# A Fragile Watermarking Scheme for Authenticity Verification of 3D Models in GLB Format
## 5 Comparison to Other Solutions  
In the field of watermarking, conducting detailed comparisons between existing works presents significant challenges. First, the models utilised in various studies are typically entirely different from one another. Second, the alterations introduced by watermark embedding are often linked to with visual characteristics and human perception, which are not always quantifiable. Moreover, the evaluation metrics employed across studies are frequently inconsistent--for instance, instead of using PSNR, some works adopt a Vertex Signal-to-Noise Ratio (VSNR) [21] or a Signal-to-Noise Ratio (SNR) [27] or define PSNR differently depending on the author. The study [26] presents an interesting and highly attack-resistant watermarking method that embeds three watermarks into a 3D model: within its geometry, within its topology, and within its spectral domain. Unfortunately, the authors did not provide specific metric values other than stating that a low mean squared error (MSE) was achieved. Only those studies that employed similar evaluation metrics were selected for reference when comparing the developed method. In the study [21], the authors proposed two novel watermarking methods. Both approaches achieved an RMSE on the order of \(10^{-3}\), whereas the method proposed in the present work maintains an RMSE level of approximately \(10^{-8}\) when utilising 1 to 4 LSBs. Study [21], references the article [39] for comparison, where the RMSE also remained at the \(10^{-3}\) level. Furthermore, in [21], a feature vector along with fuzzy C-means clustering was used to determine the vertices to be modified, which contributes to the overall computational overhead. In the present study, several models from [22] ([PERSON] and [PERSON]) were utilised, enabling a direct comparison between both methods. Table 7 presents a summary of the RMSE and PSNR metrics for the models gate.glb, pinecone.glb, and statue.glb. As shown, our method significantly outperforms the solution proposed by [PERSON] and [PERSON] in terms of both imperceptibility and algorithmic complexity. The method described in [22] employs the discrete wavelet transform and its inverse during both the embedding and verification processes, contributing to the overall computational overhead. The article [40] ([PERSON] and [PERSON]) explores the feasibility of embedding data in a distributed manner within virtual reality environments. One of the key areas investigated involves the embedding of information in textures and 3D models. As part of the evaluation, the PSNR metric was calculated for both models and textures. The method developed by [PERSON] and [PERSON] achieved a PSNR of 222 dB for embedding 64 bits and 214 dB for 256 bits. Our method maintains a comparable PSNR level while enabling the embedding of 512 bits into a 3D model. In [30], a watermarking method for Computer-Aided Plant Design (CAPD) models is presented. Although CAPD models are complex and consist of numerous components, the best PSNR result reported was 82 dB. In contrast, the method proposed in this work \begin{table}
\begin{tabular}{l c c c c} \hline \hline \multirow{2}{*}{**Method:**} & \multicolumn{2}{c}{**[PERSON] and [PERSON]**} & \multicolumn{2}{c}{**Our**} \\ \cline{2-5}  & **RMSE** & **PSNR** & **RMSE** & **PSNR** \\ \hline gate & \(2.94\times 10^{-4}\) & 150 & \(2.26\times 10^{-8}\) & 236 \\ statue & \(6.08\times 10^{-4}\) & 147 & \(0.07\times 10^{-8}\) & 221 \\ pinecone & \(7.39\times 10^{-4}\) & 132 & \(0.03\times 10^{-8}\) & 222 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Direct comparison of the proposed watermarking method for the gate.glb, pinecone.glb, and statue.glb models. achieves PSNR values in the range of 170-236 dB, indicating a significantly lower level of introduced distortion. It is worth noting that glb files can store various types of models and are applicable in diverse use cases, whereas CAPD model formats are limited to a narrow range of industrial applications. The method presented in [28] ([PERSON] et al.)