Hiding Data in Halftone Images

1
Hiding Data in Halftone Images

• Hsien-Wen Tseng, Chin-Chen Chang

INFORMATICA, 2005, Vol. 16,No. 3,419-430 2005
Institute of Mathematics and Informatics, Vilnius
2
Outline

• Introduction
• A Review of the Noise-Balanced Error Diffusion
• Proposed Method
• Experimental Results
• Conclusions

3
Introduction(1/7)

• Half-toning a technique for changing multi-tone
  images into two-tone binary images.
• Half-toning technique
• Order dithering
• Error diffusion

4
Introduction(2/7)

• Order dithering
• - Bayers, 1973.
• - A threshold of the multi-tone image with a
  spatially periodic pattern.
• - Method each pixel valve is scaled and compared
  to a threshold in the corresponding element of
  the pattern.
• If the pixel value?threshold, white.
• pixel value?threshold, black.

5
Introduction(3/7)
Use the Bayers pattern 0 8 2 10
12 4 14 6 3 11 1 9
15 7 13 5
Fig. 1. Halftone image (a) ordered dithering.
6
Introduction(4/7)

• Error diffusion
• - Floyd and Steinberg, 1976.
• - Javis et al., 1976.
• - Stucki, 1981.
• More complicated than ordered dithering and has
  better visual quality.

X 7 5 3 5 7 5 3 1
3 5 3 1
X 8 4 2 4 8 4 2 1
2 4 2 1
7
Introduction(5/7)
Fig. 1. Halftone image (b) error diffusion.
8
Introduction(6/7)

• Visual cryptography Naor and Shamir 1994.
• - It can recover a secret image without any
  computation.
• Noise-Balanced algorithm for hiding binary
  pattern into two or more error-diffused images.
• - The first one normal error-diffused image.
• - The others noise-balanced error diffusion
  images.

9
Introduction(7/7)

• The binary visual pattern can be recovered
  without any computation when theses two or more
  error-diffused images are overlaid.
• The NBEDF can be percepted as a kind of visual
  cryptography.
• The NBEDF decoded visual pattern is not clear.
• The proposed method can provide an simple
  cryptography for the mobile phone.

10
A Review of the Noise-Balanced Error
Diffusion(1/5)

• uijxi,jxi,j, where
• xi,j? ? eim,jn hm,n (1)
• ei,jui,j-bi,j, where
• 0, if ui,j?128
• 255, if ui,j?128
  (2)

11
A Review of the Noise-Balanced Error
Diffusion(2/5)
Fig. 2. Diagram of standard error diffusion.
12
A Review of the Noise-Balanced Error
Diffusion(3/5)

• NBEDF uses EDF1 and EDF2 to hide the binary
  visual pattern P.
• - EDF1 is generated by standard error diffusion
  to the original multi-tone image.
• - EDF2 is generated by applying NBEDF.
• PW all the white pixels in P.
• PB all the black pixels in P.
• EDF1W and EDF1B are defined as above.

13
A Review of the Noise-Balanced Error
Diffusion(4/5)
EDF1 P EDF2
(i,j) ? ? NBEDF (Use Eqs 3 and 4)

• In NBEDF, Eqs. (1) and (2) modified as follows
• ui,jxi,jxi,j-NB
  (3)
• ei,jui,j-bi,jNB
  (4)

14
A Review of the Noise-Balanced Error
Diffusion(5/5)
EDF1 P EDF2
(i,j) ? ? Use Eqs 5 and 6

• Eqs. (5) and (6) are applied as follows
• ui,jxi,jxi,jNB
  (5)
• ei,jui,j-bi,j-NB
  (6)

EDF1 P EDF2
(i,j) ? ? Use Eqs 3 and 4
(i,j) ? ? Use Eqs 1 and 2
15
Proposed Method(1/7)

• Requires a little additional computation when
  overlapping.
• The computation is simple and the computation
  complexity is low.
• The overlapping algorithm, the background image
  could be eliminated and the decoded visual
  pattern is more precise.

16
Proposed Method(2/7)

• The overlapping algorithm in conventional visual
  cryptography is the human visual system.

• The decoded pixel ? ? ?

17
Proposed Method(3/7)

• The modified overlapping algorithm in the
  proposed method looks slightly different as shown

• The decoded pixel
• ? ? ?
• ? ? ? or ? ? ?

18
Proposed Method(4/7)
In the same way, the modified NBEDF uses two
halftone images (EDF1 and EDF2) to hide the
binary visual pattern P.
EDF1 P EDF2
(i,j) ? ? ? (Use Eqs. 3 and 4)
(i,j) ? ? ? (Use Eqs. 5 and 6)
(i,j) ? Preferred to be identical to EDF1
19
Proposed Method(5/7)

• In this case, three conditions should be
  considered as follows.
• Firstly, a trial on EDF2(i,j) is made by using
  standard error diffusion.

