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Data Hiding in Halftone Images by Stochastic Error Diffusion

VIEWS: 6 PAGES: 23

									Data Hiding in Halftone Images by
Stochastic Error Diffusion

                   Ming Sun Fu, Oscar C. AM Department of
           Electrical and Electronic Engineering, Hong Kong
                        University of Science and Technology

                       Signal Processing, 2001. Proceedings


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Outline
   Introduction
   Data Hiding by Stochastic Error
    Diffusion (DHSED)
   Simulation Results
   Conclusion



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Introduction
   The study of data hiding techniques is
    commonly called steganography[2].
   Concern about data-hiding for halftone images.
   Halftone image data hiding techniques:
      Embed invisible digital data into halftone

       images.
      Embed hidden visual patterns into two or

       more halftone images.

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Data Hiding by Stochastic Error
Diffusion(1/10)

 Two M×N halftone images: Y0, Y1.
 Binary image H:

  H:overlaying Y0 and Y1
   Let X be the original M × N multi-tone
    image from which Y0 and Y1 are obtained.




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Data Hiding by Stochastic Error
Diffusion(2/10)
x(i,j): the pixel at location (i,j) of X
yi(i,j): the pixel at location (i,j) of Yi
H: assumed have the same size M × N as Y0 and Y1
                            * 7 5
                1
               -    ×   3 5 7 5 3
               48
                        1 3 5 3 1

           Fig. 1 Jarvis error diffusion kernel

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Data Hiding by Stochastic Error
Diffusion(3/10)

      Y0: generated by regular error diffusion
       (no hidden visual patterns)
      Each pixel location (i,j) have a value f0(i,j)
       related to the current multi-tone pixel
       value x(i,j) is compared with a threshold
       T(T=128).




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Data Hiding by Stochastic Error
Diffusion(4/10)
                  2
             1
   a0(i,j)=-∑e0(i+k,j+l)*w(k,1)
            48                       (1)
                 k,l=-2



   f0(i,j)=x(i,j)+a0(i,j)           (2)
               0,       f0(i,j)﹤T
   y0(i,j)=
              255,       otherwise   (3)
   e0(i,j)= f0(i,j) - y0(i,j)       (4)
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Data Hiding by Stochastic Error
Diffusion(5/10)
   Y1 : generated by applying Stochastic Error
    Diffusion (SED) to X with respect to Y0 to
    hide H.
   In SED, the hidden binary image H is used to
    turn on or off the stochastic properties on a
    pixel-by-pixel basis.
   HB : the collection of all the black pixels in H.
   HW : the collection of all the white pixel in H.

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Data Hiding by Stochastic Error
Diffusion(6/10)
   For (i,j) ∈HW, the pixel y1(i,j) in Y1 is forced to
    be identical to the co-located pixel y0(i,j) in Y0.
    In other words, y1(i,j) = y0(i,j) for (i,j) ∈HW.
   For HB, error diffusion is applies with some
    special boundary conditions using the same
    error diffusion kernel as in Y0 such that the
    texture and the look-and-feel of the regions in
    Y1 are very similar to, if not the same as, the
    corresponding regions in Y0.


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Data Hiding by Stochastic Error
Diffusion(7/10)
    Morphological dilation with some
     structuring element S is applied to HB to
     give C = HB⊕S.
    S = (2L+1)×(2L+1) square matrix.
    C is basically HB expanded outward both
     horizontally and vertically by L pixel.




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Data Hiding by Stochastic Error
Diffusion(8/10)
 Define region D = C ∩ HBC=C ∩ HW, which is the
   dark region outside HB in Fig.2
 In SED, the boundary condition is that the error e1(i,j )
   is assumed to be zero outside C, i.e. e1(i,j)=0 for
   (i,j)∈C.
 e1(i,j)=max(min(f1(i,j)-y1(i,j),127),-127)       (5)




  Fig. 2 An example of (left) HB; (right) C = HB ⊕ S
2008/8/6 with dark region being D = C ∩ HB
                                             C
                                                              11
Data Hiding by Stochastic Error
Diffusion(9/10)
   For (i,j)∈HB, regular error diffusion (i.e.
    Eqns. 1 to 4 with subscript changed from
    0 to 1) is applied.
   Region HB will have the characteristic
    texture of the regular error diffusion. But
    the phase of the error diffusion texture in
    region HB of Y1 would be different from
    the corresponding region of Y0.


