A Study of Multiplicative Watermark Detection in the Contourlet Domain Using Alpha-Stable Distributions
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Bibliographic record
Abstract
In the past decade, several schemes for digital image watermarking have been proposed to protect the copyright of an image document or to provide proof of ownership in some identifiable fashion. This paper proposes a novel multiplicative watermarking scheme in the contourlet domain. The effectiveness of a watermark detector depends highly on the modeling of the transform-domain coefficients. In view of this, we first investigate the modeling of the contourlet coefficients by the alpha-stable distributions. It is shown that the univariate alpha-stable distribution fits the empirical data more accurately than the formerly used distributions, such as the generalized Gaussian and Laplacian, do. We also show that the bivariate alpha-stable distribution can capture the across scale dependencies of the contourlet coefficients. Motivated by the modeling results, a blind watermark detector in the contourlet domain is designed by using the univariate and bivariate alpha-stable distributions. It is shown that the detectors based on both of these distributions provide higher detection rates than that based on the generalized Gaussian distribution does. However, a watermark detector designed based on the alpha-stable distribution with a value of its parameter α other than 1 or 2 is computationally expensive because of the lack of a closed-form expression for the distribution in this case. Therefore, a watermark detector is designed based on the bivariate Cauchy member of the alpha-stable family for which α = 1 . The resulting design yields a significantly reduced-complexity detector and provides a performance that is much superior to that of the GG detector and very close to that of the detector corresponding to the best-fit alpha-stable distribution. The robustness of the proposed bivariate Cauchy detector against various kinds of attacks, such as noise, filtering, and compression, is studied and shown to be superior to that of the generalized Gaussian detector.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it