EDF2 EDF1
(i,j) ? ? ? ? Use Eqs. 1 and 2
(i,j) ? ? Use Eqs. 3 and 4
(i,j) ? ? Use Eqs. 5 and 6
Obtain more precise decoded visual pattern
without interference from the background image.
20
Proposed Method(6/7)

• Consider the case of three EDF images

EDF1 EDF2 P EDF3
(i,j) ? ? ? ? (Use Eqs. 3 and 4)
(i,j) ? ? ? Processed with standard error diffusion (Use Eqs. 1 and 2)
(i,j) ? ? ? Processed with standard error diffusion (Use Eqs. 1 and 2)
(i,j) ? ? ? ? (Use Eqs. 5 and 6)
(i,j) ? To be identical to EDF1 and EDF2
21
Proposed Method(7/7)

• In this case, three conditions should be
  considered as follows.
• Firstly, a trial on EDF3(i,j) is made by using
  standard error diffusion.

EDF3 EDF1 EDF2
(i,j) ? ? ? Use Eqs. 3 and 4
(i,j) ? ? ? Use Eqs. 5 and 6
Otherwise, Eqs. 1 and 2 are applied. Otherwise, Eqs. 1 and 2 are applied. Otherwise, Eqs. 1 and 2 are applied. Otherwise, Eqs. 1 and 2 are applied. Otherwise, Eqs. 1 and 2 are applied.
22
Experimental Results(1/9)
(a)
(b)
(c)
(d)
Fig. 6. Input visual patterns (a) bold word, (b)
skeleton word, (c) fingerprint image, (d)
halftone baboon image.
23
Experimental Results(2/9)
24
Experimental Results(3/9)
Fig. 8. The proposed method using Fig. 6(a) bold
word as input pattern (a) embedded image, (b)
overlaid image.
25
Experimental Results(4/9)
Fig. 9. NBEDF using Fig. 6(b) skeleton word as
input pattern (a) embedded image, (b) overlaid
image.
26
Experimental Results(4/9)
Fig. 10. The proposed method using Fig. 6(b)
skeleton word as input pattern (a) embedded
image, (b) overlaid image.
27
Experimental Results(5/9)
Fig. 11. NBEDF using Fig. 6(c) fingerprint image
as input pattern (a) embedded image, (b)
overlaid image.
28
Experimental Results(6/9)
(a)
(b)
Fig. 12. The proposed method using Fig. 6(c)
fingerprint image as input pattern (a) embedded
image, (b) overlaid image.
29
Experimental Results(7/9)
(a)
(b)
Fig. 13. NBEDF using Fig. 6(d) halftone baboon
image as input pattern (a) embedded image, (b)
overlaid image.
30
Experimental Results(8/9)
(a)
(b)
Fig. 14. The proposed method using Fig. 6(d)
halftone baboon image as input pattern (a)
embedded image, (b) overlaid image.
31
Experimental Results(9/9)
Fig. 15. The result images when overlapping three
halftone images.
32
Conclusions

• The background image in the decoded image can be
  eliminated and the hidden binary visual pattern
  can be revealed precisely.
• The complexity is low, it can be applied to
  mobile system for image authentication or
  conveying of secret messages.

33
References(1/3)

• 1 Bayers, B.E. (1973). An optimum method for
  two level rendition of continuous tone pictures.
  In Proc. IEEE Int. Communication Conf. pp.
  26112615.
• 2 Floyd, R.W., and L. Steinberg (1976). An
  adaptive algorithm for spatial grayscale. In
  Proc. SID. pp. 7577.
• 3 Fu, M.S., and O.C. Au (2002). Data hiding
  watermarking for halftone images. IEEE Trans.
  Image Processing,11(4), 477484.
• 4 Fu, M.S., and O.C. Au (2003a). A novel
  self-conjugate halftone image watermarking
  technique. In Proc. of IEEE Int. Sym. on Circuits
  and Systems, Vol. 3. pp. 790793.
• 5 Fu, M.S., and O.C. Au (2003b). Steganography
  in halftone images conjugate error diffusion.
  Signal Processing, 83(10), 21712178.

34
References(2/3)

• 6 Jarvis, J.F., C.N. Judice and W.H. Ninke
  (1976). A survey of techniques for the display of
  continuous-tone pictures on bilevel displays. In
  Comp. Graph. Image Proc., Vol. 5. pp. 1340.
• 7 Noar, M., and A. Shamir (1995). Visual
  cryptography. In Advances in Cryptology
  EUROCRYPT94 Lecture Notes in Computer Science,
  Vol. 950. Springer, Berlin. pp. 112.
• 8 Pei, S.-C., and J.-M. Guo (2003a). Hybrid
  pixel-based data hiding and block-based
  watermarking for error- diffused halftone images.
  IEEE Trans. Circuits and System for Video
  Technology, 13(8), 867884.
• 9 Pei, S.-C., and J.-M. Guo (2003b). Data
  hiding in halftone images with noise-balanced
  error diffusion. IEEE Signal Processing Letters,
  10(12), 349351.

35
References(3/3)

• 10 Stucki, P. (1981). MECCA A Multiple-Error
  Correcting Computation Algorithm for Bilevel
  Image Hardcopy Reproduction. IBM Res. Lab.,
  Zurich, Switzerland, Res. Rep. RZ1060.
• 11 Ulichney, R. (1987). Digital Halftoning.
  Cambridge, MA MIT Press.