

It produce out of synchronization so it is hard for the watermark algorithm to
detect the watermark.

2.

The attacked image has no degradation.

3.

the observer can no
t judge that this image was flipped without knowing the
original image.

4.

The flipping operation can be used in the simplest image editing program even
Microsoft Paint.

So, the need of a watermarking algorithm that capable to detect the watermark even
if th
e image was flipped.

3.
The
Mathematical
Model

:

Starting with Fourier Transform equation:










1
0
1
0
2
2
)
,
(
)
,
(
N
r
N
c
N
cv
j
N
ru
j
e
e
c
r
f
v
u
F


………………………………………(1)

Where:

)
,
(
v
u
F

represent the Fourier Transform of the image
)
,
(
c
r
f

)
,
(
c
r
f
represent the original image in spatial domain where
1
0



N
r

and
1
0



N
c

If we assume that
)
,
(
c
r
f
has been flipped to produce
)
1
,
(


c
N
r
f

if it is flipped
horizontally
or

)
,
1
(
c
r
N
f



i
f it is flipped vertically.

Taking the Fourier Transform for the flipped image

we get
:

N
vc
j
N
r
N
c
N
ur
j
e
e
c
N
r
f
v
u
F


2
1
0
1
0
2
)
1
,
(
)
,
(











………………………………….(2)

If we set
1



c
N
c

then
1



c
N
c

and
making some simplifications we get:












1
0
0
1
2
2
)
1
(
2
)
,
(
)
,
(
N
r
c
N
c
N
v
c
j
N
ru
j
N
N
v
j
e
e
c
r
f
e
v
u
F





…………………………………..(5)

So, if we set
0

u

(or
0

v
) in equations (1) and (5) we get:









1
0
1
0
2
)
,
(
)
,
0
(
N
r
N
c
N
vc
j
e
c
r
f
v
F


………………………………………..(6)










1
0
0
1
2
)
1
(
2
)
,
(
)
,
0
(
N
r
N
c
N
v
c
j
N
N
v
j
e
c
r
f
e
v
F



………………………………………….(7)

From equation (6) and (7), it can easily
shown that the magnitude of equation (6) and (7)
are the same:

)
,
0
(
)
,
0
(
v
F
v
F


…………………………………………………………… (8)

And in the same way we can conclude that
)
0
,
(
)
0
,
(
u
F
u
F

.

we can conclude from the above equations that the coefficients of Fourier

Transform with
0

u
or
0

v

are unchanged for the original image and the flipped
image. So, we can use these coefficient to embed a watermark and the resultant
watermark are robust to flipping attack.

4.

The Algorithm
:

All watermarking algorithms consists of two processes: embedding process and
watermark extraction process
. First, we will explain the embedding process in details.
The embedding algorithm is shown in figure (1).








































F
irst, the watermark image is XORed with secret key to ensure the security of the
watermark image, and then, the resultant image is passed through a one way function;
this function will ensure that different watermarks produce totally different vector to
em
bed, and at this stage, we have a watermark vector to embed in the original image.
After getting the watermark vector, the next step is embedding of this vector in the
original image. This can be accomplished by first compute the Fourier Transform of the
o
riginal image to get the Fourier Coefficients. Then, these coefficients are processed
through coefficients selection function. This function ensure that the selected coefficients
are flipping invariant (as shown in the theory section, these coefficients ar
e
Figure (1) The embedding process

Selected coeff.

One way
function

Watermar
k image

XOR

Secret Key

gain

X

Watermark vector

Original

image

Fourier
Transform

Coefficients
selector

Coefficients
saving

∑

Padding

Inverse Fourier
Transform

Real

Part

Watermarked
image

Non
-
selected coeff.

corresponding to
0

u
and
0

v
). After coefficients selection, the watermark vector is
embedded in these coefficients using the equation below and the original coefficients are
saved to a file( this saving process ens
ure that the original coefficients are available to be
used in the extraction process):


Vector
k
ts
Coefficien
ts
Coefficien
old
new



………………………………….(9)

Where:

new
ts
Coefficien

are the new coefficients.

old
ts
Coefficien

are the old coefficients.

k

represents the gain
.

Vector

represents the watermark vector.

Then, the selected coefficients and the non
-
selected coefficients are padded together
and then taking the Inverse Fourier Transform of the resultant image and because the
F
ourier Coefficients were changed, it is expected that the resultant matrix will be
complex; so, we take the real
part of the complex image

to
produce the watermarked
image.




















