# Unsharp Mask Guided Filtering for Acoustic Point Cloud of Water-Conveyance Tunnel
## 4 Results
### Parameters
#### 4.2.2 Simulation Experiment  
To verify the applicability of the proposed method, we also executed our algorithm on a simulated model of the water-conveyance tunnel and nine simulated 3D point-cloud models with different shapes and sizes to highlight the advantages. Affected by the noise of the electronic components of the acquisition equipment, the acquired point-cloud model is easily polluted by noise that obeys the Gaussian distribution. Therefore, the Gaussian noise generated using a zero-mean Gaussian function with a standard deviation was added to the simulated 3D point cloud models. The Gaussian noise ranges were from 1% to 3% of the diagonal length of the model bounding box. As shown in Figure 7, the results of the guided 3D point-cloud filter, moving least-squares filter, and bilateral filter are poor, and there are many noise points around the tunnel. The bilateral filtering results were relatively smooth, but the denoising effect was not perfect, and the tunnel outline experienced distortion. Comparing the inner part of the red rectangle in Figure 7b-e, the denoising effects of the model obtained by the proposed algorithm were much better than those obtained by the other three methods, and the denoising effect of the outliers was obvious. The filtered point-cloud model was closer to the real cylindrical container. The method proposed in this study has an obvious suppressive effect on the outliers while preserving the contour. We also used the error metrics \(D_{mean}\), \(\sigma\), \(r_{ave}\), and \(r_{error}\) to quantitatively evaluate the denoising results. As shown in Table 5, the metrics of the moving least-squares filter and bilateral filter were similar. Furthermore, the metrics of the guided 3D point-cloud filter were all poor. The four error metrics of the other three methods were all larger than those of the proposed algorithm. This means that the reconstruction accuracy of the point-cloud model obtained using these methods is poor. By contrast, our method is better than the other three methods in terms of the error metrics, which reflects the superiority of our algorithm. Figures 8-10 are the filtering results of the unsharp-mask-guided filtering and several competing methods. Here, we only present pictures of the block, chair, and elephant models. Moreover, the results of these comparison algorithms were obtained according to the optimal parameters provided by their authors. It is clearly visible in Figure 8e that our algorithm can preserve the edge features well without shrinkage or deformation in the block model, while the results of the moving least-squares filter were deformed. For the 3D point-cloud model of the chair, it is shown in Figure 9b,d that the results of the guided 3D point-cloud filter and moving least-squares filter were poor. Moreover, the results of the bilateral filter were deformed. As shown in Figure 9e, the proposed method achieves more satisfactory results with the chair model. For the 3D point-cloud model of the elephant, it is shown in Figure 10 that the comparison methods all achieved satisfactorily smooth results, except for the blurring problem at the mouth of the elephant. It is clearly shown in \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & \(D_{mean}\) **(cm)** & \(\sigma\) **(cm)** & \(r_{ave}\) **(cm)** & \(r_{error}\) **(cm)** \\ \hline Guided 3D Point-Cloud Filter & 4.73 & 1.77 & 41.48 & 1.48 \\ Moving Least-Squares Filter & 4.64 & 1.75 & 41.58 & 1.58 \\ Bilateral Filter & 4.79 & 1.78 & 40.67 & 0.67 \\ Proposed algorithm & **4.49** & **1.67** & **40.45** & **0.45** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Analysis of the results of different algorithms tested on the point-cloud model of water-conveyance tunnel (the best results are displayed in bold). the enlarged map in Figure 10c that our method can preserve the local feature information of the elephant's mouth while smoothing the noise points.