PACS: Pj, Gg

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1 * 1)2) 2) 3) 2) 1) 1) (, ) 2) (, ) 3) (, ) ( ; ),..,,.,.,. :,,, PACS: Pj, Gg 1,.,, [1,2].,,, [3,4].,, [5,6].,. [7 9]., [10 17].,.,, [10]., [18 20], [11 16].,, [17]., [10 17],,.,. * ( : , , ) ( : ) ( : Y ) ( : YK ) ( : PY ). yumei2@126.com c 2012 Chinese Physical Society

2 ,,,,, ( Logistic ),,. ( ),., :. Lyapunov,. Lyapunov,,,. x n+1 = m 1 + m 2 x n + m 3 x 2 n +m 4 y n + m 5 yn 2 + m 6 x n y n, (1) y n+1 = m 7 + m 8 x n + m 9 x 2 n +m 10 y n + m 11 yn 2 + m 12 x n y n,, m i (i = 1, 2,, 12) ; x n y n.,,., x n+1 = m 4 y n + m 5 yn, 2 (2) y n+1 = m 8 x n + m 10 y n. m 4 = 1.66, m 5 = 1.30, m 8 = 1.10, m 10 = 0.10, (a) x n ; (b) y n , LL(L) LL(R). 2,.,,, 2.,. : E(x d, y d, d v ) = E data (x d, y d, d v ) +λe reg (x d, y d, d v ), (3)

3 u u E data (x d, y d, d) = I L (x d + j, y d + i) i= u j= u I R (x d + i + d v, y d + i), (4) E reg (x d, y d, d v ) = λ( d v0 (x d 1, y d ) d v + d v1 (x d 1, y d 1) d v + d v2 (x d, y d 1) d v + d v3 (x d + 1, y d 1) d v ). (5), E, E d v ; E data, d v ; u, u = 1, 3 3; E reg ; λ ; x d y d. 3, d v, d v1, d v2, d v3, d v4 d v. 2 (a) ; (b) 3 sort( ) x(n) y(n), [x (n), p] = sort(x(n)) [y (n), q] = sort(y(n)),, x (n) y (n), p q x (n) y (n) x(n) y(n),., p q M, M M(p, q),. 50 M(p, q), w. M(p, q), w = 1;, w = , 5. 1, LL (L) LL (R) k k. 4, M. p q M, M M (p, q). 5 M (p, q), w. M (p, q), w = 1;, w = 0. 3 k k. 4, M,,. x k y k, x(n) = [x(1), x(2),, x(n)] y(n) = [y(1), y(2),, y(n)]., 3, ( Photoshop ), 1 2,

4 4 (a) ; (b) ; (c) ; (d) ; (e) 1 ; (f) 2, N, u, λ k 32, 1, ,., S [9,13] S = 1 B w b w b b=1 B, (6),, B. w w 0.5 ; ,, 1,, 0.5., 1 0. [16] : e = N 1 N 0 N all, (7)

5 , N 1, N 0 N all 1 0, e, 2. 2, 1 0,. 3.2,,. ( ), R SNP,R ; ( ), R SNP,L , V NG , S R SNP 3, R SNP,R, R SNP,L., I NSP , , R SNP, S 0.83,. 2 N N e S(V NG = 0.005) R SNP,R (V NG = 0.005) S(V NG = 0.01) R SNP,R (V NG = 0.01) S(V NG = 0.005) R SNP,L (V NG = 0.005) S(V NG = 0.01) R SNP,L (V NG = 0.01) , W FM , , W FPLG , ,, S 0.89,

6 4 S(I NSP = 0.02) R SNP,R (I NSP = 0.02) S(I NSP = 0.03) R SNP,R (I NSP = 0.03) S(I NSP = 0.02) R SNP,L (I NSP = 0.02) S(I NSP = 0.03) R SNP,L (I NSP = 0.03) S(W FM = 3 3) R SNP,R (W FM = 3 3) S(W FM = 5 5) R SNP,R (W FM = 5 5) S(W FM = 3 3) R SNP,L (W FM = 3 3) S(W FM = 5 5) R SNP,L (W FM = 5 5) S(W FPLG = 2 2) R SNP,R (W FPLG = 2 2) S(W FPLG = 3 3) R SNP,R (W FPLG = 3 3) S(W FPLG = 2 2) R SNP,L (W FPLG = 2 2) S(W FPLG = 3 3) R SNP,L (W FPLG = 3 3) (JPEG), Q, Q,., ( ), 5 6., Q = 10,, (S = 0.84), JPEG

7 5 Q R SNP (a) R SNP,R ; (b) R SNP,L 6 (a); (b) , 1/8 1/16 (A CUL = 1/8, A CUL = 1/16). 7. 7,, S 0.90,. 7 S(A CUL = 1/8) R SNP,R (A CUL = 1/8) S(A CUL = 1/16) R SNP,R (A CUL = 1/16) S(A CUL = 1/8) R SNP,L (A CUL = 1/8) S(A CUL = 1/16) R SNP,L (A CUL = 1/16)