In the extraction state, as shown in figure (2), the same proce
ss for generating the
watermark vector is repeated with the same secret key and the one way function, after
getting the watermark vector, take the Fourier Transform of the watermarked image, and
select the coefficients that flipping invariant (
0

u

and
0

v
) and subtract these
coefficients from the previously saved coefficients as follow:

Vector
k
ts
Coefficien
ts
Coefficien
old
new




old
ts
Coefficien

……….(10)


Vector
k
ts
Coefficien
ts
Coefficien
old
new



………………………..
(11)

And correlate the above equation with
Vector

to get:

Watermark
image

Secret key

XOR

One Way
Functions

Watermarked
image

Fourier
Transform

Coefficients
Selector

Saved
Coefficients

−

Correlation

Figure (2) The Watermark Extraction Process

How strong the
watermark is
presen
t

)
,
(
)
,
(
Vector
Vector
k
corr
Vector
ts
Coefficien
ts
Coefficien
corr
old
new



………..(12)

And the resultant correlation coefficient is ranged between 0 (for absolutely
watermark absence) and 1 (for absolutely watermark presence).

5.

Exper
imental Results:

Simulation are performed to evaluate the proposed algorithm above. The simulation
is performed using two images. Figure 3 shows the watermark, figure 4 represent
s

the
original images. In this simulation, PSNR is used to evaluate the distor
tion of the
watermarked image with respect to the original image where PSNR is (Umbaugh, 1998):




13
........
..........
..........
..........
)
,
(
)
,
(
1
)
1
(
log
10
1
0
1
0
2
2
10






















N
r
N
c
c
r
I
c
r
I
M
N
L
PSNR

Where :

L
: the number of gray level

I
: is the watermarked image

I
: is

the original image

M
N
,
: the image dimensions.

And in order to measure the quantitative similarity between the embedded
watermark and the extracted one, the normalized correlation coefficient is used in this
paper:









14
..
..........
..........
..........
2
2























m
n
mn
m
n
mn
m
n
mn
mn
B
B
A
A
B
B
A
A
r






















Cameraman Original image

Peppers Original image

Figure 4 Original Images


The experimental results are listed in appendix A.
Table 1 represents the PSNR
values for different gain values (k)
test on both images:

It can be shown from the table that the PSNR has high values even for k=15000,
figure 5 show
s the watermarked image with k=5000 and figure 6 shows the watermarked
image with k=15000.









































Peppers with k=5000

Cameraman with k=5000

Figure 5 The Watermarked image with k=5000

Cameraman with k=15000

Peppers with k=15000

Figure 6 The Watermarked i
mage with k=5000


Even the watermarking algorithm was originally designed to stand for flipping
attacks
, the watermark was tested for differ
ent types of attacks, and tables below show
each type with its parameters and the extracted correlation coefficients for
gain values of
5000 and 15000 for
the two images.

Table 2 listed the results received from the watermarked image for flipping and
shift
ing attack, and the algorithm shows high robustness against flipping and shifting
attacks.

Table 3 is for JPEG compression attack which shows a good robustness to JPEG
compression attack.

Table 4 stands for Stirmark attack, this algorithm shows weak robust
ness against
Stirmark attack.

Table 5 show the results for cropping attack, and it can be concluded from the table
that this algorithm has no robustness against cropping attacks.

Table 6 shows the results for JPEG2000 compression attacks, and shows good
r
obustness against JPEG2000, and table 7 listed the correlation coefficients for
watermarked image applied to Weiner filter and show no robustness
against Weiner
filter, and finally, table 8 shows that the algorithm has average robustness against sample
dow
n up attack.

6.
Conclusions:

From the experimental results shown above, it can be concluded that the proposed
algorithm has high PSNR and perfect fetching for shifting and flipping attacks, good
robustness against JPEG compression and JPEG2000 compression
attacks, average
robustness against sample down up attacks, no robustness against stirmark, wiener,
cropping attacks.

