# IW-NeRF: Using Implicit Watermarks to Protect the Copyright of Neural Radiation Fields
## 5 Experiments
### Reconstruction and Watermark Extraction Quality  
We conducted a qualitative comparison of the reconstruction quality against all baselines, with the results depicted in Figure 6. The visual analysis from Figure 6 indicatesthat all methods exhibit commendable reconstruction quality. While other schemes may outperform ours in reconstruction quality due to their limited capacity stemming from text or image information embedding, our approach stands out in terms of embedded capacity. Despite the reduction in reconstruction quality caused by the embedding of watermark network parameters, likely attributed to fixed parameters impacting the carrier network's fitting effect, the overall NeRF model information remains retrievable visually. Notably, our designed key facilitates lossless recovery of watermark information from a carrier network containing watermarks, offering a significantly larger embedded capacity compared to alternative schemes. For a quantitative assessment, we further analyzed the rendering quality and watermark information extraction effects across various schemes, as detailed in Tables 1 and 2. By examining the outcomes outlined in Tables 1 and 2, a notable observation is the ineffectiveness of the two-dimensional watermarking techniques applied to the NeRF model in retrieving watermark information. The alteration of information embedded via the \begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{3}{c}{**NeRF Rendering**} & \multicolumn{3}{c}{**Watermark Extraction**} \\ \cline{2-6}  & **PSNR \(\uparrow\)** & **SSIM \(\uparrow\)** & **LPIPS \(\downarrow\)** & **Acc (\%)** \(\uparrow\) & **SSIM \(\uparrow\)** \\ \hline Standard NeRF & 33.23 & 0.9143 & 0.1113 & N/A & N/A \\ LSB + NeRF & 27.45 & 0.8446 & 0.1410 & N/A & N/A \\ DeepStega + NeRF & 26.41 & 0.8457 & 0.1429 & N/A & N/A \\ HiIDDeN + NeRF & 27.88 & 0.8964 & 0.1418 & N/A & N/A \\ StegaNeRF & 30.31 & 0.9847 & 0.0276 & 100 & 0.9643 \\ CopyRNeRF & 30.54 & 0.9689 & 0.0327 & 100 & N/A \\ IW-NeRF (ours) & 21.32 & 0.6364 & 0.2852 & 100 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Quantitative analysis of reconstruction quality and watermark extraction effect of NeRF models under different baselines (Synthetic-chair). \begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{3}{c}{**NeRF Rendering**} & \multicolumn{3}{c}{**Watermark Extraction**} \\ \cline{2-6}  & **PSNR \(\uparrow\)** & **SSIM \(\uparrow\)** & **LPIPS \(\downarrow\)** & **Acc (\%)** \(\uparrow\) & **SSIM \(\uparrow\)** \\ \hline Standard NeRF & 27.76 & 0.8546 & 0.1453 & N/A & N/A \\ LSB + NeRF & 27.59 & 0.8435 & 0.1399 & N/A & N/A \\ DeepStega + NeRF & 26.98 & 0.8356 & 0.1269 & N/A & N/A \\ HiIDDeN + NeRF & 27.64 & 0.8865 & 0.1512 & N/A & N/A \\ StegaNeRF & 28.21 & 0.8453 & 0.1423 & 100 & 0.9698 \\ CopyRNeRF & 30.67 & 0.9683 & 0.0457 & 100 & N/A \\ IW-NeRF (ours) & 22.54 & 0.6539 & 0.2798 & 100 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Quantitative analysis of reconstruction quality and watermark extraction effect of NeRF models under different baselines (LLFF-trex). Figure 6: Comparison of reconstruction quality of NeRF models with different baselines. two-dimensional watermarking method due to NeRF's view synthesis led to the method's failure. Conversely, the utilization of three-dimensional watermarking approaches facilitated accurate extraction of watermark information. Notably, while other algorithms incorporate bit strings into the model, our methodology visualizes the 3D reconstruction and watermark extraction effects. Our experimentation involved utilizing diverse 360-degree scenes such as 'Lego', 'drums', and 'chairs' from the NeRF Semantic dataset for training the watermark network and carrier network. The resulting experimental findings, as illustrated in Figure 7, showcase various images representing original watermark information, carrier information, samples from both the watermark and carrier networks, and extracted watermark network samples.