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Optics Express

Optics Express

  • Editor: J. H. Eberly
  • Vol. 3, Iss. 12 — Dec. 7, 1998
  • pp: 485–490
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Improved robust watermarking through attack characterization

Deepa Kundur and Dimitrios Hatzinakos  »View Author Affiliations


Optics Express, Vol. 3, Issue 12, pp. 485-490 (1998)
http://dx.doi.org/10.1364/OE.3.000485


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Abstract

In this paper, we propose an approach to improve the performance of a broad class of watermarking schemes through attack characterization. Robust and reference watermarks are both embedded into a signal. The reference watermark is used to characterize any modifications of the resulting marked signal, so that the robust watermark can be more reliably extracted. Analysis and simulations are provided to demonstrate the effectiveness of the approach.

© Optical Society of America

1. Introduction

Various techniques for robust watermarking have been proposed in the literature [1

1. N. Nikolaidis and I. Pitas, “Robust Image Watermarking in the Spatial Domain,” Signal Process. 66, 385–403 (1998). [CrossRef]

,2

2. J. F. Delaigle, C. De Vleeschouwer, and B. Macq, “Watermarking Algorithm Based on a Human Visual Model,” Signal Process. 66, 319–335 (1998). [CrossRef]

,3

3. C. I. Podilchuk and W. Zeng, “Image-Adaptive Watermarking using Visual Models,” IEEE J. Sel. Area in Commun. 16(4), 525–539 (1998). [CrossRef]

,4

4. X.-G. Xia, C. G. Boncelet, and G. R. Arce, “A Multiresolution Watermark for Digital Images,” Proc. IEEE Int. Conf. on Image Processing 1, 548–551 (1997). [CrossRef]

,5

5. G. W. Braudaway, “Protecting Publicly-Available Images with an Invisible Image Watermark,” Proc. IEEE Int. Conf. on Image Processing 1, 524–527 (1997). [CrossRef]

,6

6. D. Kundur and D. Hatzinakos, “Digital Watermarking using Multiresolution Wavelet Decomposition,” Proc. IEEE Int. Conf. on Acoustics, Speech and Signal Processing 5, 2969–2972 (1998).

(Please note that this is not an exhaustive list)]. However, studies have shown that there still exists a need to improve reliability [7

7. M. D. Swanson, M. Kobayashi, and A. H. Tewfik, “Multimedia Data-Embedding and Watermarking Technologies,” Proceedings of the IEEE 86(6), 1064–1087 (1998). [CrossRef]

]. Previously proposed research has concentrated on sophisticated embedding strategies. In addition, the potential of error-correction codes has been assessed [8

8. J. R. Hernández, F. Pérez-González, and J. M. Rodriguez, “The Impact of Channel Coding on the Performance of Spatial Watermarking for Copyright Protection,” Proc. IEEE Int. Conference on Acoustics, Speech and Signal Processing 5, 2973–2976 (1998).

]. In this paper we consider the importance of a watermark extraction stage which makes use of information concerning the attacker’s actions. To the best of the authors’ knowledge this is the first paper which formally addresses the importance of characterizing the attacker’s transformations on the marked signal to optimally estimate the watermark. By optimal we mean that the probability of bit error for watermark extraction is minimized. Our approach can be easily applied to a broad class watermarking methods to improve reliability. We assume that the original host signal is not available for watermark extraction and that the watermark is a binary data stream which is repeatedly embedded throughout the signal.

The contributions of this paper include 1) the incorporation of reference watermarking for attack identification prior to robust watermark extraction, 2) the use of a localized binary symmetric channel model to characterize the watermark attacks, and 3) the design of a weighted linear receiver structure which minimizes the probability of bit error for watermark extraction. We also demonstrate the improved performance of our technique through simulation results.

2. Robust Watermarking through Attack Characterization

2.1 Overview

In digital watermarking a host signal is transformed to a watermark domain in which modifications are imposed on the domain coefficients to embed the watermark. The modified coefficients are then inverse transformed to produce the marked signal1. Our proposed approach to improved robust watermarking is applicable to the general class of watermarking methods with the following basic properties:

  • The watermark data stream consists of binary elements.
  • The host signal (which refers to the original multimedia signal before watermarking) is not available or exploited for watermark extraction.
  • The entire watermark is repeatedly embedded throughout the signal and each repetition of the watermark is positioned in a distinct localized region of the watermark domain. We will discuss this later in greater detail.

2.2 Reference Watermarking for Channel Identification

Robust watermarking techniques which do not make use the host signal for watermark extraction are more practical than their counterparts which exploit the host. The tradeoff, however, is that the former class of methods are, on average, less robust as little information is available on how the marked signal has been modified. We propose an approach to characterize the attacks on the watermark without use of the host signal. We define an attack as any signal modification, intentional or otherwise, which is applied to the marked signal and which effects the reliability of the extracted watermark. It has been shown in [9

9. D. Kundur and D. Hatzinakos, “Towards a Telltale Watermarking Technique for Tamper-Proofing,” Proc. IEEE Int. Conf. on Image Processing , 2, 409–413 (1998).

