## Improved robust watermarking through attack characterization

Optics Express, Vol. 3, Issue 12, pp. 485-490 (1998)

http://dx.doi.org/10.1364/OE.3.000485

Acrobat PDF (520 KB)

### 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

*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

*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.

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]

### 2.2 Reference Watermarking for Channel Identification

*w*

_{i},

*i*= 1, 2, …

*M*(where

*M*is the total number of repetitions), has an associated binary reference watermark sequence

*v*

_{i}, with the same statistical properties as

*w*

_{i}2. Figure 1(b) demonstrates the embedding procedure where each

*w*

_{i}is placed in a localized region denoted

*D*

_{i}of the watermark domain. The bits of

*w*

_{i}are alternated with those of

*v*

_{i}such that an attack on the marked signal will reflect in the same way statistically on both

*w*

_{i}and

*v*

_{i}. Thus, if we let

*ŵ*

_{i}and

*v̂*

_{i}be the extracted versions of

*w*

_{i}and

*v*

_{i}after an attack, it is expected that the probability of bit error for

*ŵ*

_{i}is equal to that for

*v̂*

_{i}.

*watermark channel*. Proper identification of this channel will allow more accurate “transmission” (i.e., extraction) of the robust watermark as optimal processing may be incorporated at the receiver. The channel estimation is performed with the use of the reference watermark. In the next section we discuss the particular model of the channel we assume.

### 2.3 The Binary Symmetric Channel Model

*w*

_{i}and its associated reference watermark

*v*

_{i}are embedded in the same localized region

*D*

_{i}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

*w*

_{i}and

*v*

_{i}. That is, we can assume that the degree of distortion experienced by both

*w*

_{i}and

*v*

_{i}due to an attack is the same; hence they have they same watermark channel.

*w*

_{i}and

*v*

_{i}as a binary symmetric channel (BSC) with probability of bit error

*p*

_{Ei}. Each bit of the embedded robust watermark

*w*

_{i}(

*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

*ŵ*

_{i}(

*k*). We assume in our model that 0 ≤

*p*

_{Ei}≤ 0.5. If

*p*

_{Ei}> 0.5 we merely complement the output and effectively use 0 ≤ 1 -

*p*

_{Ei}< 0.5 as the BSC parameter.

*v*

_{i}is used to estimate the parameter

*p*

_{Ei}for each

*i*. If we let

*N*be the length of the binary stream

*v*

_{i}, and

*v̂*

_{i}be the corresponding extracted binary stream after an attack, we can approximate the probability of bit error for the watermark channel associated with

*D*

_{i}with

*v*

_{i}(

*k*) and

*v̂*

_{i}(

*k*) are the

*k*th watermark bits of

*v*

_{i}and

*v̂*

_{i}, respectively. It can be shown using the law of large numbers that the expected value of

*p̂*

_{Ei}is

*p*

_{Ei}and that the variance of estimate decreases for increasing

*N*.

*p*

_{Ei}is easy to accurately estimate using the associated reference watermark. In addition, a different parameter

*p*

_{Ei}for each

*w*

_{i}is incorporated which provides a localized assessment of the attack in the watermark domain. In most watermarking schemes, the extracted watermark repetitions

*ŵ*

_{i}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]. 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

*ŵ*is computed as the weighted sum of the individual extracted repetitions. That is,

*ŵ*(

*k*) and

*ŵ*

_{i}(

*k*) are the

*k*th watermark bits of

*ŵ*and

*ŵ*

_{i}, respectively, and

*α*

_{i}is the associated scalar nonnegative weight dependent on

*p*

_{Ei}such that

*α*

_{i}= 1. The rounding operation makes sure that

*ŵ*is a binary data string comprised of zeros and ones. If the argument of round is 0.5, an arbitrary value of 0 or 1 is assigned. In any type of watermark attack, some regions in

*D*

_{i}are likely to undergo greater distortion than others. It is a direct advantage to be able to determine the regions which are less distorted and, hence, contain a more reliable watermark estimate. It is intuitively clear that a larger weighting for repetitions with a lower probability of bit error will improve the reliability of

*ŵ*. In the next section we show how the following assignment for

*α*

_{i}minimizes the bit error of

*ŵ*to produce an optimal linear watermark extraction.

