J. K. Su and B. Girod, "On the imperceptibility and robustness of digital fingerprints," submitted for publication.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....method and the set of attacks. Moreover, they lack a strong theoretical foundation and development. This paper also attempts to answer at least in part the question posed at the beginning of this section. We take a theoretical approach to watermarking, which we initially presented in [13] and [14] and investigate further here. Section II introduces a general watermarking model. In Section III, we present the Wiener attack, which includes two interesting special cases: removal and anticorrelation attacks. This framework leads to the idea of energy efficient watermarking, and it ....

....when is minimized, and from (11) is minimized when is maximized. Hence, regardless of , the watermarker should choose to maximize and hence create an energy efficient watermark under the variance constraint. The solution of this problem leads to the theorem below; the proof appears in [13]. Theorem 2 (Power Spectrum Condition) For the watermarking model (1) is maximized if and only if D (17) and, for any dimensionality , the maximum MSE is (18) where . We remarked in [13] that one could use a frequency weighted MSE instead of . Such a weighting might be desirable for ....

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J. K. Su and B. Girod, "On the imperceptibility and robustness of digital fingerprints," in Proc. IEEE Int. Conf. Multimedia Computer Systems, vol. 2, Florence, Italy, June 1999, pp. 530--535.

.... compression (e.g. MP3 for audio, JPEG for images, and MPEG 2 for video) or geometric transformations such as rotation, shifting, and scaling [35] Recently, more theoretical approaches have attempted to provide watermarking, and the larger field of information hiding, with a stronger foundation [44, 16, 27, 47, 10, 33, 51, 31, 34, 8, 48]. Of particular note, Moulin and O Sullivan [34] have introduced a powerful information theoretic framework for studying watermarking. They cast the problem as a game between the owner and the attacker. The owner s goal is to send and receive as much information as possible, while the attacker s ....

....makes sense intuitively: The watermark appears white relative to the original, which makes it hardest to estimate or distinguish from the original. Indeed, the PSC was first derived as a necessary and sufficient condition for resisting MMSE estimation of the watermark from the watermarked signal [47]. For this attack, Eq. 11) simplifies to # # . When the PSC is satisfied, ##### and # ## #### become constant for all ##, and closed form expressions for # # # and # # ## result [48] Then a direct relationship between # and # # ## can be obtained (App. C) # # # # # ## # # ....

[Article contains additional citation context not shown here]

J. K. Su and B. Girod, "On the imperceptibility and robustness of digital fingerprints," In Proc. IEEE Intl. Conf. Multimedia Computing & Systems, Vol. 2, pp. 530--535, Florence, Italy, Jun. 1999.

.... compression (e.g. MP3 for audio, JPEG for images, and MPEG 2 for video) or geometric transformations such as rotation, shifting, and scaling [35] Recently, more theoretical approaches have attempted to provide watermarking, and the larger field of information hiding, with a stronger foundation [44, 16, 27, 47, 10, 33, 51, 31, 34, 8, 48]. Of particular note, Moulin and O Sullivan [34] have introduced a powerful information theoretic framework for studying watermarking. They cast the problem as a game between the owner and the attacker. The owner s goal is to send and receive as much information as possible, while the attacker s ....

....makes sense intuitively: The watermark appears white relative to the original, which makes it hardest to estimate or distinguish from the original. Indeed, the PSC was first derived as a necessary and sufficient condition for resisting MMSE estimation of the watermark from the watermarked signal [47]. log 2 (1 o w o m) When the PSC is satisfied, G( and For this attack, Eq. 11) simplifies to C = 2 and Dx result [48] Then a direct vv (w) become constant for all , and closed form expressions for o m relationship between C and D can be obtained (App. C) 1 ( Px Dx) Dembed ) 13) ....

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J. K. Su and B. Girod, "On the imperceptibility and robustness of digital fingerprints," In Proc. IEEE Intl. Conf. Multimedia Computing & Systems, Vol. 2, pp. 530-535, Florence, Italy, Jun. 1999.

....are selected to minimize ##x# # x# #. By symmetry, the filters are identical, and the problem becomes equivalent to estimating x#### from x##### # w# ####, where # w# #### # w ####. The solution is a Wiener filter with impulse response ###### # =L ####. It can be shown (e.g. see [6]) that ##x# # x### # # ### ###. # ### ### indicates that this distortion is also the minimum that the coalition can achieve; # ### ### # # as # ##. Consider image watermarking, where the original signal takes on integer values in ### ####. If we neglect quantization of the watermarked ....

J. K. Su and B. Girod. On the imperceptibility and robustness of digital fingerprints. In Proc. IEEE Intl. Conf. Multimedia Comp. Sys., vol. 2, pp. 530--535, Jun. 1999.

.... xL ) By symmetry, the filters are identical, and the problem becomes equivalent to estimating x[ n] from x[ n] wL [ n] where wL [ n] 1 L P 2L w [ n] The solution is a Wiener filter with impulse response h[ n] 2 x 2 x 2 w =L [ n] It can be shown (e.g. see [6]) that D(x; xL ) 2 x 2 w L 2 x 2 w = D min (L) D min (L) indicates that this distortion is also the minimum that the coalition can achieve; D min (L) 0 as L 1. Consider image watermarking, where the original signal takes on integer values in [0; 255] If we neglect ....

J. K. Su and B. Girod. On the imperceptibility and robustness of digital fingerprints. In Proc. IEEE Intl. Conf. Multimedia Comp. Sys., vol. 2, pp. 530--535, Jun. 1999.

....to attacks. However, others have proposed placing the watermark in the middle or high frequencies to make it easier to separate from the original image [7, 8] or making it white, as in conventional spread spectrum. This paper elaborates on a simple theoretical watermarking and attack model from [9]. Analysis leads to a meaningful way to evaluate robustness. It is shown that watermarks that resist the attack should satisfy a powerspectrum condition. Finally, experiments with theoretical signal models and natural images verify and reinforce the importance of this condition. 2. WATERMARK ....

.... (2) y[ n] Gamma fl w[ n] v[ n] 3) where the asterisk ( denotes M D convolution, fl 0 is a scalar gain factor, and v[ n] is additive WSS Gaussian noise that is independent of w[ n] and x[ n] We call this attack the Wiener attack ; it is a generalization of an attack model presented in [9]. A block diagram appears in Fig. 1. 3.2. Analysis By independence, the Wiener filter has transfer function H( Phi wy( Phi yy( Phi ww( Phi xx ( Phi ww ( 4) Letting E denote the MSE of the Wiener estimate, it is readily shown [10] that E = E Theta (w[ n] ....

[Article contains additional citation context not shown here]

J. K. Su, B. Girod, "On the imperceptibility and robustness of digital fingerprints," in Proc. IEEE Intl. Conf. Multimedia Computing and Systems, Florence, Italy, Jun. 1999, vol. 2, pp. 530--535.

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J. K. Su and B. Girod, "On the imperceptibility and robustness of digital fingerprints." Submitted to IEEE ICMCS 99, 1999.

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J. K. Su and B. Girod, "On the imperceptibility and robustness of digital fingerprints," submitted for publication.

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J. K. Su and B. Girod, "On the imperceptibility and robustness of digital fingerprints," in Proc. IEEE Intl. Conf. Multimedia Comp. Sys., vol. 2, pp. 530-535, (Florence, Italy), Jun. 1999.

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J. Su and B. Girod, "On the imperceptibility and robustness of digital fingerprints," in submitted to IEEE ICMCS 99, Florence, Italy, June 1999.

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