## 5 Experimental Results
### Comparison with Alternative Methods
According to Table 18, it can be \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Attack** & **[14]** & **[12]** & **Our Method** \\ \hline No attacks & 1.0 & 1.0 & 1.0 \\ Noise 0.10\% & 1.0 & 1.0 & 1.0 \\ Smoothing & 0.88 & 0.87 & 1.0 \\ Cropping 10\% & 0.2 & 1.0 & 0.66 \\ \hline \hline \end{tabular}
\end{table} 
Table 16: Robustness comparison with [PERSON]’s [14], and [PERSON]’s [12] schemes measured in terms of NC. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Object** & **Venus** & **Horse** & **Rabbit** \\ \hline MRMS (\(10^{-3}\)) & 1.21/**0.72** & 0.64/**0.62** & 1.12/**0.54** \\ HD (\(10^{-3}\)) & 5.87/**2.18** & 2.65/**1.86** & 3.99/**3.63** \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Imperceptibility comparison with [PERSON] et al.’s [3] method measured in terms of MRMS and MSDM for Horse and Venus models. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Object** & **Method** & **Hausdorff Distance (\(\times 10^{-3}\))** \\ \hline \multirow{3}{*}{Bunny} & [14] & 0.73 \\  & [12] & 0.41 \\  & Our method & 0.36 \\ \hline \multirow{3}{*}{Venus} & [14] & 2.50 \\  & [12] & 3.90 \\  & Our method & 1.71 \\ \hline \multirow{3}{*}{Horse} & [14] & 3.21 \\  & [12] & 2.90 \\ \cline{1-1}  & Our method & 1.57 \\ \hline \hline \end{tabular}
\end{table} 
Table 15: Imperceptibility comparison with [PERSON]’s [14], and [PERSON]’s [12] schemes measured in terms of HD. For quantization attack, 9 bits, 8 bits, and 7 bits are the parameters used in the comparison, respectively. It can be seen from Table 19 that the proposed method is able to withstand quantization attack for Venus and Horse 3D meshes. In addition, Table 19 shows high robustness and imperceptibility performances compared to [PERSON] et al. 's [3] scheme. Moreover, the robustness comparison with [PERSON] et al. 's method sketched in Table 9 demonstrates the superiority of the proposed method. For comparison purposes, Venus and Horse models have undergone Laplacian smoothing using \(\lambda=0.10\) with 10, 30, and 50 iterations. The robustness and imperceptibility performances were evaluated using NC, MRMS, HD, and MSDM. In Table 20, it can be observed that the proposed technique exhibits superiority over [PERSON]'s method in terms of robustness. Moreover, the quality performance illustrates the superiority of the proposed method in terms of MRMS, HD, and MSDM. Table 21 presents the robustness comparison with [PERSON]'s method [14] in terms of NC for the Bunny object. According to Table 21, it can be seen that our method shows good robustness against noise, quantization, smoothing, and simplification. Moreover, the proposed method outperforms [PERSON] et al. 's method in terms of the mentioned attacks. It can be seen in Table 22 that the proposed method outperforms [PERSON] et al. 's method in a wide range of attacks including noise addition, quantization, smoothing, and simplification. embed the watermark. The novelty of the proposed method is that it gives good results for both imperceptibility and robustness thanks to the exploitation of the advantages of QIM quantification of wavelets and mesh saliency.