# Voxel-Based Navigation: A Systematic Review of Techniques, Applications, and Challenges
## 4 Key Techniques for Voxel-Based Navigation
### Voxel-Based Analysis  
Voxel-based spatial analysis is the core of voxel navigation. The intuitive description of spatial topology by voxels gives them a significant advantage in analyzing complex spatial relationships, such as topology, direction, and connectivity. The voxel model discretizes continuous 3D space into regular cubic units and clearly represents the connections and interactions between each voxel and its surrounding voxels through defined neighborhood relationships (6-neighbor, 18-neighbor, or 26-neighbor) and voxel indexing. This structure allows complex spatial relationships to be expressed and analyzed through simple and efficient computational methods without the need to compute and restore the spatial coordinates of the voxels. Additionally, by quantifying the geometric features of each unit in space, voxels provide an accurate description of spatial directional information. The directionality of each voxel in space can be obtained by calculating its normal vector or gradient, and this directional information helps in understanding the arrangement and distribution of elements in space. By combining the above information, the similarity between voxels can be measured, enabling the assessment of spatial connectivity, which is commonly used in geometric space segmentation [58; 59; 60; 61].  
Visibility analysis, which focuses on evaluating of line-of-sight, obstructions, and spatial relationships within a voxelized environment, is a specialized subcomponent of 3D spatial analysis and is also essential for voxel-based navigation. This type of analysis has widespread applications in generating path-planning networks and assessing urban environment safety. Ref. [62] proposed a voxel-based visibility-analysis technique, using voxel models and Unity software to simulate fields of view and areas of interest. Ref. [19] calculated the volume of visible space from specific viewpoints, using Digital Elevation Models (DEMs) to partition urban environments into voxels, providing a comprehensive  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline
**Method** & **Voxel** & **Voxel** & **Voxel** & **Voxel** & **Voxel** & **Voxel** & **Voxel** & **Voxel** & **Voxel** \\ \hline Mar53D [54] & 52.7 & 95.1 & 78.4 & 36.6 & 10.0 & 16.2 & 58.0 & 89.9 & 74.3 & 68.2 & 62.8 & 64.8 \\ KPConv [55] & 51.2 & 93.7 & 69.4 & 38.6 & 4.7 & 21.6 & 67.5 & 86.5 & 70.5 & 64.5 & 57.0 & 53.9 \\ Cylinder3D [47] & 52.5 & 94.6 & 74.9 & 38.8 & 0.1 & 12.5 & 65.7 & 90.7 & 74.5 & 66.0 & 63.1 & 61.4 \\ TemporalLidarSeg [56] & 47.1 & 91.6 & 59.7 & 23.0 & 5.9 & 9.4 & 51.0 & 91.5 & 75.3 & 65.3 & 57.2 & 60.4 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Quantitative results of the deep-learning-based methods on SemanticKITTI [57] multi-scan public validation set.  
evaluation of visible areas. Additionally, ref. [63] proposed a quantification method using 3D isovists and voxels to measure the visible and occluded portions of the view volume for landmark-based navigation, focusing on visual pollution, especially from outdoor billboards. Ref. [64] focused on the impact of vegetation on the visibility of traffic lights and signs in urban street environments, using highly detailed 3D city models and ray-tracing techniques to assess the visibility of signals and signs while considering visibility differences for various subjects (e.g., cars, bicycles, or pedestrians) (see Figure 8). In summary, these visibility-analysis methods not only have significant implications for urban safety and visual pollution assessment but also provide valuable insights for voxel-based navigation, helping to build more efficient and safe navigation solutions.