# A Unified Denoising Framework for Restoring the LiDAR Point Cloud Geometry of Reflective Targets
## 3 Experiments and Results
### Experimental Results  
To evaluate the algorithm's performance, we randomly selected one sample from each of the 14 distances in the dataset. The denoising results of the UDF for 14 samples are summarized in Table 2. The algorithm achieved an overall average total error of 2.09% and a kappa coefficient of 95.46%, with standard deviations of 0.89% and 2.05%, respectively. These results demonstrate the algorithm's robust performance and high classification accuracy across targets at varying distances and orientations. For the MSE and MCD metrics, the average values across all samples were 0.15 cm\({}^{2}\) and 0.05 cm, respectively. Notably, Sample 14 exhibited the highest MSE and MCD values, likely due to its longer distance, which resulted in a sparser point cloud. This sparsity appears to have negatively impacted the accuracy of target boundary extraction during the blooming effect denoising step. The average relative height error and relative width error across all samples were approximately 1.9%. For a target with dimensions of 60 cm in height and width, this corresponds to absolute errors in height and width not exceeding 2 cm. To compare the proposed framework with previous point cloud denoising approaches, we selected five representative methods from recent years, including four traditional denoising algorithms and one deep learning-based algorithm. Some algorithms adjust the spatial positions of the original point cloud during the denoising process, making it difficult to calculate total error and kappa coefficient. Therefore, we selected MSE, MCD, relative height error, and relative width error as metrics to evaluate the feature preservation and recovery capabilities of the algorithms. The results for MSE and MCD are presented in Tables 3 and 4. As shown, the UDF achieved the highest accuracy across all samples, which is primarily due to its precise recovery of range-anomalous points and its effective denoising of the blooming effect. In contrast, other algorithms, which treat range-anomalous points as noise and are less effective at denoising the blooming effect, exhibited higher MSE and MCD values. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Sample** & **T.I (\%)** & **T.II (\%)** & **T.E (\%)** & **Kappa (\%)** & **MSE (cm\({}^{2}\))** & **MCD (cm)** & **R.H (\%)** & **R.W (\%)** \\ \hline Sample 1 & 2.59 & 2.10 & 2.47 & 93.32 & 0.02 & 0.05 & 0.40 & 3.12 \\ Sample 2 & 0.06 & 5.74 & 2.22 & 95.24 & 0.03 & 0.06 & 1.25 & 2.78 \\ Sample 3 & 0.01 & 4.53 & 1.85 & 96.14 & 0.02 & 0.02 & 1.53 & 2.01 \\ Sample 4 & 0.01 & 3.73 & 1.64 & 96.66 & 0.02 & 0.02 & 1.40 & 1.57 \\ Sample 5 & 0.41 & 3.20 & 1.73 & 96.52 & 0.03 & 0.02 & 1.65 & 2.47 \\ Sample 6 & 0.42 & 3.33 & 1.87 & 96.26 & 0.06 & 0.03 & 2.29 & 0.16 \\ Sample 7 & 0.42 & 3.91 & 2.29 & 95.40 & 0.07 & 0.04 & 3.19 & 2.08 \\ Sample 8 & 0.43 & 0.42 & 0.42 & 99.15 & 0.02 & 0.01 & 0.12 & 0.52 \\ Sample 9 & 0.44 & 5.54 & 3.51 & 92.78 & 0.17 & 0.07 & 5.00 & 4.05 \\ Sample 10 & 0.01 & 1.27 & 0.79 & 98.33 & 0.06 & 0.02 & 0.69 & 1.25 \\ Sample 11 & 1.05 & 2.76 & 2.16 & 95.32 & 0.17 & 0.06 & 2.86 & 2.35 \\ Sample 12 & 2.76 & 0.85 & 1.50 & 96.65 & 0.11 & 0.05 & 1.42 & 0.85 \\ Sample 13 & 4.56 & 2.89 & 3.45 & 92.29 & 0.12 & 0.04 & 0.42 & 2.03 \\ Sample 14 & 6.94 & 1.60 & 3.40 & 92.32 & 1.18 & 0.23 & 4.60 & 1.51 \\ Avg. & 1.44 & 2.99 & 2.09 & 95.46 & 0.15 & 0.05 & 1.92 & 1.91 \\ Max. & 6.94 & 5.74 & 3.51 & 99.15 & 1.18 & 0.23 & 5.00 & 4.05 \\ Min. & 0.01 & 0.42 & 0.42 & 92.29 & 0.02 & 0.01 & 0.12 & 0.16 \\ Std. & 2.01 & 1.58 & 0.89 & 2.05 & 0.29 & 0.05 & 1.46 & 1.01 \\ \hline \hline \end{tabular} Note: The bolded numbers represent the lowest MSE values for each sample.  
\end{table} 
Table 2: Performance evaluations of the UDF on the self-constructed dataset.