8 L MR,, ; R MD. 2 (L MR = 2) 2 (R MD = 2), 8. 8,, S 0.84, ,,, (R R,A = 4) (R A,R = 0.25), 9. 9,, S 0.9,., 3 9 6,,. S S th,., S = 0.83 S th. 8 S(L MR = 2) R SNP,R (L MR = 2) S(R MD = 2) R SNP,R (R MD = 2) S(L MR = 2) R SNP,L (L MR = 2) S(R MD = 2) R SNP,L (R MD = 2) S(R R,A = 4) R SNP,R (R R,A = 4) S(R A,R = 0.25) R SNP,R (R A,R = 0.25) S(R R,A = 4) R SNP,L (R R,A = 4) S(R A,R = 0.25) R SNP,L (R A,R = 0.25)

9 3.3,,,, Kerckhoff., 7(a) 100,, S. 7 : 0.5 ; 1, 7(a) 38 7(b) 68. 7,, 0.5,. (),,,. 4 7 (a) ; (b), 7(b) 100,,., : (1), ; (2),, ; (3), ; (4), ; (5),.,. [1] Fan Y C, Chiou J C, Jiang Y H 2011 IEEE Trans. Magn [2] Shen L Q, Liu Z, Yan T, Zhang Z Y, An P 2011 IEEE Trans. Circ. Syst. Video Techn [3] Shao F, Jiang G Y, Wang X, Yu M, Chen K 2010 IEEE Trans. Consume Electron [4] Fan Y C, Kung Y T, Lin B L 2011 IEEE Trans. Magn [5] Zhu Z J, Wang Y E, Jiang G Y, Liang F 2007 J. Image Graph (in Chinese) [,,, ] [6] Lin Y H, Wu J L 2011 IEEE Trans. Broadcas [7] Alattar A M, Digimarc C, Tualatin O 2004 IEEE Trans. Image Proces [8] Zhang X P, Wang S Z, Qian Z X, Feng G R 2011 IEEE Trans. Image Proces [9] Zeng G R, Qiu Z D 2010 Acta Phys. Sin (in Chinese) [, ]

10 [10] Wen Q, Sun T F, Wang S X 2003 Acta Electron. Sin (in Chinese) [,, ] [11] Wu X Y, Guan Z H 2007 Phys. Lett. A [12] Mooney A, Keating J G 2009 Chaos Solitons Fract [13] Song W, Hou J J, Li Z H, Huang L 2009 Acta Phys. Sin (in Chinese) [,,, ] [14] Hu Y F, Zhu S A 2008 J. Zhejiang Univ. (Eng. Sci.) (in Chinese) [, 2008 ( ) ] [15] He H J, Zhang J S 2007 Acta Phys. Sin (in Chinese) [, ] [16] Zou L J, Wang B, Feng J C 2008 Acta Phys. Sin (in Chinese) [,, ] [17] Xu T, Zhang Y N, Sun J Q, Zheng J B,Ling Z G 2009 J. Image Graph (in Chinese) [,,,, ] [18] Jin J X, Qiu S S 2010 Acta Phys. Sin (in Chinese) [, ] [19] Zhang C X, Yu S M 2010 Acta Phys. Sin (in Chinese) [, ] [20] Sun K H, He S B, Sheng L Y 2011 Acta Phys. Sin (in Chinese) [,, ] A zero-watermarking algorithm of stereoscopic image based on hyperchaotic system Zhou Wu-Jie 1)2) Yu Mei 2) Yu Si-Min 3) Jiang Gang-Yi 2) Ge Ding-Fei 1) 1) ( School of Information and Electronic Engineering, Zhejiang University of Science and Technology, Hangzhou , China ) 2) ( Faculty of Information Science and Engineering, Ningbo University, Ningbo , China ) 3) ( College of Automation, Guangdong University of Technology, Guangzhou , China ) ( Received 16 June 2011; revised manuscript received 31 October 2011 ) Abstract In order to protect the copyright of stereoscopic images in the condition of the image quality, a zero-watermarking stereoscopic image algorithm is presented based on hyperchaotic system. In the proposed algorithm, disparity zero-watermark is constructed according to the stability of disparity between low frequency bands of wavelet decomposition of the left and the right views and direct coefficients of discrete cosine transform; in the process of zero-watermark construction, the zero-watermark position mapping according to the features of the sensitivity of hyperchaotic discrete system initial value, ampleness of parameter key space and complexity of dynamic behavior, enhances the security of algorithm. The relationship between security and watermark capacity is also analyzed. Experimental results show that the proposed algorithm is strong robust to noise, filtering, compression, and the shearing of asymmetrical and symmetrical attacks. Keywords: stereoscopic image, disparity zero-watermarking, hyperchaotic system, robustness PACS: Pj, Gg * Project supported by the National Natural Science Foundation of China (Grant Nos , , ), the Specialized Research Foundation for the Doctoral Program of Higher Education of China (Grant No ), the Natural Science Foundation of Zhejiang Province, China (Grant No. Y ), the Scientific Research Foundation for the Graduate Students of Zhejiang Province, China (Grant No. YK ), and the Outstanding Dissertation Cultivation Foundation of Ningbo University, China (Grant No. PY ). yumei2@126.com

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