Sparse LiDAR point clouds cause severe loss of detail of static structures and reduce the density of static points available for navigation. Reduced density can be detrimental to navigation under several scenarios. We observe that despite high sparsity, in most cases, the global topology of LiDAR outlining the static structures can be inferred. We utilize this property to obtain a backbone skeleton of a static LiDAR scan in the form of a single connected component that is a proxy to its global topology. We utilize the backbone to augment new points along static structures to overcome sparsity. Newly introduced points could correspond to existing static structures or to static points that were earlier obstructed by dynamic objects. To the best of our knowledge, we are the first to use this strategy for sparse LiDAR point clouds. Existing solutions close to our approach fail to identify and preserve the global static LiDAR topology and generate sub-optimal points. We propose GLiDR, a Graph Generative network that is topologically regularized using 0-dimensional Persistent Homology (PH) constraints. This enables GLiDR to introduce newer static points along a topologically consistent global static LiDAR backbone. GLiDR generates precise static points using 32x sparser dynamic scans and performs better than the baselines across three datasets. The newly introduced static points allow GLiDR to outperform LiDAR-based navigation using SLAM in several settings. GLiDR generates a valuable byproduct - an accurate binary segmentation mask of static and dynamic objects that is helpful for navigation planning and safety in constrained environments.

翻译：稀疏LiDAR点云会导致静态结构细节严重丢失，并降低用于导航的静态点密度。在多种场景下，密度降低可能对导航产生不利影响。我们观察到，尽管存在高度稀疏性，但在大多数情况下，勾勒静态结构的LiDAR全局拓扑仍可推断。利用这一特性，我们以单个连通分量的形式获取静态LiDAR扫描的骨干骨架，该骨架可作为其全局拓扑的代理。我们利用该骨架沿静态结构增补新点以克服稀疏性。新引入的点可能对应现有静态结构，或原本被动态物体遮挡的静态点。据我们所知，我们是首个将这一策略用于稀疏LiDAR点云的研究。与我们的方法相近的现有解决方案未能识别并保留全局静态LiDAR拓扑，导致生成次优的点。我们提出GLiDR——一种利用0维持续同调（PH）约束进行拓扑正则化的图生成网络。这使得GLiDR能够沿拓扑一致的全局静态LiDAR骨干引入新的静态点。GLiDR利用稀疏32倍的动态扫描生成精确的静态点，在三个数据集上的性能均优于基线方法。新引入的静态点使GLiDR在多种设置下基于SLAM的LiDAR导航表现更优。此外，GLiDR还生成一种有价值的副产品——精确的静态与动态物体二值分割掩码，有助于受限环境下的导航规划与安全保障。