A Novel Digital Watermarking Algorithm Based on Wavelet Lifting Scheme and Linear Regression

−

y

i

x y

i

i

)(

(

∑

∑ ∑

x

x y

i

i

i

)2

(

∑

∑

2

−

n

x

x

i

i

)

)(

)(

(

∑ ∑

∑ ∑

2

x

y

x

i

i

i

)

(

∑

∑

n

x

i

= ∑ , when we put x and y into the formula (5) and a new simple formula (7)

= ∑ and

ix

n

can be achieved.

(

)(

∑

y

i

∑

−

(7)

Because

(6)

−

)2

−

(

(5)

2

x

i

iy

n

y

x

x

i

x

i

−

)

=

a

x

y

x

2

At last, we make the value of slope a as our constrain condition.

2.2. Arnold scrambling technology

We use two-dimensional Cat-Map algorithm to do the chaos scrambling for watermark image. Then the

two-dimensional Cat-Map can be defined as follow:

x

y

m o d

x

y

x

y

a

a

a

a

A

F

=

=

1 2

1 1

+

n

1

n

n

2 1

2 2

n

n

+

1

⎞

⎟

⎠

⎡

⎢

⎣

⎡

⎢

⎣

⎤

⎥

⎦

⎤

⎥

⎦

⎡

⎢

⎣

⎤

⎥

⎦

⎛

⎜

⎝

n

(8)

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Li Song and Gu Qiaolun / Procedia Engineering 29 (2012) 1602 – 1606

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In this formula, MOD function is to obtain the remainder and F is a column matrix,

a a a

11

12

,

,

,

a are

22

21

the non-negative integers. According to

3

a

parameters. When 11

=

a

12

=

a

21 1

= and

22

−

11 22

a a

21 12

=

A a a

a = , it is called Arnold Scrambling.

2

1

= , we can determine Cat-Map by its three

3. Watermarking Embedding and Extraction

Firstly, let the original image be denoted as

{

(

i

I= h ,

j

)

,1

< <

i M

,1

< <

j N

}

and the binary watermarking be

denoted as

{

remainder matrix.

W

=

(

w i

,

j

)

,1

< <

i

P

,1

<

j

<

R

}

. Then we define a fixed matrix Q, by which we can get a

For example, we define a matrix Q as 5 5

5 5

⎡

⎢

⎣

⎤

⎥

⎦

and assume the sub-block of low-frequency data is 189 161

⎤

⎡

⎥

⎢

158 148

⎦

⎣

.

If we directly calculate the mean value of sub-block and use the mean value matrix to cover the original

data, the new matrix of sub-block is 164 164

(when take the mean value, it usually uses the method of

⎡

⎢

164 164

⎣

⎤

⎥

⎦

Rounded Down ) recorded as 1m . However, if we use the matrix Q MOD the sub-block data, then the sub-

block matrix can be divided into the remainder matrix 4 1

. Because the

3 3

and the divisible matrix 185 160

⎡

⎢

155 145

⎣

⎤

⎥

⎦

⎤

⎥

⎦

⎡

⎢

⎣

mean value of the remainder matrix is 2 2

2 2

⎡

⎢

⎣

⎤

⎥

⎦

, then let the mean value matrix plus the divisible matrix and

get a new matrix 187 162

⎡

⎢

157 147

⎣

⎤

⎥

⎦

recorded as 2m .Comparing 1m and 2m with original sub-block data, the

matrix

2m is more similar to original sub-block. The data that processed with the second method

approximates original data more, thus we can greatly reduce the distortion of carrier image by using this

method.

The process of watermarking embedding and extraction can be described as follows:

Step 1: Scrambling the original watermarking by Arnold image scrambling algorithm, which not only can

improve the security of watermarking but also can improve the algorithm robustness to against clipping

attacks. Then the shuffled watermarking is arrayed into a vector in column-wise order, which is denoted

as:

*

w

=

{

*

w i

|

i

=

1,2,3.....,

*

×

P R w

;

i

}

{

}

∈

0,1

Then define a fixed 4 4× matrix Q:

Q

=

5 5 5 5

5 5 5 5

5 5 5 5

⎡

⎢

⎢

⎢

⎢

⎣

⎤

⎥

⎥

⎥

⎥

⎦

5 5 5 5

Step 2: Dividing the original image into 8 8× non-overlapping sub-image, then for each sub-image

conducting 1-level integer LWT operation, extracting low-frequency sub-band data as a new 4 4× Sub-

block

iB . From top to bottom and from left to right, the Sub-blocks order is denoted as:

B i

,

i

=

1, 2, 3....

