# Robust Image Watermarking withZernike Moments by sa20392

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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

CCECE 2005, May 1 - 4, 2005

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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