1. Visual Cryptography for Gray-Level Images by Dithering Techniques
Author：Chang-Chou Lin, Wen-Hsiang Tsai
Source：Pattern Recognition Letters 24 （2003）
Speaker：Shu-Fen Chiou（邱淑芬）

2. Outline Introduction Space-filling Curve Ordered Dithering (SFCOD)
(k, n)-threshold visual encryption of gray-level images
Experimental results
Conclusions
Comments

3. Introduction (1/2) Input a gray-level image Share image1
Transform by SFCOD
decode
encode
Apply (2, 2) visual cryptography
The decoded image
An approximate binary image
Share image2

4. Introduction (2/2)
Binary images are usually restricted to represent text-like messages.
Verheul and van Tilborg (1997) first tried to extend visual cryptography into gray-level images, but their method has the disadvantage of size increase in the decoded image.

5. Space-filling Curve Ordered Dithering (SFCOD)
Yuefeng Zhang
Comput. & Graphics, Vol. 22 No.4, pp , 1998

6. Hilbert curve
Rule
Iteration = 0
Iteration = 1
Iteration = 2

7. Subdividing a 88 image into 4 4 regions by using a Hilbert curve7 7 7 10 1 2 3 4 7 6 5 8 9 11 12 15 13 14 48 51 52 53 49 50 55 54 62 61 56 57 63 60 59 58 42 41 38 37 43 40 39 36 44 45 34 35 47 46 33 32 26 25 22 21 27 24 23 20 28 29 18 19 31 30 17 16 5 6 9 10 5 6 9 10 6 6 6 4 7 8 11 4 7 8 11 5 5 5 3 2 13 12 3 2 13 12 4 4 4 1 14 15 1 14 15 3 3 3 15 12 11 10 5 4 3 2 2 2 14 13 8 9 6 7 2 1 1 1 1 1 2 7 6 9 8 13 14 3 4 5 10 11 12 15 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7

8. Dithering Technique (1/3)
PROCEDURE SFCOD (M, B, t ,I ,H)
BEGIN
FOR i = 0 TO m – 1 DO
FOR j = 0 TO m – 1 DO IF
I (i, j) /256 ≥ (B (M (i, j) MOD t )+0.5)/ t
THEN
H (i, j) = 1(白色)
ELSE
H (i, j) = 0 ;(黑色)
END 定義
I：大小為m*m的灰階影像
M(i, j)：traversal-order number
B：space-filling curve dither array
t：array length
H(i, j)：轉 binary image 後的 pixel value

9. Dithering Technique (2/3)
Step1: Gray-level image I with mm.
Step2: Divide I into many pixels of a block.
Step3: Transform each gray block into binary block
M(0,0)
I(0,0) 1 2 3 4 5 6 7 10 8 9 11 12 15 13 14 48 51 52 53 49 50 55 54 62 61 56 57 63 60 59 58 42 41 38 37 43 40 39 36 44 45 34 35 47 46 33 32 26 25 22 21 27 24 23 20 28 29 18 19 31 30 17 16
Original Image I
Hilbert curve order
t=4, t<=M

10. Dithering Technique (3/3)
Space-filling curve dither array B, size(B)=t
作用在於打亂, B 對於每一個block 可以Fixed or not fixed
t=4
B(0)=1, B(1)=0, B(2)=2, B(3)=3

11. Example of Dithering Technique
Step1: y=I(0,0)/256=100/256=
Step2: x=M(i, j) mod t = M(0, 0) mod 4= 21 mod 4=1
Step3: B(x)=B(1)= B(0)=1, B(1)=0, B(2)=2, B(3)=3
Step4: q= (B(x)+0.5) / t
=(0+0.5)/4=0.125
Step5: Test (y >= q) ?
If yes, white color else black color.

12. (k, n)-threshold visual encryption of gray-level images
Verheul and van Tilborg, 1997
We describe an example for the case of a (3, 3)-threshold scheme.
If there are 3 gray levels original image.

13. An example (1/4)
Gray-level 0
Gray-level 1
Gray-level 2
original image

14. An example (2/4) share1 share2 share3 0 0 0 1 1 1 2 2 2
share1
A0 =
share2
share3
A1 =
A2 =

15. An example (3/4)
C0 = { all the matrices obtained by permuting the columns of A0 }
C1 = { all the matrices obtained by permuting the columns of A1 }
C2 = { all the matrices obtained by permuting the columns of A2 }
EX：
A0 =
A1 =
original image
share1
share2
share3
result
A2 =

16. An example (4/4) (k, n)-threshold visual cryptography k = 3, n = 3
share1
share2
share3
(k, n)-threshold visual cryptography
k = 3, n = 3
size increase ck-1 at least when c ≥ n
Decoding image

17. Experimental results (1/2)
The original image
with 16 gray levels
The image after
using SFCOD

18. Experimental results (2/2)
share1 +
The decoded image
share2

19. A person authentication application
Public key
Secret key
authentication
Encrypting a portrait of the user

20. Conclusions
This scheme possesses the advantages of inheriting any developed cryptographic technique for binary images and having less increase of image size in ordinary situations.
EX：
If there are 3 gray levels original image
before
this scheme
33-1 = 9 times
4 times

21. Comments
可以直接用灰階影像或是彩色影像來做視覺密碼學。
還原的影像可以和原始影像的尺寸大小一樣。