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A chaos-based robust wavelet-domain watermarking algorithm

Source: Chaos, Solitions and Fractals, Vol. 22, 2004, pp. 47-54.Authors: Zhao Dawei, Chen Guanrong, Liu WenboSpeaker: Hao-Cheng Wang(王皓正 )Date: 2004/9/22

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Outline

Introduction Watermarking in the wavelet domain DWT (Discrete Wavelet Transformation) Chaos and its application to watermarking

The new watermarking algorithm Watermark embedding Watermark detection

Results and analysis Conclusions Comment

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Watermarking in the wavelet domain The digital watermarking technology includes

Spatial-domain Transform-domain

DCT, DWT

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DWT (Discrete Wavelet Transformation)(1/2) 低頻 (low frequency)：像素之間的變化小，影像較平滑，人眼的敏感度高． LL1

高頻 (high frequency)：像素之間的差異大，影像較粗糙、模糊，人眼的敏感度較低． HH1

中頻：介於低頻與高頻之間． HL1、 LH1

LH1 HH1

HL1LL1

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DWT (Discrete Wavelet Transformation)(2/2)

LH1 HH1

HL1LL1

LH1 HH1

HL1LH2 HH2

HL2LL2

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Logistic map

Where

When , the map is in the chaotic state.

Where

Chaos and its application to watermarking

)1(1 kk xx

40

45699456.3

10 kx

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Logistic map(1/3)

Example

)1(1 kk xx

4

269

72

18

5

1023

529

868

712

229

963

622.0

10

9

8

7

6

5

4

3

2

1

0

x

x

x

x

x

x

x

x

x

x

x

1023

524

154

40

1014

563

856

720

233

962

623.0

10

9

8

7

6

5

4

3

2

1

0

x

x

x

x

x

x

x

x

x

x

x

45699456.3

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Logistic map(2/3)

Example

)1(1 kk xx

5.2

614

614

614

614

615

614

616

611

620

602

622.0

10

9

8

7

6

5

4

3

2

1

0

x

x

x

x

x

x

x

x

x

x

x

45699456.3

614

614

614

614

615

614

616

611

621

601

623.0

10

9

8

7

6

5

4

3

2

1

0

x

x

x

x

x

x

x

x

x

x

x

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Logistic map(3/3)

We will use the logistic map twice: To generate a label sequence To generate the watermark

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The new watermarking algorithm Apply the wavelet transform locally

Watermarkembedding

Iori (256×256)Isub (128×128)

DWT

IDWT

I’sub (128×128)

I’ori

(256×256)

8×8 block

8×8 block

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Watermark embedding(1/7)

1 2

1024

32

993

………………..

………………………………..

………………………………..

………………………………..

………………………………..

………………………..

Original Image (256×256 pixels)

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Watermark embedding(2/7)

1024)1(1 kk xx

seqk ix

33, 1023, 112, 36, 77……………96, 1, 64…………………….983, 124, 33

33 1023 112 64196………………………………

Label Sequence (Length=256)

(1)

(2)

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Watermark embedding(3/7)

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Watermark embedding(4/7)

LH1 HH1

HL1

LH2 HH2

HL2LH3 HH3

HL3LL3

DWT

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Watermark embedding(5/7)

Type 1

11111000011001110010……

Type 2

[1, -1]

11111-1-1-111-111-1

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Watermark embedding(6/7)

),1(1 kk xx wmk ix

)()()(' iwiCiC bandband , i=1, 2, …, N

Cband are the original wavelet coefficientsC’band are the watermarked wavelet coefficientsαis a global parameter accounting for the watermark strengthw is the watermark signalN is the element number of subband HL1 or HH1 or LH1

band {HL1, HH1, LH1}

(1)

(2)

(3)

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Watermark embedding(7/7)

4123.0wmi

)()()(' iwiCiC bandband , i=1, 2, …, N

i 1 2 3 4 5 6 7 8 9 10 …

iwm(i) 0.969 0.119 0.420 0.974 0.099 0.375 0.919 0.297 0.835 0.548 …

w(i) 1 -1 -1 1 -1 -1 1 -1 1 1 …

Cband 10 45 53 32 34 54 65 46 93 64 …

C’band 11 44 52 33 33 53 66 45 94 65 …

1 5.0wT

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Watermark detection(1/2)

The detection method we use is similar to the method proposed in [1]

We adopt the Neyman-Pearson criterion to determine the threshold Tp

[1] Barni M, Bartolini F. Improved wavelet-bsed watermarking through pixel-wise masking. IEEE Trans Image Processing 2001;10(5):789-91.

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Watermark detection(2/2)

band

N

iband iwiC

N 1

' )()(3

1

if ρ>T ρ: a watermark signal exists; otherwise, a watermark signal does not exist

see [1] for more details

(1)

(2)

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Results and analysis(1/3)

Test images: “Lena” and “Barbara”(256×256 pixels)

α=6.0, iseq=0.1564 and iwm=0.4123

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Results and analysis(2/3)

PSNR=39.3PSNR=39.300

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Results and analysis(3/3)

When we set α=1.0, or smaller, we cannot detect the watermark correctly

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Robustness against various attacks α=6, Pf=10-8, iseq=0.1564, iwm=0.4123 Additive noise attacks

Gaussian noise Salt and pepper noise

JPEG compression Geometric manipulations

Cropping, resizing, rotation

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Cropping

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Resizing and rotation

Resizing Zoom scale m

Zoom in (m>1) Zoom out (m<1)

m >0.625

Rotation 25°

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Conclusions

This scheme applies the wavelet transform locally, based on the chaotic logistic map, and embeds the watermark into the DWT domain.

Introduced a blind watermarking detection technique using the Neyman-Pearson criterion.

Highly robust against geometric attacks and signal processing operations and JPEG compression.

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Comment(1/2)

結合圖片的浮水印技術

11111000011001110010……

LH1 HH1

HL1

LH2 HH2

HL2LH3 HH3

HL3LL3

c1

c1 mod 2 = 1 or 0 ?c1 ±1

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Comment(2/2)

p1

p1 mod 2 = 1 or 0 ?

p1 ±1