,10

10. D. Kundur and D. Hatzinakos, “Semi-Blind Image Restoration Based on Telltale Watermarking,” to appear in Proc. 32nd Asilomar Conference on Signals, Systems, and Computers, (1998).

] that elementary characteristics of the signal distortions are easily estimated using a reference watermark. A reference watermark is one which is embedded into a signal for the purpose of detecting signal distortions. In this paper we show the importance of such tamper modeling to robust watermark extraction.

We propose the scenario shown in Figure 1. The host signal is embedded with both robust and reference watermarks. The two kinds of watermarks are placed orthogonally so that they do not interfere with one another. The trade-off is that fewer repetitions of the robust watermark can be placed in the signal as a portion of the watermark “bandwidth” is consumed by the presence of the reference watermark. Each embedded repetition of the robust watermark sequence, which we denote wi , i = 1, 2, …M (where M is the total number of repetitions), has an associated binary reference watermark sequence vi , with the same statistical properties as wi 2. Figure 1(b) demonstrates the embedding procedure where each wi is placed in a localized region denoted Di of the watermark domain. The bits of wi are alternated with those of vi such that an attack on the marked signal will reflect in the same way statistically on both wi and vi . Thus, if we let ŵi and i be the extracted versions of wi and vi after an attack, it is expected that the probability of bit error for ŵi is equal to that for i.

Figure 1. Combined Reference and Robust Watermarking for Channel Characterization and Reliable Watermark Extraction. (A) The watermark embedding and extracting scenarios, (B) We consider a 2-D host image. The watermark domain coefficients are divided into localized regions Di (outlined with bold lines). Reference and robust watermark bits are alternatively embedded in each region.

2.3 The Binary Symmetric Channel Model

Each watermark repetition wi and its associated reference watermark vi are embedded in the same localized region Di of the watermark domain as shown in Figure 1(b). Assuming that the function used to transform the signal to the watermark domain is continuous, most degradations which maintain the perceptual quality of the signal will have a similar effect on both wi and vi . That is, we can assume that the degree of distortion experienced by both wi and vi due to an attack is the same; hence they have they same watermark channel.

We model the watermark channel for wi and vi as a binary symmetric channel (BSC) with probability of bit error pEi . Each bit of the embedded robust watermark wi (k), k = 1, 2, …, N (where N is the length of the watermark) is modeled as passing through a BSC to produce the corresponding extracted watermark bit ŵi(k). We assume in our model that 0 ≤ pEi ≤ 0.5. If pEi > 0.5 we merely complement the output and effectively use 0 ≤ 1 - pEi < 0.5 as the BSC parameter.

The reference watermark vi is used to estimate the parameter pEi for each i. If we let N be the length of the binary stream vi , and i be the corresponding extracted binary stream after an attack, we can approximate the probability of bit error for the watermark channel associated with Di with

p̂Ei=1NΣk=1Nvi(k)v̂i(k)
(1)

where ⊕ is the exclusive-OR operator and vi (k) and i(k) are the kth watermark bits of vi and i, respectively. It can be shown using the law of large numbers that the expected value of Ei is pEi and that the variance of estimate decreases for increasing N.

There are important advantages to using this model of the watermark channel. The model is simple and the parameter pEi is easy to accurately estimate using the associated reference watermark. In addition, a different parameter pEi for each wi is incorporated which provides a localized assessment of the attack in the watermark domain. In most watermarking schemes, the extracted watermark repetitions ŵi are averaged to produce the overall extracted watermark. Our attack characterization allows us to combine these repetitions based on a measure of their reliability to minimize the probability of watermark bit error. It should be emphasized that degradations such as filtering additive noise and lossy compression are reliably modeled using the BSC [9

9. D. Kundur and D. Hatzinakos, “Towards a Telltale Watermarking Technique for Tamper-Proofing,” Proc. IEEE Int. Conf. on Image Processing , 2, 409–413 (1998).

]. This characterization, however, is not appropriate for geometric transformations on the signal such as rotation and scaling.

