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# Data Hiding in Halftone Images by Stochastic Error Diffusion

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```									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

2008/8/6                                                       1
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).

2008/8/6                                                6
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.

2008/8/6                                                8
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.

2008/8/6                                                  9
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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