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Data Hiding by Stochastic Error
Diffusion(10/10)
   When Y0 and Y1 are overlaid, the regions
    corresponding to the white regions of H
    should have normal intensity while those
    corresponding to the black regions of H
    should have lower-than-normal intensity.




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Simulation Results(1/4)




    Fig. 3 Y0 from 512×512 Lena with nothing hidden
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Simulation Results(2/4)




           Fig. 4 Y1 with H hidden
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Simulation Results(3/4)




           Fig. 5 H to be hidden
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Simulation Results(4/4)




       Fig. 6 Y0 with Y1 overlaid showing the hidden H .

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Conclusion
 Data Hiding Stochastic Error Diffusion
  (DHSED) :
  To hide binary visual patterns in two error-
  diffused halftone images.
 The halftone images with the embedded visual

  patterns retain good visual quality.
 The contrast is good in smooth regions with

  mid-gray brightness.

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 References(1/4)
[1] F. Mintzer, et al., “Effective and Ineffective Digital
    Watermarks”, Proc. of IEEE Int. Con$ on Image
    Processing, Vol. 3, pp. 913, Oct. 1997.
[2] N.F. Johnson, S. Jajodia, “Exploring Steganography:
    Seeing the Unseen”, IEEE Computer, Vo1.31, No.2,
    pp.2634, Feb. 1998.
[3] B. E. Bayers, “An Optimum Method for Two Level
    Rendition of Continuous Tone Pictures,” Proc. of IEEE
    Int. Communication onf.,pp2611-2615, 1973.
[4] R.W. Floyd, L. Steinberg, “An Adaptive Algorithm for
    Spatial Grayscale,” Proc. SID, pp. 75-77, 1976.

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References(2/4)
[5] Z. Baharav, D. Shaked, “Watermarking of Dither
   Halftoned Images”, Proc. of SPIE Security and
   Watermarking of Multimedia Contents, pp. 307-313,
   Jan 1999.
[6] R.T. Tow, “Methods and Means for Embedding
   Machine Readable Digital Data in Halftone Images”,
   United States Patent Number 5,315,098
[7] M.S. Fu, O.C. Au, “Data Hiding in Halftone Image
   by Pixel Toggling”, Proc. Of SPIE Int. Con$    On
   Security and Watermarking of Multimedia Content4
   Vol. 3971, pp. 228-236, Jan 2000.



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References(3/4)
[8] M.S. Sun, O.C. Au, “Data Hiding by Smart Pair
    Toggling for Halftone Images”, Proc. Of IEEE Int.
    Con$ On Acoustics, Speech and Signal Processing,
    Vol. 4, pp. 2318-232 1, Jun. 2000.
[9] M.S. Sun, O.C. Au, ‘Modified Data Hiding Error
    Diffusion for Image Halftoning’, Proc. Of SPIE
    Con$ On Visual Communication and Image
    Processing, Vol. 3, pp. 1671- 1680, Jun 2000.
[10] K.T. box, “Digital Watermarking Using
    Stochastic Screen Patterns”, United States Patent
    Number 5,734,752.

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References(4/4)
[11] S. G. Wang, ”Digital watermarking Using
    Conjugate Halftone ~ Screens‘‘, United States
    Patent Number , 790,703.




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                                f0=130+(-15)=115       150≧128 y0=255

            +                      f0(i,j)     Threshold          y0(i,j)
 xi,j           ⊕                                 128
 150
                  +
            a0(i,j) a0=-105*7/48=-15

                wk,l                               +    -
                * 7 5                                  ⊕
-
 1
        ×   3 5 7 5 3                                   e0(i,j)
48                                                 e0=150-255=-105
            1 3 5 3 1

            Standard error diffusion flowchart.

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