# Unsharp Mask Guided Filtering for Acoustic Point Cloud of Water-Conveyance Tunnel
## 4 Results
### Parameters
#### 4.2.1 Scene Experiment  
The purpose of developing the proposed algorithm is to filter the acoustic point-cloud model of water-conveyance tunnels. Therefore, we conducted an experiment on a real test site to verify the performance of our algorithm. The test site is a small water-conveyance tunnel with a diameter of 80 cm. The ground-truth shape of the tunnel is known. An underwater robot was used as the carrier to collect data [20]. The point-cloud model of the tunnel was corrected by the carrier-attitude information. The raw point-cloud model and the ground-truth model are shown in Figure 5; there are many noise points around the inner surface of the tunnel. In this experiment, we compared the results obtained by the proposed method with the results of the three different filtering algorithms mentioned above.  
Compared with Figure 5a, it is demonstrated in Figure 6a,c,e,g that the four denoising algorithms all achieved the purpose of filtering. This can be more clearly observed in Figure 6b,d,f,h. For the small-scale noise points near the inner surface of the tunnel, it is clearly visible in Figure 6b that the guided 3D point-cloud filter achieved poor effects in smoothing the small-scale noise points. As shown in the blue circular dotted-line area in Figure 6d,f, the bilateral filter and the moving least-squares filter had the problem of over-smoothing while filtering the noise points. Figure 6h demonstrates that the proposed method can prevent over-smoothing while filtering out small-scale noise points. For large-scale noise far away from the inner surface of the tunnel, none of the three methods achieved a good result. By contrast, the results of the proposed method are better than other those of the other three algorithms.  
Figure 5: Raw point-cloud model of water-conveyance tunnel. (**a**) Raw point-cloud model; (**b**) front view of (**a**); (**c**) the ground-truth model of real water-conveyance tunnel; (**d**) front view of (**c**).  
To quantitatively evaluate the denoising results, four error-metrics, \(D_{mean}\), \(\sigma\), \(r_{ave}\), and \(r_{error}\), were used in our experiment. \(D_{mean}\) represents the average distance between the points in the resulted point-cloud and the corresponding points in the ground-truth model [29]. \(\sigma\) represents the variance of the distance. \(r_{ave}\) is the average radius of the filtered point-cloud model of the tunnel. \(r_{error}\) represents the reconstruction accuracy of the point-cloud model of the water-conveyance tunnel. The calculation results of the error metrics are shown in Table 4.  
Figure 6: The results of different algorithms tested on the point-cloud model of water-conveyance tunnel. (**a**) The result of guided 3D point-cloud filter; (**b**) front view of (**a**); (**c**) the moving least-squares filter results; (**d**) front view of (**c**); (**e**) the bilateral filter results; (**f**) front view of (**e**); (**g**) the results of proposed algorithm (\(k=300\) and \(\lambda=0.5\)); (**h**) front view of (**c**).  
In Table 4, the best results are displayed in bold. It is clearly demonstrated that the results of our method were the best in \(D_{mean}\) and \(\sigma\). In other words, the filtered points were close to the inner surface of the tunnel and had good aggregation properties. The results of the proposed method also have high accuracy in \(r_{ave}\) and \(r_{error}\). Moreover, it is clearly seen from \(r_{error}\) that the point-cloud model of the real tunnel obtained by the proposed method has a high reconstruction accuracy, which provides important support for defects detection on the tunnel surface.