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Visual Cryptography for Gray-Level Images by Dithering Techniques

Learn about Space-filling Curve Ordered Dithering, threshold encryption, decoding, experimental results, and more.

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Visual Cryptography for Gray-Level Images by Dithering Techniques

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  1. Visual Cryptography for Gray-Level Images by Dithering Techniques Author：Chang-Chou Lin, Wen-Hsiang Tsai Source：Pattern Recognition Letters 24 （2003） 349-358 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. 559-563, 1998

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

  7. 21 22 25 26 37 38 41 42 20 23 24 27 36 39 40 43 19 18 29 28 35 34 45 44 16 17 30 31 32 33 46 47 15 12 11 10 53 52 51 48 14 13 8 9 54 55 50 49 1 2 7 6 57 56 61 62 0 3 4 5 58 59 60 63 Subdividing a 88 image into 4 4 regions by using a Hilbert curve 7 7 7 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 0 1 14 15 0 1 14 15 3 3 3 15 12 11 10 4 3 0 5 2 2 2 14 13 8 9 6 7 2 1 1 1 1 1 2 7 6 9 8 13 14 0 3 4 5 10 11 12 15 0 0 0 0 1 2 3 4 5 6 7 7 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6

  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. 7 21 22 25 26 37 38 41 42 M(0,0) I(0,0) 6 20 23 24 27 36 39 40 43 5 19 18 29 28 35 34 45 44 4 16 17 30 31 32 33 46 47 3 15 12 11 10 53 52 51 48 2 14 13 8 9 54 55 50 49 1 1 2 7 6 57 56 61 62 0 3 4 5 0 58 59 60 63 0 1 2 3 4 5 6 7 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 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=0.390625 Step2: x=M(i, j) mod t = M(0, 0) mod 4= 21 mod 4=1 Step3: B(x)=B(1)=0 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. share1 share2 share3 An example (2/4) 0 0 0 1 1 1 2 2 2 0 1 2 0 1 2 0 1 2 0 1 2 1 2 0 2 0 1 A0 = 0 0 0 1 1 1 2 2 2 0 1 2 0 1 2 0 1 2 2 0 1 0 1 2 1 2 0 A1 = 0 0 0 1 1 1 2 2 2 0 1 2 0 1 2 0 1 2 1 2 0 2 0 1 0 1 2 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： 0 0 0 1 1 1 2 2 2 0 1 2 0 1 2 0 1 2 0 1 2 1 2 0 2 0 1 A0 = 0 0 0 1 1 1 2 2 2 0 1 2 0 1 2 0 1 2 2 0 1 0 1 2 1 2 0 A1 = 0 0 0 1 1 1 2 2 2 0 1 2 0 1 2 0 1 2 1 2 0 2 0 1 0 1 2 original image share1 share2 share3 result A2 =

  16. An example (4/4) share1 share2 share3 (k, n)-threshold visual cryptography k = 3, n = 3 size increase ck-1at 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。

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