# A Unified Denoising Framework for Restoring the LiDAR Point Cloud Geometry of Reflective Targets
## 4 Discussion  
To qualitatively evaluate the performance of the veiling effect denoising module, two samples from the dataset were selected. A comparison of the results using the pass-through filter with a constant-intensity threshold and our modified strategy is presented in Figure 7.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Sample** & **Original** & **Rusu** & **Nurunnabi** & **Digne** & **Rakotosaona** & **Duan** & **Ours** \\  & **Data** & [19] & [22] & [25] & [34] & [27] & **Ours** \\ \hline Sample 1 & 50.03 & 6.37 & 2.66 & 34.27 & 6.24 & **2.06** & 3.12 \\  
It can be observed that the geometric features of the target in the original point cloud are noticeably distorted, particularly in the vertical direction. For the first selected data sample, the results of both algorithms show no significant differences. However, for another sample at a longer distance, the constant-threshold method removes part of the edge of the target's point cloud, resulting in substantial feature loss. In contrast, our improved method is adaptable to targets at different distances, effectively removing noise points caused by the veiling effect while preserving the target's features. To qualitatively analyze the performance of the range anomalies' correction module, two representative samples were selected in the dataset. The results for the two samples are shown in Figures 8 and 9. It can be observed that a large number of outliers caused by range anomalies are corrected to the target surface. The corrected outliers fill the sparse regions in the inliers, especially the area where the letter \"P\" is located on the traffic sign. Figure 8: Results of range anomalies’ correction for Sample 1: (**a,e**) point cloud after the veiling effect denoising from the side and front perspectives; (**b,f**) inliers and outliers classified by the MSAC plane fitting; (**c,g**) corrected outliers; (**d,h**) the combination of inliers and the corrected outliers. Note: (**a–d**) are shown from the side perspective, (**e–h**) are shown from the front perspective, and all point clouds are displayed at the same scale. For reflective targets, the distortion of target features caused by the blooming effect is more pronounced compared to the veiling effect and range anomalies. To visually compare the denoising performance of different algorithms, we selected Sample 12 as a representative example from the dataset, as the target is located at a relatively great distance, resulting in a more pronounced target distortion. The blooming factors were determined through a simple experiment in which data were collected from a reflective target with known dimensions. The difference in height and width between the blooming point cloud and the actual target corresponds to the major and minor axes of the error ellipse, respectively. The blooming factors were then calculated using Equation (3). Specifically, the values of \(\lambda_{V}\) and \(\lambda_{H}\) were 0.615 and 0.415, respectively. Figure 10 illustrates the original point cloud, the ground truth, and the denoising results of different algorithms. It can be observed that the shape and size of the denoised point cloud obtained by our proposed method align most closely with the ground truth. In contrast, the results of other algorithms exhibit noticeable distortions, particularly in the height dimension, where the size of the denoised point cloud remains larger than the actual dimensions of the target. Figure 10: Comparison of blooming effect denoising results using different algorithms for Sample 12: (**a**): original point cloud; (**b**) ground truth; (**c**-**g**) results of algorithms from References [19; 22; 25; 27; 34] respectively; (**h**) result of the proposed framework. Note: All point clouds are shown from the front perspective at the same scale.