# Robust and High-Fidelity 3D Face Reconstruction Using Multiple RGB-D Cameras
## 4 Experiments
### Quantitative Comparison  
We first compared our filtering algorithm with other classical filtering algorithms by mesh reconstruction error. We used the ICP algorithm to densely align each of our generated 3D face meshes with the ground truth meshes corresponding to the synthetic data, and we followed [30] using the average symmetry point-to-plane distance as the evaluation metric for this error measure. The normalized point-to-plane errors on reconstructed face mesh with different filtering methods are shown in Table 1 in mm. We can see in the final results that our method is on par with the best-performing method (radius filtering) for mean error, and very close to the best-performing method (statistical filtering) for standard deviation. The reason our method is not significantly better than the other methods we analyzed is that the accidental noise we added to the synthetic data was not explicitly filtered in our fast two-stage filtering method, allowing other methods to narrow the gap in accuracy with our method. However, in practice, the range of accidental noise of the depth camera we used is less than 2 mm under calibration, which means that the accidental noise caused by the regular depth camera is minimal (much smaller than the interval of \(\pm\)10 mm we set); so, this experimental condition is actually unfavorable for us. In other words, the smaller the interval of the level of accidental noise, the higher the accuracy of our method will be. Even so, our method still achieves the best performance. The reason why we chose such a considerable error interval (beyond the conventional error range) is that we feel if we want to promote the practical application of our face reconstruction method, we should overcome the drawbacks of the lower cost and worse measurement quality of the consumer-grade depth cameras that bring more accidental noise. We set a considerable error interval that all the depth cameras we know can satisfy. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Method** & **Mean** & **Std** \\ \hline Voxel filtering & 1.75 & 0.272 \\ Statistical filtering & 1.46 & 0.147 \\ Radius filtering & 1.42 & 0.165 \\ \hline Fast two-stage filtering & 1.42 & 0.153 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of reconstruction accuracy of mesh on synthetic data using point-to-plane distance with different filtering methods. The table reports the mean error (Mean) and the standard deviation (Std). We also tested the speed of our filtering method and compared it with voxel filtering, radius filtering, and statistical filtering. Fast face reconstruction can now be effectively applied in virtual reality interaction scenarios, such as future 3D digital conferences and the hot metaverse games of today. A real-time or quasi-real-time 3D reconstruction of the user's face is required to achieve real-time face view correction and rendering of the digital face after correction. Thus, time consumption must be taken into consideration for the vision of the practical application of face reconstruction; as point cloud filtering is an essential component of the face reconstruction process, the evaluation of the filtering speed is also necessary. We used the PCL library implementations of statistical filtering, radius filtering, and voxel filtering. The machine used in the experiment is equipped with an Intel Core i7 2.80 GHz CPU. Speed is measured by the average time for point cloud filtering, in seconds per frame (point cloud), and the results are shown in Table 2. It can be seen that our method outperforms other filtering algorithms in terms of filtering efficiency; it is also nearly twice as fast as the best-performing method (voxel filtering). Although the statistical filtering performed best on the reconstructed standard deviation, it is also the slowest. One possible reason is that the statistical filtering method requires information about the nearest neighbors of each point and this search process is time-consuming.