Robustness to Temporal and Geometric Distortions

1. Robustness to Temporal and Geometric Distortions Multimedia Security

2. Robustness to Temporal and Geometric Distortions • One of the most difficult outstanding areas of watermark research! • There are five categories • Extensive search • Synchronization or registration • Auto-correlation • Invariant Watermarks • Implicit Synchronization

3. 1. Temporal and Geometric Distortion • Audio: Changing speed in tape players • Video: Conversion between the frames of different TV standards. In both audio and video, shifts can occur whenever a watermark detector is presented with signals taken from an arbitrary point in the audio or video signal stream.

4. A Work that has been subjected to a time scaling of s and then a delay of δ can be written as (1)

5. Geometric Distortions to Video: video undergoes format changes Geometric distortions to photos: user manipulations (intentional / unintentional)Often, printing, photocopying, and scanning will introduce a variety of unintentional geometric distortions.In 2-D visual data there are two, potential different, scaling parameters and two different translation parameters. When the vertical and horizontal scaling factors differ, there will be a change in the aspect ratio. A work can undergo rotation and shear.

6. All of these geometric distortions can be expressed as an affine transformation given by where (x0,y0) represents the undistorted location of each pixel and (xn, yn) represents the distorted location.The translation is completely represented by the vector (xt, yt), the 2x2 matrix is used to define all other affine transformations. (2)

7. scaling matrix , change in aspect ratio occurring when Sx≠Sy Rotation matrix with angle Shear in x- and y- dimension: ,

8. In 1-D case, the linear correlation between a delayed, time-scaled work and the reference matrix, Wr, will only be high if is high. the correlation between a reference mark and a delayed, time-scaled version of itself defines its natural robustness to small shifts. • Low-pass signals exhibit some natural robustness to small shifts. • The auto-correlation of a truly white noise signal drops to zero at a shift of only one sample.

9. 2. Exhaustive Search: the simplest approach After defining a range of likely values for each distortion parameter and a search resolution for each, every combination of parameters is examined. • Search range can often be constrained by the assumption that if any distortions were applied they have had minimum impact on the perceptual quality of the work. • Search Resolution can be determined by the natural robustness of the reference pattern to the distortion of interest.

10. Issues for Exhaustive Search • Computational Costthe amount of computation increases with the size of the search space Ex1: An audio source sampled at 14.1 kHz in which a watermark is embedded once each second. • Temporal scaling of ±3% exhaustive search examines all temporal scalings from 97% to 103% in 0.1% increments. (resolution) • Temporal delays of ±0.5 seconds in increments of 1 sample. This search requires about N = 860 k detection operations.

11. Ex2: An exhaust search that examines all rotations from -179 to 180 degrees in 1-degree increments, horizontal and vertical scalings from 50% to 200% in 1% increments, and vertical and horizontal translations of ±100 pixels in increments of 1 pixel.This search would require about N = 330 billion detection operation.

12. The effect on the false positive probability For each unwatermarked works, we test N distorted versions in the detector. If the watermark is found in at least one of these versions, the detector will produce a false positive. Denoting the random-works false positive probability of any signal version of a work by Pfp, the probability that at least one of the N versions will cause a false positive is bounded by N× Pfp. When N is large, this can be unacceptable. Remark: Exhaustive search could be effective only when the search space is small.

13. 3. Synchronization / Registration in Blind Detectors: The suspected work contains a watermark that can be aligned with the reference pattern prior to a single application of the watermark detector. synchronization Audio (1-D) registration Image (2-D) A common synchronization approach for blind detectors is the embedding of a dedicated synchronization pattern in addition to the payload- carrying reference patterns. The process is called in literature.

14. References • C. Xu, J. Wu, and Q. Sun, “Audio Registration and Its Application to Digital Watermarking,” Security and Watermarking of Multimedia Contents, SPIE-3971:393-401, 2000. • A. Z. Tirkel, C. F. Osbourne, and T. E. Hall, “Image and Watermark Registration,” Signal Processing, 66(3): 373-383, 1998.

15. Because the Synchronization pattern is known, the detector can employ one of many well-known registration techniques. [ L. G. Brown, “A Survey of Image Registration Techniques,” ACM Computing Survey, 24(4): 325-376, 1992] As with all watermark patterns, synchronization patterns are designed to have very low power compared to that of the work. To ease the registration tasks in such a “noisy” environments, the synchronization pattern can be specially designed for “easy identification” in the face of temporal and geometric distortions [G. B. Rhoads, “Image Steganography System Featuring Perceptual Adaptive and Globally Scalable Signal Embedding,” US patents 5,748,763, 1998].

16. With this approach, watermark detection involves first finding the registration patterns in a suspect work. The temporal/geometric distortion that had been applied to that work can then be identified by comparison of the extracted registration pattern and the embedding registration pattern. Then, that distortion is inverted and detection of the payload-carrying watermark proceeds. Issues: A correct positive detection requires that both the payload-carrying marks and the synchronization pattern be successfully embedded and detected.

17. The use of a synchronization pattern has a negative security implication: Typically, the same synchronization pattern is used for many different works. This eases the task of the detector in finding a distorted synchronization pattern, but it may also allow the synchronization pattern to be discovered from a set of marked works.Once the synchronization pattern is discovered by an adversary, it can be removed, thus limiting the ability of the watermarking scheme to counter the effects of temporal and geometric distortions.

18. 4. Auto-correlation In some case, the embedded pattern can serve both as the synchronization pattern and the payload-carrying pattern. Typically, This required that the data-carrying watermark have some properties that allow for synchronization. In the Autocorrelation approach , this property is “periodicity”. The autocorrelation of a Work typically has a large peak at zero (corresponding to the signal energy) and then decays rapidly at non-zero shift. This is even more true when examining the autocorrelation of a “white” or uniformly distributed signal.

