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IMAGE WATERMARKING BASED ON GENETIC ALGORITHM

Zhicheng Wei1,2 ,Hao Li1, Jufeng Dai1,Sashuang Wang1

1School of Electronic Information Engineering, Tianjin University, Tianjin 300072, China

2Department of Network Engineering, Hebei Normal University, Shijiazhuang 050016, China

ABSTRACT

In order to improve the robustness and imperceptibleness of

the image spread spectrum watermark algorithm, a new

approach for optimization in 8×8 DCT domain using

genetic algorithm (GA) was proposed. GA was used to

choose the AC coefficients, which were modified to embed

the spread spectrum watermark. The bands were varied to

find the most suitable for image with different

characteristics. Performance improvement with respect to

existing algorithm is obtained by GA adaptive global

search. The experimental results show that the proposed

algorithm yields a watermark that is invisible to human

eyes and robust to various image manipulation, and show

that some special positions are the best choices for

embedding the watermark. The authors also compare their

experimental results with the results of the previous work of

others.

1. INTRODUCTION

With the widespread use of the Internet, a lot of digital

media, including audio, video and image, have been

duplicated, modified by anyone easily and unlimitedly. The

copyright protection of the intellectual property of the

sensitive or critical digital information is an important legal

issue globally. Recently, we have seen the trend of the

studies in digital watermarking [1] since the techniques

provide the essential mechanism for the ownership

authentication.

Digital image watermarking provides

protection of image data by hiding appropriate information

in the original image. There are a variety of schemes for

embedding the watermark.

watermarking were based on DCT[2], DWT[3], DFT[4],

spatial-domain schemes[5], and vector quantization (VQ)

domain methods[6]. One major disadvantage for these

methods is if the attackers dissolve the relationships

between the original image and the pre-determined set for

watermark embedding, the watermarking capability for

copyright protection no longer exists. Another disadvantage

for typical schemes is how to decide and choose the pre-

determined set. Therefore, genetic algorithm (GA) is

copyright

Typical methods of

employed to solve the problems. In this paper, genetic

algorithm is employed to choose the best suitable positions

to embed the spread spectrum watermark [7][8].

This paper is organized as follows. Section 2 describes

the genetic spread spectrum watermark algorithm. Section 3

illustrates the simulation results, and we also show the

superiority of our scheme over the results proposed by other

researcher in this section. And we conclude this paper in

Section4.

2. GENETIC WATERMARKING ALGORITHMS

We propose the algorithm whose block diagrams appear in

Fig.1. The input image is I with size M

perform the 8?8 block DCT onI and get the coefficients

in the frequency bands,Y . The embedding and extraction

method was proposed by Cox [7]. A watermark consists of

X

N

×

. We first

a sequence of real numbers

1,,

n

xx

=

?

. In practice, we

create a watermark where each value

ix is chosen

independently according to

watermark, n , was decided by the number of bits of

embedding in every 8?8 block.

' (1

ii

YYx

α=+

[7] were not suitable because the 8×8 DCT transform

coefficients don’t vary widely. So we insert the watermark

intoY to obtain '

Y according to (1).

'

ii

YY

α=+

The gaussian random vector is imperceptibly inserted in

a spread-spectrum-like fashion into the components of the

data chosen by genetic algorithm, which are commonly

used as adaptive approaches that provide a randomized,

parallel, and global search method.

To evaluate the best coefficients for a cluster containing

M?N/64 DCT blocks, a sequence of numbers from 2 to 64

is used as the chromosome. Its magnitudes index AC

coefficients following zigzag path in the DCT domain. In

the beginning, all chromosomes are generated randomly. k

bits of the watermark are embedded into distinct DCT

blocks and the coefficients chosen for embedding

watermark bits are indexed by the chromosome.

(0,1)

N

. The length of

Equations

)

i

and

'()

ix

ii

Y Y eα

=

in

(1)

i

x

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Then, four attacks are chosen to evaluate the robustness

of the embedded watermark. They are low pass filtering

(LPF) with normalized radius 0.1, Image Scaling with

factor 0.1, Gaussian Noise with strength 1, and JPEG

coding distortion with parameter of 5% quality. The fitness

of the chromosome is evaluated after attacking procedure.

The middle generation is then generated with crossover

and mutation operators. The possibility of crossover and

mutation,Pc ,Pm are defined as (2) and (3) separately:

PcInitial

Pc PcInitial

GenerationMax

PmFinal

PmPmInitial

GenerationMax

0.9

PcInitial =

,

PmInitial =

and

0.2

PmFinal =

.The pre-specified number of

generation, GenerationMax , is 100. g is the value of

current iteration. The top 50% individuals are selected from

the initial generation and the middle generation, then put

them into the next generation.

Generally, the fitness of the chromosome can be

calculated by evaluating the robustness and the image

quality. But the fidelity is high when α is suitable. So the

items about image quality such as PSNR or UQI are not

included in the fitness. The watermark is extracted after an

attack is applied on the watermarked simulated image.

Then, the similarity (Sim) value between the original

watermark X and extracted mark

The Sim values are taken into account to evaluate the

fitness of a chromosome. The fitness function of GA is

defined as (5).

