## 5 Experiments and Results
### Filtering Evaluation  
In order to evaluate the results of the filtering, we performed experiments by applying white noise [39] to the set of different models. We varied the noise intensity and compared the results with Bilateral [40] and Gaussian filters. We then calculated the mean-squared error (MSE) [41] between the noisy models and filtered models. Table 1 shows the quantitative errors on the models used in this experiment. Our method presents the lowest error compared to other filters and preserves the details of the mesh (sharpness). These sharp details can be seen in Figure 16d. Figure 15 shows the differences between the results obtained by the tested methods. Column (a) illustrates the applied noise, while columns (b), (c) and (d) show the difference between the noisy model and the model filtered by the Bilateral and Gaussian filters and our filter, respectively. The noise is a random number in the interval \([-\alpha\sigma,\alpha\sigma]\), where \(\sigma\) is the standard deviation of the target model. The alpha values per row are 0, 0.5, 0.7, 1.0 and 2.0. Figure 16 exhibits the results obtained by the tested filters. Column (a) illustrates the noisy model (\(\alpha\) equals 0.5, 0.7, 1.0 and 2.0), while columns (b), (c) and (d) show the models filtered by the Bilateral and Gaussian filters and our filter, respectively. Additionally, Figure 17 illustrates the correction of a mesh obtained using the Depth-Sense camera [23]. We first standardized the scale and sampling frequency with relation to the database, and then we corrected it using our filter. Figure 18 demonstrates the results obtained by our filter on different models. Column (a) illustrates the model with texture, column (b) shows the ground truth of the mesh obtained by a 3D scanner, (c) is the same mesh after noise, (d) shows models filtered by our method without texture and (e) illustrates the textured filtered models. The use of the Bosphorus Database [42] allowed us to use these models as a ground truth. We used 20 randomly chosen models as examples. Future work may involve the determination of the minimum amount of examples that minimize filtering error. Reducing the amount of neighborhoods per \(FFP\) region (by removing intraclass redundancy) is left for future work. Finally, our filtering approach was based on a division of the model into regions in which all points have an intrinsic geometric similarity. We presented how to define these regions for the specific case of faces with the usage of facial features in Section 3.2.2. A future research direction would be to define general descriptors that can be used for general-purpose filtering. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Noise level** & **Bilateral** & **Gaussian** & **Ours** \\ \hline
0.0 & 0.6615 & 1.8459 & **0.4859** \\
0.5 & 0.6782 & 1.8484 & **0.4991** \\
0.7 & 0.6970 & 1.8595 & **0.5289** \\
1.0 & 0.7117 & 1.8819 & **0.5383** \\
2.0 & 0.8236 & 1.9450 & **0.7218** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The quantitative errors of the models used in this experiment. The first column is the noise level. Columns 2, 3 and 4 are the results of the mean-squared error (MSE) [40] between the noisy models and filtered models. Figure 15: The differences of the results of the tested methods. Column (**a**) illustrates the applied noise, while columns (**b–d**) show the difference between the noisy model and the model filtered by the Bilateral and Gaussian filters and our filter, respectively. The noise is a random number in the interval \([-\alpha\sigma,\alpha\sigma]\), where \(\sigma\) is the standard deviation of the target model. The alpha values per row are 0, 0.5, 0.7, 1.0, 2.0 and 5.0. Figure 16: The results obtained by the tested filters. Each row shows the noise levels applied to the models, which are 0.5, 0.7, 1.0 and 2.0 (respectively) multiplied by standard deviation. Column **(a)** illustrates the noisy model, while columns **(b–d)** show models filtered by the Bilateral and Gaussian filters and our filter, respectively.