2.4 A Weighted Receiver Structure for Watermark Extraction

In this section, we discuss how information about the BSC parameters can be used to obtain a more accurate estimate of the watermark information compared to simple averaging of the extracted repetitions. Our goal is to keep computational complexity low so we limit ourselves to linear estimation. The overall extracted watermark ŵ is computed as the weighted sum of the individual extracted repetitions. That is,

ω̂(k)=round[Σi=1Mαiω̂i(k)]
(2)

αi=log(1pEipEi)/(Σi=1Mlog(1pEjpEj))
(3)

3. Weights for Optimal Linear Watermark Extraction

It can be shown that Equation 2 implies that there is no bit error in ŵ(k) if Σi=1M αibi (k) < 0.5 (For simplicity, we let ξ(b(k)) ≜ Σi=1M αibi (k) for the remainder of the analysis.). In addition, Equation 2 with the constraints that Σi=1M αi = 1 and αi ≥ 0 imposes the restriction that ξ(b(k)) = 1 - ξ(b(k))̅ where (·)̅ is the binary complement operator. This suggests that if the elements of ŵ(k) accurately estimate ŵ(k) using Equation 2, then the elements of ŵ() produce a bit error. To clarify this point we consider the sets A and in which A ⊂ {ŵ(k)|ξ(b(k)) > 0.5} and ⊂ {ŵ(k)|ξ(b(k)) < 0.5}. Any remaining complement pairs for which ξ(b(k)) = ξ(b(k))̅ =0.5 are arbitrarily distributed among A and such that their cardinalities are both 2M-1 and ŵ(k) ∊ A if and only if ŵ(k)̅.

The probability of bit error for ŵ(k) is given by PE (k) = Σŵ(k)∊A͂ P{ŵ(k)} where P{ŵ(k)} is the probability of extracting the sequence ŵ(k) which is given by

P{ŵ(k)}=i=1M(1pEi)b¯ i(k)pEibi(k)
(4)

since ŵ(k) is an ordered set of Bernoulli random variables. It can be shown that the minimization of PE (k) is equivalent to selecting a set of weights {αi } such that ŵ(k) ∊ A implies that P{ŵ(k)} ≥ P{ŵ(k)̅}. Equivalently, for each complement pair {ŵ(k), ŵ(k)̅}, we want to place the element with the lower probability of occurrence in A ~ to minimize the overall bit error rate. It can be easily shown that a selection of αi given in Equation 3 implies that P{ŵ(k)} ≥ P{ŵ(k)} if and only if ξ(b(k)) ≤ ξ(b(k)) and thus ŵ(k) ∊ A͂ which suggests that PE (k) is minimized. The analysis is omitted for compactness.

4. Simulation Results

We apply our proposed approach to the wavelet-based watermarking technique proposed by the authors in [6

6. D. Kundur and D. Hatzinakos, “Digital Watermarking using Multiresolution Wavelet Decomposition,” Proc. IEEE Int. Conf. on Acoustics, Speech and Signal Processing 5, 2969–2972 (1998).

]. Figure 2 displays the 256 × 256 pixel host and watermarked colour images used in our simulations. A 32 byte watermark, randomly generated with a uniform probability distribution, is embedded in the luminance image component. The performance of optimal weighting during watermark extraction is compared to that of simple averaging. In each case, the correlation coefficient3 of the extracted and the embedded watermarks were used to assess the robustness of the technique. The results for linear filtering with a radially symmetric blur of the form h(m,n)=am2+n2K where K = Σ∀(m,n) h(m,n) are displayed in Figure 3 for different values of a. Similar results are presented for JPEG compression. The pink line represents the correlation for the weighted extraction and the blue corresponds to averaging. In both cases a significant increase in the correlation coefficient is observed which indicates a higher accuracy in the extracted watermark. The weights {αi } are calculated from Equation 3 using Ei from the reference watermark calculated by Equation 1.

Figure 2. The (a) host image and (b) watermarked image used for simulations.
Figure 3. The improved performance of the proposed approach.

An improvement in performance was also noticed for other distortions such as median filtering. The only type of tampering for which little improvement was observed was that of additive white Gaussian noise. We believe that the whiteness of the noise made it difficult to predict its effects using the reference watermark.

5. Conclusion

In this paper we demonstrate how improved performance for robust watermarking can be achieved through assessment of attacker tampering. Watermark repetition throughout the signal provides diversity to combat a broad class of degradations. Characterization of the attacks can be used to optimally combine the extracted watermark repetitions to minimize the probability of error in watermark extraction. Future work involves extending the method to detect and identify geometric transformations on the marked signal to decrease the computational load required for watermark synchronization.

Footnotes

1Popular transforms found in the watermarking literature are the wavelet transform and the DCT. The definition does not preclude techniques which embed the watermark in the time/spatial domain as the transformation will reduce to the identity operator.
The reader is reminded that since wi is a repetition of the robust watermark, wi = wj for all i and j. The reference watermarks {vi } do not necessarily have to be identical as long as their individual bit elements have the same statistical properties as that of the robust watermark. Both {wi } and {vi } are generated using a pseudo-random number emulating the same probability distribution.
3The correlation coefficient of u and v is defined as Σku(k)v(k)(Σku2(k)Σkv2(k)).

References

1.

