# Robust JND-Guided Video Watermarking via Adaptive Block Selection and Temporal Redundancy
## 5 Analysis and Discussion
### Error and Recovery Analysis  
The experimental evaluation presented in Section 4 demonstrates that the proposed watermarking method consistently achieves low BER and high recovery accuracy across various test conditions. Under non-attacked conditions, the average BER remained below 0.3% when using a redundancy factor of \(r=5\), and recovery accuracy reached 99.8%. These results are indicative of the method's effectiveness in ensuring reliable watermark retrieval through majority voting, even when embedded information is distributed across multiple frames.  
From a signal-level perspective, the error distribution was not uniform across frames or spatial regions. Visual inspection of the decoding process revealed that most residual bit errors under mild distortion occurred in blocks with intermediate perceptual scores  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Values Tested** & **BER (\%)** & **PSNR (dB)** \\ \hline Semantic weight (\(\gamma\)) & 0.2/0.3/0.4 & 0.21/0.09/0.07 & 52.7/51.2/49.4 \\ \hline Quantization & & & \\ scaling factor (\(Q\)) & 0.5/0.75/1.0 & 0.27/0.10/0.09 & 53.1/52.1/49.3 \\ \hline Block threshold (\(\tau\)) & 25/30/35 & 0.10/0.08/0.08 & 52.3/50.9/48.2 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Sensitivity analysis of key parameters used in the watermarking method.  
Figure 3: **(a)** Keyframe of “Suzie” video sequence, **(b)** its watermarked version, **(c)** Gaussian noise, **(d)** H.264 compression (CRF 28), **(e)** V78 compression (Q = 30), and **(f)** Cropping (10%).  
those on the threshold between inclusion and exclusion during the embedding process. In particular, frames with rapid scene changes or low-texture regions exhibited slightly higher error rates, highlighting the sensitivity of the perceptual block selection mechanism to local variability. However, the redundancy mechanism proved effective in mitigating these issues by averaging detection outcomes across spatial and temporal instances.  
The proposed method maintained high recovery accuracy when analyzing robustness against different attacks, with BER values ranging from 1.03% (Gaussian noise) to 2.3% (cropping). The corresponding recovery accuracies--always above 97%--confirm that even under moderate distortion, the watermark can be reconstructed with high fidelity. Importantly, no complete bit loss was observed under any tested conditions, validating the sufficiency of the distributed redundancy strategy.  
Another notable observation relates to resolution-dependent behavior. The method showed slightly better BER performance for CIF videos compared to HD videos under compression and cropping attacks. This trend is expected, as higher-resolution frames contain more embedding candidates, which increases both the potential for distortion during encoding and the number of possible mismatches during extraction. Despite this, the recovery accuracy remained within a narrow and acceptable range across all formats, underscoring the scalability of the method.  
In summary, the combined use of perceptual embedding, redundancy coding, and temporal majority voting provides a robust error-tolerant mechanism capable of withstanding realistic distortions. The observed errors are minor, localized, and statistically compensated by the system's redundancy-aware design. These findings affirm the scheme's practical viability for applications requiring blind and robust watermark extraction without access to the original content.