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 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 such a 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 ($\mathcal{PH}$) constraints. This enables GLiDR to introduce newer static points along a topologically consistent global static LiDAR backbone. GLiDR generates precise static points using $32\times$ sparser dynamic scans and performs better than the baselines across three datasets. GLiDR generates a valuable byproduct - an accurate binary segmentation mask of static and dynamic objects that are helpful for navigation planning and safety in constrained environments. The newly introduced static points allow GLiDR to outperform LiDAR-based navigation using SLAM in several settings. Source code is available at https://kshitijbhat.github.io/glidr

翻译：稀疏激光雷达点云会导致静态结构细节严重丢失，并降低可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，尽管点云高度稀疏，但在大多数情况下仍可推断出描述静态结构的激光雷达全局拓扑。利用这一特性，我们以单连通分量的形式获取激光雷达扫描的骨架结构，作为其全局拓扑的代理。通过该骨架沿静态结构生成新点以克服稀疏性问题。新增点可能对应于现有静态结构，或先前被动态物体遮挡的静态点。据我们所知，我们是首个将此类策略应用于稀疏激光雷达点云的研究。现有相近方法未能识别并保持全局静态激光雷达拓扑，且生成的点云次优。我们提出GLiDR——一种通过0维持续同调（$\mathcal{PH}$）约束进行拓扑正则化的图生成网络。该设计使GLiDR能沿拓扑一致的全局静态激光雷达骨架生成新的静态点。GLiDR使用$32\times$稀疏动态扫描生成精确静态点，在三个数据集上均优于基线方法。GLiDR还产生一项有价值的副产品——精确的静态与动态物体二值分割掩码，这对受限环境中的导航规划与安全性具有重要价值。新增的静态点使GLiDR在多种设置下超越了基于SLAM的激光雷达导航性能。源代码发布于https://kshitijbhat.github.io/glidr