N. Nikolaidis and I. Pitas, “Robust Image Watermarking in the Spatial Domain,” Signal Process. 66, 385–403 (1998). [CrossRef]

2.

J. F. Delaigle, C. De Vleeschouwer, and B. Macq, “Watermarking Algorithm Based on a Human Visual Model,” Signal Process. 66, 319–335 (1998). [CrossRef]

3.

C. I. Podilchuk and W. Zeng, “Image-Adaptive Watermarking using Visual Models,” IEEE J. Sel. Area in Commun. 16(4), 525–539 (1998). [CrossRef]

4.

X.-G. Xia, C. G. Boncelet, and G. R. Arce, “A Multiresolution Watermark for Digital Images,” Proc. IEEE Int. Conf. on Image Processing 1, 548–551 (1997). [CrossRef]

5.

G. W. Braudaway, “Protecting Publicly-Available Images with an Invisible Image Watermark,” Proc. IEEE Int. Conf. on Image Processing 1, 524–527 (1997). [CrossRef]

6.

D. Kundur and D. Hatzinakos, “Digital Watermarking using Multiresolution Wavelet Decomposition,” Proc. IEEE Int. Conf. on Acoustics, Speech and Signal Processing 5, 2969–2972 (1998).

7.

M. D. Swanson, M. Kobayashi, and A. H. Tewfik, “Multimedia Data-Embedding and Watermarking Technologies,” Proceedings of the IEEE 86(6), 1064–1087 (1998). [CrossRef]

8.

J. R. Hernández, F. Pérez-González, and J. M. Rodriguez, “The Impact of Channel Coding on the Performance of Spatial Watermarking for Copyright Protection,” Proc. IEEE Int. Conference on Acoustics, Speech and Signal Processing 5, 2973–2976 (1998).

9.

D. Kundur and D. Hatzinakos, “Towards a Telltale Watermarking Technique for Tamper-Proofing,” Proc. IEEE Int. Conf. on Image Processing , 2, 409–413 (1998).

10.

D. Kundur and D. Hatzinakos, “Semi-Blind Image Restoration Based on Telltale Watermarking,” to appear in Proc. 32nd Asilomar Conference on Signals, Systems, and Computers, (1998).

OCIS Codes
(100.2000) Image processing : Digital image processing
(100.2960) Image processing : Image analysis

ToC Category:
Focus Issue: Digital watermarking

History
Original Manuscript: November 6, 1998
Published: December 7, 1998

Citation
Deepa Kundur and Dimitrios Hatzinakos, "Improved robust watermarking through attack characterization," Opt. Express 3, 485-490 (1998)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-3-12-485


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References

  1. N. Nikolaidis and I. Pitas, "Robust Image Watermarking in the Spatial Domain," Signal Process. 66, 385-403 (1998). [CrossRef]
  2. J. F. Delaigle, C. De Vleeschouwer and B. Macq, "Watermarking Algorithm Based on a Human Visual Model," Signal Process. 66, 319-335 (1998). [CrossRef]
  3. C. I. Podilchuk and W. Zeng, "Image-Adaptive Watermarking using Visual Models," IEEE J. Sel. Area in Commun. 16(4), 525-539 (1998). [CrossRef]
  4. X.-G. Xia, C. G. Boncelet and G. R. Arce, "A Multiresolution Watermark for Digital Images," Proc. IEEE Int. Conf. on Image Processing 1, 548-551 (1997). [CrossRef]
  5. G. W. Braudaway, "Protecting Publicly-Available Images with an Invisible Image Watermark," Proc. IEEE Int. Conf. on Image Processing 1, 524-527 (1997). [CrossRef]
  6. D. Kundur and D. Hatzinakos, "Digital Watermarking using Multiresolution Wavelet Decomposition," Proc. IEEE Int. Conf. on Acoustics, Speech and Signal Processing 5, 2969-2972 (1998).
  7. M. D. Swanson, M. Kobayashi and A. H. Tewfik, "Multimedia Data-Embedding and Watermarking Technologies," Proceedings of the IEEE 86(6), 1064-1087 (1998). [CrossRef]
  8. J. R. Hernandez, F. Perez-Gonzalez and J. M. Rodriguez, "The Impact of Channel Coding on the Performance of Spatial Watermarking for Copyright Protection," Proc. IEEE Int. Conference on Acoustics, Speech and Signal Processing 5, 2973-2976 (1998).
  9. D. Kundur and D. Hatzinakos, "Towards a Telltale Watermarking Technique for Tamper-Proofing," Proc. IEEE Int. Conf. on Image Processing, 2, 409{413 (1998).
  10. D. Kundur and D. Hatzinakos, "Semi-Blind Image Restoration Based on Telltale Watermarking," to appear in Proc. 32nd Asilomar Conference on Signals, Systems, and Computers, (1998).

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