# Unsharp Mask Guided Filtering for Acoustic Point Cloud of Water-Conveyance Tunnel
## 4 Results
### Parameters  
As introduced in Section 3, the proposed algorithm has two key parameters in addition to the constant parameter \(\zeta\) and the neighborhood parameter \(k^{\prime}\) for edge perception. One is the parameter \(k\) of KNN, which is used to calculate the geometrical neighborhood. For point-cloud models with different numbers of points, the choice of \(k\) has a great influence on the filtering effect. Another key parameter is \(\lambda\), which is a regularization parameter penalizing large \(a_{i}\). It can simply control the filtering quality. Therefore, we selected a point-cloud model with a different number of points to analyze the impact on the results under different \(k\) and \(\lambda\). The models and parameters used in this experiment are shown in Table 1. Figures 2-4 illustrate the results of our method using different values of \(k\) and \(\lambda\), respectively. Tables 2 and 3 illustrate the quantitative evaluation of the results using the error metric \(D_{mem}\) in [29]. When verifying the influence of one parameter on the experimental results, we kept the other parameter constant. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Models** & **Points** & \multicolumn{4}{c}{**Parameters**} \\ \hline Horse & 48,485 & 4 & 10 & & 50 & 100 \\ \hline Cactus & 3280 & 4 & 10 & & 50 & 100 \\ \hline Bunny & 35,947 & 0.01 & & \(\lambda\) & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The models and parameters used in experiment. Figure 3: Filtering results with different \(k\) values on cactus model (\(\lambda=0.1\)). (**a**) Cactus model with noise; (**b**) filtering result with \(k=4\); (**c**) filtering result with \(k=10\); (**d**) filtering result with \(k=50\); (**e**) filtering result with \(k=100\); (**f**) the ground-truth model of cactus. Figure 2: Filtering results with different \(k\) values on horse model (\(\lambda=0.1\)). (**a**) Horse model with noise; (**b**) filtering result with \(k=4\); (**c**) filtering result with \(k=10\); (**d**) filtering result with \(k=50\); (**e**) filtering result with \(k=100\); (**f**) the ground-truth model of horse. It can be clearly seen from Figure 2b,c that some noise points may not be removed when \(k\) is too small. Furthermore, if \(k\) is too large, as shown in Figure 2e, the point-cloud model shrinks obviously. It is clearly demonstrated in Table 2 that \(k=50\) provides the best error-metrics values for the horse model. However, it reveals the different views in Figure 3. The cactus model shrinks obviously when \(k\) is 50, and the desirable result appears when \(k\) is 10. It is also demonstrated in Table 2 that \(k=10\) provides the best error-metrics values for the cactus model. The reason for the phenomenon of the different \(k\) values is that the number of points contained in the model and the shape of the model are all different. Furthermore, the choice of \(k\) is also different under different noise levels. The second key parameter is \(\lambda\), which is a regularization parameter penalizing large \(a_{i}\). It simply controls the filtering quality. As shown in Figure 4d, if the value of \(\lambda\) is too large, the filtered results of the bunny model are overly smoothing. Furthermore, if the value of \(\lambda\) is too small, the excessively large filtering coefficient \(a_{i}\) creates negative effects. It is demonstrated in Figure 4 and Table 3 that \(\lambda=0.1\) provides a desirable result for the point-cloud model of bunny. Therefore, the parameters of the point-cloud model (e.g., the number of points, the size of the model and shape features, etc.) should be fully considered in order to obtain the desired filtering results. Both of  
methods, with the aim of exhibiting its performance. In our experiments, we chose three different filtering algorithms, namely, bilateral filter [14], moving least-squares filter [15], and guided 3D point-cloud Filter [16]. Moreover, the results of these algorithms were reproduced on the same computer according to the optimal parameters provided by their authors.