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,

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-
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Appen
dix

A
: The Tables of Experimental Result

Table (1) PSNR versus Gain ( k)













Table (2) the flipping shifting attacks











Table (3) JPEG compress
ion attacks

compression ratio

correlation coefficient k=15000

correlation coefficient k=5000

image

100

0.9407

0.9398

cameraman

90

0.9376

0.9283

cameraman

80

0.9289

0.8947

cameraman

70

0.9182

0.8723

cameraman

60

0.9096

0.8465

cameraman

50

0.9011

0.816

cameraman

40

0.8796

0.7546

cameraman

30

0.8603

0.6645

cameraman

20

0.8131

0.5248

cameraman

10

0.6491

0.2659

cameraman

100

0.9407

0.9402

peepers

90

0.9327

0.9074

peepers

80

0.9133

0.8534

peepers

70

0.8903

0.827

peepers

60

0.863

0.7948

peepers

50

0.8402

0.733

peepers

40

0.8224

0.7243

peepers

30

0.8075

0.6851

peepers

20

0.741

0.5411

peepers

10

0.7075

0.4685

peepers

Peepers

Cameraman

Gain (k)

48.7305

48.6621

5000

47.1469

47.0785

6000

45.808

45.7396

7000

44.6481

44.5797

8000

43.6251

43.5567

9000

42.7099

42.6415

10000

41.8821

41.8137

11000

41.1263

41.0579

12000

40.4311

40.3627

13000

39.7874

39.719

14000

39.1881

39.1197

15000

flipping &shifting

correlation coefficient

image

up down

0.9408

cameraman

left right

0.9408

cameraman

up dow
n+ left right

0.9408

cameraman

up down+ left right +shift (50,50)

0.9408

cameraman

up down

0.9408

peepers

left right

0.9408

peepers

up down+ left right

0.9408

peepers

up down+ left right +shift (50,50)

0.9408

peepers

Table (4) Stirmark attack






Table (5) Cropping attack










Table (6)

JPEG2000 compression attacks


compression
rate bpp

correlation
coefficient k=5000

correlation
coefficient k=
1
5000

image

0.5

0.9399

0.9407

cameraman

0.4

0.9399

0.9407

cameraman

0.3

0.9399

0.9407

cameraman

0.2

0.9399

0.9407

cameraman

0.1

0.9184

0.9342

cameraman

0.09

0.9044

0.9239

cameraman

0.08

0.8889

0.9188

cameraman

0.07

0.8866

0.9128

cameraman

0.06

0.8594

0.9039

cameraman

0.05

0.8074

0.8943

cameraman

0.04

0.7354

0.8736

cameraman

0.03

0.7055

0.8528

cameraman

0.02

0.4648

0.7521

cameraman

0.01

0.1701

0.4366

cameraman

0.5

0.9403

0.9407

peepers

0.4

0.9403

0.9407

peepers

0.3

0.9403

0.9407

peepers

0.2

0.9403

0.9407

peepers

0.1

0.9354

0.9396

peepers

0.09

0.9284

0.9392

peepers

0.08

0.9158

0.9386

peepers

0.07

0.9087

0.9267

peepers

0.06

0.8761

0.9261

peepers

0.05

0.7971

0.9036

peepers

0.04

0.7455

0.8685

peepers

0.03

0.6545

0.8241

peepers

0.02

0.4995

0.7278

peepers

0.01

0.0999

0.4543

peepers


correlation coefficient
k=5000

correlation coefficient
k=5000

image

-
0.1834

-
0.0371

cameraman

0.1734

0.
317

peepers

percentage
cropping

correlation
coefficient k=
1
5000

correlation
coefficient k=5000

image

2

0.8013

0.4909

cameraman

4

0.4767

0.1166

cameraman

2

0.7161

0.3917

peepres

4

0.4995

0.2196

peepres

Table (7) Weiner filter attack


window
size

correlation
coefficient
k=5000

k=15000

image

2

0.6173

0.8567

camerman

3

0.1878

0.7143

camerman

2

0.7964

0.8568

peepers

3

0.7324

0.828

peepers


Table (8) Sample down up attack


















sample
down up

correlation
coefficient
k=5000

correlation
coefficient
k=
1
5000

image

1

0.9408

0.9408

cameraman

0.9

0.3143

0.7712

cameraman

0.8

0.286

0.7769

cameraman

0.7

-
0.0888

0.5023

cameraman

0.6

-
0.258

0.411

cameraman

1

0.9408

0.9408

peepers

0.9

0.7672

0.8584

peepers

0.8

0.8197

0.869

peepers

0.7

0.5538

0.741

peepers

0.6

0.5969

0.7669

peepers