19. When a periodic, white synchronization pattern is embedded in a Work, the resulting autocorrelation will contain a periodic train of peaks identifying periodicity of the added pattern in the Work. This characteristic can be used to identify and invert any scaling applied to the Work since the embedding of the synchronization pattern, [ M. Kutter, “Watermarking Resisting to Translation, Rotation , and Scaling” in Multimedia Systems and Applications, SPIE-3528:423-431,1998.] Remark: For successful detection , both the identification of the temporal/geometric distribution and the detection of the watermark after inversion of that distribution must be successful

20. 5. Invariant Watermark: the designed watermarks are invariant to temporal and Geometricdistribution The work is projected to an invariant feature vectors as part of the signal extraction process. A commonly used feature vector that is invariant to shifts or delays: the ”Fourier Magnitude .” [R. N. Bracewell, The Fourier Transform and Its Applications,McGraw-Hill,1996] (3)

21. Scaling of a work’s “time axis” appears as a scaling of the “frequency axis” in the Fourier Domain!! This scaling of frequency axis can be treated as a shift along a log-axis by defining the Signal C ,as follows: So that (4) (5)

22. Egn.(3) can then be written as In this domain, temporal delay has no effect, and temporal scaling is seen as a coordinate shift and a change in amplitude. By applying a second Fourier Transform we can ensure that the only effect of temporal scaling and delay is a change in amplitude ; that is (6)

23. We can then use a detection statistic that is invariant to amplitude changes, such as normalized correlation. This is an example of a time-scale and time-delay invariant representation of a 1-D signal. These ideas have been extended to 2-D to build feature vectors that are invariant to rotation, scaling, and translation. (7) (8)

24. The trick is to represent the Fourier image in “polar coordinates” and then apply a logarithmic transformation to the radial axis. This can be implemented with a “Fourier-Mellin transform”. Reference: ‧ E. Lin and R. D. Brandt, “Toward Absolute Invariants of Image Under Translation, Rotation, and Dilation, ”Pattern Recognition Letters,14(5):369-379-1993. ‧ Y. Sheng and H. H. Arsenault, “Experiment on Pattern using Recognition Invariant Fourier-Mellin Descriptors,” Journal of Optical Society of AmericaA, 3:771-776,1986 ‧Y. Sheng and J. Duvernoy, “Circular-Fourier-Radial- Mellin Transform Descriptors for Pattern Recognition," Journal of Optical Society of AmericaA 885-888,1986

25. Watermarking methods have been proposed that use these techniques as part of the watermark extraction process. ‧C.-Y. Lin, M. Wu, et al., “Rotation, Scale, and Translation-resilient Public Watermarking for Image,” Security and Watermarking of Multimedia Contents,SPIE-3971:90-98,2000. ‧J.J.K O’ Ruanaidh and T. Pun. ” Rotation, Scale, and Translation-invariant Spread Spectrum Digital Image Watermarking ,” Signal Processing ,66(3):303-317,1998. A similar approach has been taken to generate watermarks that are invariant to changes in aspect ratio[ C.-Y. Lin & S. F. Chang, ”Distortion Modeling and Invariant Extraction for Digital Image Print-and-Scan Process,” International Symp. On Multimedia Information Processing ,1999.]

26. 6. Implicit Synchronization The suspect work also goes through a synchronization process prior to detection; however, rather than a synchronization pattern, the actual features of the work are used.The watermark is embedded at a time or geometric to the features of the original work. This type of synchronization is referred to as “Implicit Synchronization,” because the synchronization pattern is implied by the work itself.Ex: C.-P. Wu, P.-C. Su and C.-C. J. Kuo, “Robust and Effective Digital Audio Watermarking Using Audio Content Analysis,” Security and Watermarking of Multimedia Content, SPIE-3971:382-392, 2000.

27. In the above work, a watermark signal is embedded in an audio stream just after the detection of “Salient points,” where salient points are defined as locations at which the signal is climbing fast to a peak value. Such an approach provides robustness to delay because the location of the watermark remains constant relative to the salient points.

28. Similarly: • J. Ditfman et al., “A New Approach Transformation-invariant Image and Video Watermarking in the Spatial Domain: SSP Self-spanning Patterns,” Security and Watermarking of Multimedia Content II, SPIE-3971: 176-185, 2000. • P. M. J. Rongen et al., “Digital Image Watermarking by Salient Point Modification Practical Results,” Security and Watermarking of Multimedia Content, SPIE-3657: 237-282, 1999.are examples in which feature points are extracted from an image. The reference patterns representing the watermark are then warped to fit the geometries implied by these points.

29. In another approach, the marking space is defined as a canonical, normalized space based on the geometric image moments [M. Alghoniemy and A. H. Tewfik, “Geometric Distortion Correction Through Image Normalization,” Processing of ICME, vol.-3, pp. 1291- 1294, 2000]. Based on these moments, an image is transformed into a form that is independent of its scale or orientation. This form is also invariant to horizontal and vertical reflection. The marking is applied in this space. and then the inverse transformation restores the original reflection, orientation, and scale.

30. During detection, the moments are again calculated and used to estimate the normalized parameters. Once the image is normalized, the watermark can be detected. Implicit synchronization requires that the salient features be reliably extracted during detection. Some distortion may effect the locations of salient features relative to the work. When these distortions are applied after watermark embedding but before detection, the implicit synchronization can fail and the watermark can go undetected.