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A chaos-based robust wavelet-domain watermarking algorithm

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									A chaos-based robust wavelet-
domain watermarking algorithm
 Author: Zhao Dawei, Chen Guanrong, Liu Wenbo
 From: Chaos, Solitons and Fractals 22(2004) 47-54


 Advisor: Chin-Chen Chang
 Speaker: Jui-Yi Chang
 Date: 2004/5/26
Outline
   Introduction
   Logistic map
   A new watermarking algorithm
   Watermark detection
   Experimental results
   Conclusions
    introduction
            Chaotic Logistic map:
            Label sequence
                                          DWT       Subimage
Original image                 subimage               DWT
                                                    coefficients


                               Logistic map:
                               Watermark sequence


                Label                               Watermarked
 Watermarked sequence Watermarked         IDWT          DWT
 original image        subimage                      coefficients
      Logistic map
         Xk+1=μXk(1-Xk) , 0<μ≦4
         Use Chaotic Logistic map to selection
          elements.

                         Sequence (Length=1024)


                33    1023   112   …              42   88



Select 256 elements
            A new watermarking algorithm
                          Label Sequence (Length=256)
                    33   1023    112      …             1          64


  1     2                   31     32

  33    34                  63     64
                                                   33       1023



              …….
                                                                   ……




                                                                        1   64
  993   994                 1023   1024

                                              Subimage(128x128 pixels=256 blocks)
Original image(256x256 pixels=1024 blocks)
A new watermarking algorithm
    LL3         HL3

                      HL2
    LH3         HH3
                                    HL1
          LH2         HH2




                LH1                 HH1




          DWT Subimage (128x128 pixels)
    A new watermarking algorithm
                                Sequence (Length=64)
Use Chaotic Logistic map
                           7       17   64   …               50       43




                                                  iwm(i) >Tw  1
                                                  iwm(i) ≦Tw  -1

                                                  If Tw=40


  Watermark signal w(i)    -1      -1   1     …                   1        -1
        A new watermarking algorithm
           C’band(i)=Cband(i)+αw(i) , i=1,2…,N

           If α=2
            C’band(1)=0+2*(-1)=-2
            …
                                                    -2   -2        25   12
Cband are the original wavelet coefficients
                                                    11   15        -7   -10
C’band are the watermarked wavelet coefficients
α is global parameter
                                                              ……



                                                    13   19        14   20
                 Watermarked wavelet coefficients
                                                    2    1         -8   19
                 (in HH)
      A new watermarking algorithm
  -2     -2             25   12                77    92               128   33

                                               49    66               45    92
  11     15             -7   -10
                                    IDWT
                                                             ……
               ……

  13     19             14   20                13    15               14    55
  2      1              -8   19                2     1                0     128


Watermarked wavelet coefficients               Watermarked pixel value


                                   Label Sequence (Length=256)

       Original image              33   1023   112       …        1   64
    Watermark detection
                      N
   ρ=(1/3N) ΣΣC’band(i)w(i)
                     band i=1

   Pf is a false alarm.
   If |ρnew -ρold |< Pf , then watermark can be
    detect.
   Use α, Pf, Tρ to determine watermark exist?
   α≦1, cannot detect the watermark correctly.
          Experimental results




(a) Original image. (b) Watermarked image. (c) Extracted subimage. (d) Watermarked subimage.
                Experimental results (Cont.)
                         Relations between α and PSNR ρ, Tρ(Pf =10-8)


α      2.0          2.5       3.0      3.5      4.0      4.5      5.0      5.5      6.0      6.5      7.0      7.5      8.0


PSNR   48.45        46.91     45.32    42.83    43.36    42.33    41.42    40.59    39.38    39.14    38.50    37.90    37.34


ρ      2.5355       3.1551    3.7747   4.3942   5.0138   5.6334   6.2530   6.8725   7.4921   8.1117   8.7313   9.3508   9.9704


Tρ     1.5686       1.5708    1.5736   1.5769   1.5807   1.5850   1.5898   1.5950   1.6008   1.6070   1.6137   1.6209   1.6286
      Experimental results (Cont.)




Half cropped
watermarked image
(ρ=3.6549, Tρ=1.6385).   (a) Rotated watermarked image.
                         (b) Recovered image.
Conclusion
   This scheme applies the wavelet transform
    locally, based on
    (1) the chaotic logistic map, and
    (2) embeds the watermark into the DWT
    domain.
   This new schem has high fidelity and is
    highly robust against geometric attacks .

								
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