M

⎡

⎢

⎤

⎥

8

×

⎡

⎢

N

⎤

⎥

8

⎡ ⎤⎢ ⎥ is the function of Rounded Down.

Step 3: Using matrix Q to MOD each sub-block iB , the remainder matrix is called

divisible matrix as

iC and save the

thn column

thn column pixel ,which are belong to each sub-block iC . The slope of the straight

iD .The coordinates for fitting straight line is constituted by the

row ,

thm row ,

m +

1)th

pixel and (

line recorded as a .

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LI SONG/ Procedia Engineering 00 (2011) 000–000

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Step 4: Defining a range for the slope which is from 0.9 to 1.1.If the slope of the

iC contained in the

range, then this sub-block will be selected to embed watermark. When the corresponding bit of

watermarking is equal to 0, choosing four adjacent pixels in matrix iC , calculating their mean and making

iC . If the corresponding bit of watermarking is

their mean value to cover those selected pixels record as

iD as new

equal to 1, all the sub-block pixels will not be modified .Then record the sum of

iC and

'

'

'

iB and conduct inverse integer LWT.

matrix

Step 5: Loop step 2 to step 4 until all the sub-blocks be traversed, getting watermarked image 'I .

Watermarking extraction process is the same as embedding watermark process. According to the value

of slope, we can judge watermarking information exists or not .If the watermarking information exists,

iC whether it has four adjacent pixels that are the same value in the

then check corresponding sub-block

selected position or not, by which we can judge extracted watermarking information is 1 or 0.

'

4. Simulation Results

The standard image “ lena ” with 512 512 8

× bits is used to carry out the experiment and the binary

× bits is embedded in the carrier image and then generates the

watermarking image with 32 32 2

watermarked image, which is shown in the Figure 1. NC as normalized correlation coefficient is used to

express the distortion of extracted watermark.

×

×

When the watermarked image is without under attack, the Peak-Signal-to-Noise Ratio (PSNR) between

the carrier image and the watermarked image is 58.9. Comparing original watermark with A, the value of

NC is 1. Comparing carrier image with Reference [7], the PSNR is 48.5 and the corresponding NC is

0.9981.

Figure 1.Watermarking, Carrier image and Watermarked image.

Do the clipping and the noise attack operation separately for the watermarked image, the degree of

clipping are 25%, 55% and 70%. In the Figure 2, Figure 2(a), Figure 2( b), Figure 2(c) are the

watermarking which are extracted from the corresponding clipping watermarked image. The results show

that the watermarking can be extracted perfectly and the algorithm can resist the 70% clipping attack. For

the watermarked image add salt & pepper noise, Figure 2(d) and Figure 2(e) are the corresponding

extracted watermarking. The NC is 0.9867 under the situation of 0.02 salt & pepper noise attack.

However, the algorithm of Reference [7] can’t resist the noise attack.

Li Song and Gu Qiaolun / Procedia Engineering 29 (2012) 1602 – 16061606

Li Song and Gu Qiaolun / Procedia Engineering 29 (2012) 1602 – 1606

LI SONG/ Procedia Engineering 00 (2011) 000–000

5

Figure 2. The experimental results for the clipping and noise attacks.

5. Conclusion

In this paper, a simple digital watermarking algorithm is proposed, which is based on IWT and Linear

Regression Constraints. A novel method of obtain the remainder matrix is introduced to the algorithm,

which assumes a fixed matrix Q firstly, then lets the matrix Q MOD the low-frequency data, at last we

get a new remainder matrix. According to the remainder matrix, we can determine the watermarking

embedding and extraction. Especially, it can greatly reduce the distortion of carrier image. The

experimental results demonstrate that the robustness of invisible watermarking algorithm is very good and

PSNR can be improved to 58. It not only can perfectly extract the watermarking but also has strong

robustness against the clipping and the noise attacks. How to improve the robustness of algorithm to resist

other watermarking attack is the further issue that we need to study.

Acknowledgements

This work is partially supported by the key program of Natural Science Foundation of Tianjin

(11JCZDJC16000).

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