# A Fragile Watermarking Scheme for Authenticity Verification of 3D Models in GLB Format
## 4 Results and Discussion
### Effects of Using Vertex Attributes Other than Position  
The watermark can be embedded in vertex attributes other than position. The method allows embedding the HMAC code in any available attribute, such as the normal vector (shortcut: norm or normal) or texture coordinates (shortcut: tex or texcoord). The authors conducted a study to determine the effect of the number of bits used on the degree of visibility of visual artefacts. The analysis started with normal vectors. In the duck.glb and statue.glb models, clear visual distortions appeared due to modifying a large number of bits of selected vertices (more than 20) (Figures 7 and 8). Figure 7 shows the changes that appeared in the duck.glb model. The top row shows images of the original model, and the bottom row shows the marked model, along with an indication of the visible changes. The 32-bit and 25-bit swap scenarios were considered for two different light settings. In this case, a considerable area of erroneous shading appeared. Depending on the angle of incidence of the light rays, a dark or light spot is visible, standing out in \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 & 176 & 173 & 169 & 163 & 160 & 155 & 146 & 142 \\ statue & 171 & 168 & 163 & 157 & 153 & 147 & 143 & 138 \\ pinecone & 169 & 166 & 160 & 155 & 151 & 144 & 140 & 135 \\ troll & 168 & 164 & 161 & 155 & 152 & 146 & 141 & 135 \\ duck & 162 & 158 & 155 & 149 & 144 & 138 & 134 & 128 \\ trolloduck & 170 & 166 & 163 & 157 & 153 & 148 & 143 & 136 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Summary of SNR metric (dB) for test models by number of LSBs used. \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}{**2**} & \multicolumn{2}{c}{**3**} & \multicolumn{2}{c}{**4**} \\ \cline{2-9}  & **RMSE** & **HD** & **RMSE** & **HD** & **RMSE** & **HD** & **RMSE** & **HD** \\ \hline gate & 2.26 & 2.14 & 3.40 & 6.03 & 6.03 & 12.8 & 10.4 & 24.8 \\ statue & 0.07 & 0.04 & 0.12 & 0.09 & 0.21 & 0.22 & 0.41 & 0.43 \\ pinecone & 0.03 & 0.01 & 0.04 & 0.03 & 0.07 & 0.05 & 0.12 & 0.10 \\ troll & 0.85 & 0.48 & 1.37 & 0.95 & 2.02 & 1.67 & 3.82 & 3.59 \\ duck & 2.19 & 0.49 & 3.05 & 0.96 & 5.01 & 2.39 & 8.19 & 3.39 \\ trolloduck & 0.07 & 0.27 & 1.20 & 0.76 & 1.74 & 1.55 & 2.86 & 2.87 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Evaluation of the proposed method based on RSME \(\times 10^{-8}\) and HD \(\times 10^{-6}\) metrics. colour from the surroundings. In contrast, swapping 10 LSBs did not cause visible artefacts. The number of modified bits and the modified attribute are described in each figure. The inscription NormXXb indicates that the watermark was embedded into the normal vectors using XX LSBs. In the statue.glb model, changes include the occurrence of discernible single triangles, one corner of which is incorrectly shaded (Figure 8). The visible changes are marked with a red envelope. However, this issue arises only in the 32 and 25 LSBs substitution scenario. Analysis of the modification of the normal vectors for the trolloduck.glb model showed that the bit swap did not result in the appearance of visible changes. Each column in Figure 9 shows the modification of the same vertices with the indicated artefacts--the top row refers to the bit swap in the texture coordinates, and the bottom row refers to the bit swap in the normal vectors. The inscriptions NormXXb and TexXXb indicate that the watermark was embedded into the normal vectors or the texture coordinates, respectively, using XX LSBs. Figures 10 and 11 show two snapshots of the resulting graphic artefact in the pinecone.glb and gate.glb models, respectively. In both cases, the changes are only visible from very close up, so Figures 10 and 11 highlight the area of the artefact's occurrence in a shot from a further perspective. On the other hand, the trolloduck.glb model contains a very visible artefact but only when used above 18 bits.