(2)

PcFinal

g

−

=−×

(3)

PmInitial

g

−

=+×

0.05

,

0.3

PcFinal =

,

*

X is calculated as (4).

*

*

**

(,) (4)

XX

Sim X X

XX

⋅

=

⋅

4

1

(5)

i

i

FitnessSim

=

=?

To decide whether the suspected image is a

watermarked version of the original image, the similarity is

compared with a fixed threshold δ . If the similarity is

greater than the fixed threshold, the watermark has been

detected. It is proved as (6) that

standard normal distribution.

~(0,1)

XN

?

*

( ,)

Sim X X

follows the

***

**

i

1

*

***

**

~ (0,)

~ (0,)~ (0,1)(6)

T

n

i

i

XXN X X

XX x x

XX

XXNXXN

XX

=

?

??

?

??

⋅

⋅=

⋅

⋅

?

⋅⋅

?

So set the threshold δ =6 makes the probability of false

watermark detection very small. It can be estimated as (7):

∞∞

−

==

??

2

2

2

2

10

112

π

2

2

1

2

1

2

6

()()

22

9.8659 10(7)

x

t

ePedxe dt

erfcerfc

δ

δ

π

δ

−

−

==

=×

Fig.1. The block diagram of the present algorithm

Fig.2. Original “Goldhill” image

Fig.3. Watermarked version of present

approach. PSNR=51, α =5

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3. EXPERIMENTAL RESULTS

In our simulation, we take nine well-known 256?256 test

images with

5

α =

. One of them is Goldhill, shown in

figure 2. Two bits of watermark are embedded in every 8×8

DCT block. The size of corresponding watermark is 2048.

The watermarked version of Goldhill generated with the

present algorithm is shown in figure 3. Its PSNR 51 is much

better than Cox’s PSNR 37.34. We can see although no

evaluation about image quality is included in the fitness, the

PSNR of watermark image is high.

The two watermarked versions of Goldhill, present

approach and Cox’s approach, then go through four

attacking methods separately. In figure 4, we can see how

the average similarity measure is affected under these

attacks. The plots of the present approach are all above the

threshold δ =6 under the attacks of LPF and gaussian noise

addition. So the spread spectrum watermark can be detected

correctly in any strength of the two attacks. Meanwhile the

false detector responses of Cox’s are down to 30% in the

case of LPF, to 50% in the case of noise addition.

When the watermarked images are attacked by scaling,

the plot of the present approach is under the threshold at

few points, but it is found that the lowest similarity of the

plot is equal to 5.77?a relatively high value. At the same

time, about 20% plot of Cox is below the threshold. And

we can see the responses to the JPEG of the two methods

are similar except for the situation of 5% quality. Also, by

increasing the parameter α , it is possible to maintain the

same level of similarity measure while lowering the PSNR.

In this way, robustness is improved for all possible attacks.

Other eight testing images have been processed. All

PSNR and Sim values are shown in table 1. Also applying

the algorithm on other testing images shows that the

watermarked images are perceptually equal to the originals,

and that the watermarks are still detectable after attack, as

indicated in above experimental results.

In our algorithm, the bands for the watermark to be

embedded differ from one block to another. The selected

bands also differ from one test image to another. Therefore,

from a statistical point of view, we find that the low

frequency domain is the bands needed to acquire the best

fitness value. Y(2) is always the maximum of them. Fig.5

and 6 compare the bands at the 0th and 100th iteration in GA

of one test image.

4. CONCLUSIONS

A robust algorithm for DCT-based GA spread spectrum

watermarking has been presented in this paper. We can

extract the watermark correctly almost in all kinds of the

four attacks. It is robust because we make use of GA to

train the frequency set for embedding the watermark.

The motivation of proposing this method is to find the

most suitable bands in the DCT coefficients. The best bands

Images

Boat

Boy

Zelda

Baboon

Mary

Girl

Goldhill

Lena

Pepper

PSNR

51.68 8.588 7.626 6.672 7.281

51.82 7.008 6.793 6.209 8.384

51.93 6.546 7.174 8.017 7.813

51.87 7.121 7.191 6.192 8.565

51.92 6.938 6.859 7.764 7.264

51.84 7.454 6.197 7.799 7.546

51.65 8.488 7.877 8.284 7.392

51.55 7.579 7.289 7.715 8.247

51.86 7.936 7.158 7.726 7.403

Sim1 Sim2 Sim3 Sim4

Table 1. PSNR and Similarity of test images

Fig.5. The histogram of bands at 0th iteration

Fig.6. The histogram of bands at 100thiteration

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include not only the low frequency components but also

high frequency coefficients. Y(2) is found to be the most

popular band for robust watermarking. In comparison with

the Cox’s method, watermark embedding with our scheme

can get better-watermarked image qualities and more robust

to the attacks.

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Spectrum Watermarking for

Fig.4. Performance comparison between the present approach and Cox’s approach.(Top left)

Similarity against lowpass filter, (top right) Image Scaling, (bottom left) gaussian noise and

(bottom right) JPEG coding distortion. The

sim =

6

threshold is included in all plots.

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