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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