# A Fragile Watermarking Scheme for Authenticity Verification of 3D Models in GLB Format
## 4 Results and Discussion
### Effect of Embedding a Watermark in Position Bits on Interference Levels
In this case as well, an increase in the number of bits used per coordinate of the vertex attribute vector results in greater distortion within the model. The decrease in the SNR metric value between the second and the last column is consistent across all models, indicating the stability of the proposed method. To compare the proposed method with the work of other authors, the metrics RMSE and Hausdorff distance were also calculated for each model. The results are included in Table 5. As expected, swapping more bits leads to a larger RMSE error. However, when only the least significant bits are modified, the error remains very small. Changes on the order of \(10^{-8}\) are unnoticeable and even insignificant if we assume that calculations are performed in single precision, as in the case of the float type (IEEE-754 binary32). The gate.glb and duck.glb models have the highest RMSE error, as the changes made caused the individual vertices to clearly detach from the model and seem to 'run away' indefinitely as the number of modified bits increased (Figure 6). The smallest error was observed in the \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline \multirow{2}{*}{**LSBs Used:**} & \multicolumn{2}{c}{**1**} & \multicolumn{2}{c}{**8**} & \multicolumn{2}{c}{**23**} & \multicolumn{2}{c}{**32**} \\ \cline{2-9}  & **W** & **A** & **W** & **A** & **W** & **A** & **W** & **A** \\ \hline gate & 2019 & 1216 & 2211 & 1363 & 2282 & 1349 & 2299 & 1207 \\ statue & 175 & 93 & 167 & 114 & 171 & 115 & 198 & 108 \\ pinecone & 924 & 508 & 931 & 564 & 933 & 582 & 952 & 606 \\ troll & 906 & 497 & 993 & 525 & 978 & 530 & 992 & 527 \\ duck & 937 & 532 & 959 & 533 & 976 & 519 & 963 & 550 \\ trolloduck & 1888 & 996 & 1864 & 1040 & 1931 & 1080 & 1910 & 1068 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The average duration in milliseconds of the watermarking process (W) and the authenticity check (A) for various numbers of bits used. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline
**LSBs Used:** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** \\ \hline gate & 236 & 232 & 227 & 222 & 218 & 213 & 209 & 200 \\ statue & 221 & 216 & 211 & 206 & 202 & 195 & 191 & 185 \\ pinecone & 222 & 217 & 213 & 208 & 204 & 197 & 192 & 188 \\ troll & 217 & 213 & 209 & 204 & 199 & 195 & 187 & 182 \\ duck & 204 & 202 & 197 & 193 & 188 & 181 & 178 & 170 \\ trolloduck & 220 & 216 & 217 & 207 & 201 & 198 & 192 & 187 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of the PSNR metric (dB) for test models by number of LSBs used. pinecone.glb model, where a 512 LSB swap resulted in an error of \(\approx\)3 \(\times 10^{-10}\), even though the geometry of this model is not one of the simplest. The Hausdorff distance measures the degree of similarity between two representations of the same model. An interesting case is duck.glb, where the Hausdorff distance value for modifications 1, 2 and 3 LSBs is the second largest in a given column. This is because modifying the LSBs in this model causes clearly noticeable graphical artefacts (Figure 6). In contrast, in the pinecone.glb model (Figure 6), changes do not cause such noticeable artefacts as in duck.glb, so the Hausdorff distance is the smallest. The described situation depends primarily on the geometry of the model and the selected vertices. The watermarking algorithm uses a distributed vertex selection algorithm, so the Hausdorff distance can vary significantly depending on the grain of the pseudorandom number generator.