# Privacy-Preserved Visual Simultaneous Localization and Mapping Based on a Dual-Component Approach
## 4 Results
### Effectiveness of Point Cloud Lifting  
Section 3.3 introduces a 3D point cloud encryption algorithm into SLAM, which is based on point dimensionality lifting. In this section, the 3D point clouds generated by the original ORB-SLAM3 [18] and ORB-SLAM3 with various image privacy preservation algorithms are first encrypted into 3D line clouds. These encrypted line clouds are then attacked by the Line2 Point [30] algorithm, which is divided into two stages: neighborhood estimation and peak finding. In the neighborhood estimation stage, the algorithm first finds the nearest neighboring lines for each line and then uses these neighboring lines to generate candidate 3D points on the line. The peak finding stage determines the final point locations by analyzing the distribution of these candidate points and identifying high-density areas. The algorithm aims to restore the original 3D point clouds. To evaluate the effectiveness of the point cloud encryption algorithm, a k-dimensional tree is used to match the original and restored point clouds. The average point-to-point Euclidean distance error between the original and restored point clouds, for the same sequence, is employed as an evaluation metric. Euclidean distance represents the straight-line distance between two points in three-dimensional space and can be used to measure the positional difference between corresponding points in two different point clouds. The larger the Euclidean distance error, the greater the difference between corresponding points, indicating poorer alignment between the two point clouds. In this experiment, this means that the point cloud restored by the Line2 Point [30] algorithm differs more from the original point cloud.  
\begin{table}
\begin{tabular}{l c c c c c c c} \hline
**Sequence** & **Proposed Method** & **Black** & **Grey** & **White** & **Gaussian** & **Ran25** & **Ran50** \\ \hline Oxford-54 & **0.006** & 0.008 & 0.012 & 0.008 & 0.213 & 0.153 & 0.017 \\ Oxford-58 & **0.007** & 0.008 & 0.019 & 0.010 & 0.182 & 0.12  
Table 3 shows the average point cloud error results across different sequences. Even in the 54 sequences with the smallest error, the average point-to-point Euclidean distance error reached 0.579 m, while errors in the remaining sequences were generally greater than 1m. This indicates that the point cloud encryption algorithm effectively preserves privacy, as evidenced by the significant error between the restored and original point clouds. The primary factor behind the robust privacy preservation lies in the transformation of the point cloud into a line cloud. This transformation increases the complexity of accurately reconstructing the original point cloud, as any point along the line could represent the original location. Additionally, the outdoor test scenario leads to a more scattered point cloud, which makes it harder for the Line2 Point algorithm to restore the original point clouds accurately.  
Figure 6 visualizes the original point cloud, the lifted line cloud, and the restored point cloud for 58 sequences. Although the Line2 Point attack approximates the general shape of the point cloud, the reconstruction lacks fine details and exhibits mismatched point cloud density.  
The preceding experimental results demonstrate that the point cloud encryption algorithm generates a line cloud that is difficult for humans to interpret, effectively concealing the original scene. Moreover, following the Line2 Point attack, accurately reconstructing the 3D point cloud of the original scene proves challenging, highlighting the algorithm's effectiveness in privacy preservation.