Multiplicative Watermark Decoder in Contourlet Domain Using the Normal Inverse Gaussian Distribution
Bibliographic record
Abstract
In recent years, many works on digital image watermarking have been proposed all aiming at protection of the copyright of an image document or authentication of data. This paper proposes a novel watermark decoder in the contourlet domain . It is known that the contourlet coefficients of an image are highly non-Gaussian and a proper distribution to model the statistics of the contourlet coefficients is a heavy-tailed PDF. It has been shown in the literature that the normal inverse Gaussian (NIG) distribution can suitably fit the empirical distribution. In view of this, statistical methods for watermark extraction are proposed by exploiting the NIG as a prior for the contourlet coefficients of images. The proposed watermark extraction approach is developed using the maximum likelihood method based on the NIG distribution. Closed-form expressions are obtained for extracting the watermark bits in both clean and noisy environments. Experiments are performed to verify the robustness of the proposed decoder. The results show that the proposed decoder is superior to other decoders in terms of providing a lower bit error rate. It is also shown that the proposed decoder is highly robust against various kinds of attacks such as noise, rotation, cropping, filtering, and compression.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.001 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".