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

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
                                                                                        6
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
                                                               8
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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