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Robust Image Watermarking
with Zernike Moments
Qing Chen Xiaoli Yang Jiying Zhao
School of Information Department of School of Information
Technology and Engineering Software Engineering Technology and Engineering
University of Ottawa Lakehead University University of Ottawa
qingchen@site.uottawa.ca lucy.yang@lakeheadu.ca jyzhao@site.uottawa.ca
CCECE 2005, May 1 - 4, 2005
Saskatoon, Saskatchewan, Canada
Outline
1. Introduction
2. Zernike Moments
3. Embedding and Detection
4. Conclusions and Future Work
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1.Introduction
The digital watermark is a signal added to digital
contents that can be detected later.
Robust image watermarking against image rotation,
scaling and translation (RST) is still a challenge.
Moment-based image invariants have the desirable RST
properties which can be employed for RST
watermarking.
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2.Zernike Moments
The Zernike moments of order n with repetition m for
an image f( x, y ) which vanishes outside the unit disk
of x2+y2≤1 are:
n +1
Anm = ∫∫ 2 2 f ( x , y )Vnm ( x , y ) dxdy
*
π x + y ≤1
where n is a positive integer or zero; m is an integer
subject to constraints n-|m| is even, and |m| ≤ n.
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2.Zernike Moments
Vnm is defined by:
Vnm = Vnm ( ρ , θ ) = Rnm ( ρ )e imθ
ρ : the length of the vector from the origin
to the pixel (x, y);
θ : the angle between the vector ρ and x axis;
Rnm is defined by:
(n− m )/ 2
( n − s )!
R nm ( ρ ) = ∑
s=0
( − 1) s
n+ m n− m
ρ n−2s
s! ( − s )! ( − s )!
2 2
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2.Zernike Moments
The magnitudes of Zernike moments are invariant to
image rotations.
128X128 lena.tiff (without rotation) 90°
128X128 lena.tiff (90° rotation)
Moment value Magnitude Moment value Magnitude
5.0420 5.0420 5.0420 5.0420
0.4936 + 0.2967i 0.5759 0.2967 - 0.4936i 0.5759
0.1753 0.1753 0.1753 0.1753
-0.0010 - 0.4354i 0.4354 0.0010 + 0.4354i 0.4354
-0.0533 - 0.5805i 0.5830 -0.5805 + 0.0533i 0.5830
-0.3400 - 0.2357i 0.4137 0.2357 - 0.3400i 0.4137
0.0869 0.0869 0.0869 0.0869
0.5671 - 0.1504i 0.5867 -0.5671 + 0.1504i 0.5867
0.3562 + 0.0810i 0.3653 0.3562 + 0.0810i 0.3653
0.3518 + 0.1602i 0.3866 0.1602 –0.3518i 0.3866
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2.Zernike Moments
Image reconstruction with Zernike moments:
Zernike
moments
order
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3.Embedding and Detection
Embedding: an iterative embedding process by adjusting
the embedding strength α to get satisfied result.
Cover image
Watermarked
Watermark image
Reduce embedding
strength α Watermark
Yes visible?
No
Increase embedding
strength α Watermark
No detectable?
Yes
Embedding Successful
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3.Embedding and Detection
Embedding example:
α
1
0.5
+ =
0.1
0.01
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3.Embedding and Detection
Detection process:
Watermarked image
Compute Zernike moments
No RST Yes
attack?
Extract feature vector Extract feature vector
Anm | Anm |
of the watermark of the watermark
Reconstruct the Compute the RMSE
embedded watermark
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3.Embedding and Detection
Detection example:
[256X1] vector
with order up to 30
Watermarked image Detected watermark
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4.Conclusions and Future Work
Zernike moments based watermarking scheme is
robust against image rotation.
Two different detection algorithms are proposed to
successfully detect the embedded watermark.
The invariance property of Zernike moments against
image translation and scaling need to be studied and
tested for the future work.
More efficient watermark embedding algorithm needs
to be explored to fully employ the advantages of
Zernike moments.
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