## 3. Weights for Optimal Linear Watermark Extraction

**ŵ**(

**k**) if

*α*

_{i}

*b*

_{i}(

*k*) < 0.5 (For simplicity, we let

*ξ*(

**b**(

**k**)) ≜

*α*

_{i}

*b*

_{i}(

*k*) for the remainder of the analysis.). In addition, Equation 2 with the constraints that

*α*

_{i}= 1 and

*α*

_{i}≥ 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**(

**k̅**) produce a bit error. To clarify this point we consider the sets

*A*and

*A͂*in which

*A*⊂ {

**ŵ**(

**k**)|

*ξ*(

**b**(

**k**)) > 0.5} and

*A͂*⊂ {

**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

*A͂*such that their cardinalities are both 2

^{M-1}and

**ŵ**(

**k**) ∊

*A*if and only if

**ŵ**(

**k**)

*A͂*̅.

**ŵ**(k) is given by

*P*

_{E}(

*k*) = Σ

**ŵ**(

**k**)

*∊A͂*

*P*{

**ŵ**(

**k**)} where

*P*{

**ŵ**(

**k**)} is the probability of extracting the sequence

**ŵ**(

**k**) which is given by

**ŵ**(

**k**) is an ordered set of Bernoulli random variables. It can be shown that the minimization of

*P*

_{E}(

*k*) is equivalent to selecting a set of weights {

*α*

_{i}} 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

*α*

_{i}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

*P*

_{E}(

*k*) is minimized. The analysis is omitted for compactness.

## 4. Simulation Results

## 5. Conclusion

## Footnotes

1 | Popular 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 w_{i}
is a repetition
of the robust watermark, w_{i}
=
w_{j}
for all i and
j. The reference watermarks {v_{i}
} 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
{w_{i}
} and {v_{i}
}
are generated using a pseudo-random number emulating the same probability
distribution. | |

3 | The correlation coefficient of u and v is
defined as |

## References

1. | N. Nikolaidis and I. Pitas, “Robust Image Watermarking in the Spatial Domain,” Signal Process. |

2. | J. F. Delaigle, C. De Vleeschouwer, and B. Macq, “Watermarking Algorithm Based on a Human Visual Model,” Signal Process. |

3. | C. I. Podilchuk and W. Zeng, “Image-Adaptive Watermarking using Visual Models,” IEEE J. Sel. Area in Commun. |

4. | X.-G. Xia, C. G. Boncelet, and G. R. Arce, “A Multiresolution Watermark for Digital Images,” Proc. IEEE Int. Conf. on Image Processing |

5. | G. W. Braudaway, “Protecting Publicly-Available Images with an Invisible Image Watermark,” Proc. IEEE Int. Conf. on Image Processing |

6. | D. Kundur and D. Hatzinakos, “Digital Watermarking using Multiresolution Wavelet Decomposition,” Proc. IEEE Int. Conf. on Acoustics, Speech and Signal Processing |

7. | M. D. Swanson, M. Kobayashi, and A. H. Tewfik, “Multimedia Data-Embedding and Watermarking Technologies,” Proceedings of the IEEE |

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 |

9. | D. Kundur and D. Hatzinakos, “Towards a Telltale Watermarking Technique for Tamper-Proofing,” Proc. IEEE Int. Conf. on Image Processing , |

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

- N. Nikolaidis and I. Pitas, "Robust Image Watermarking in the Spatial Domain," Signal Process. 66, 385-403 (1998). [CrossRef]
- J. F. Delaigle, C. De Vleeschouwer and B. Macq, "Watermarking Algorithm Based on a Human Visual Model," Signal Process. 66, 319-335 (1998). [CrossRef]
- C. I. Podilchuk and W. Zeng, "Image-Adaptive Watermarking using Visual Models," IEEE J. Sel. Area in Commun. 16(4), 525-539 (1998). [CrossRef]
- 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]
- G. W. Braudaway, "Protecting Publicly-Available Images with an Invisible Image Watermark," Proc. IEEE Int. Conf. on Image Processing 1, 524-527 (1997). [CrossRef]
- 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).
- 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]
- 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).
- D. Kundur and D. Hatzinakos, "Towards a Telltale Watermarking Technique for Tamper-Proofing," Proc. IEEE Int. Conf. on Image Processing, 2, 409{413 (1998).
- 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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