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Sparse LiDAR point clouds cause severe loss of detail of static structuresand reduce the density of static points available for navigation. Reduceddensity can be detrimental to navigation under several scenarios. We observethat despite high sparsity, in most cases, the global topology of LiDARoutlining the static structures can be inferred. We utilize this property toobtain a backbone skeleton of a static LiDAR scan in the form of a singleconnected component that is a proxy to its global topology. We utilize thebackbone to augment new points along static structures to overcome sparsity.Newly introduced points could correspond to existing static structures or tostatic points that were earlier obstructed by dynamic objects. To the best ofour knowledge, we are the first to use this strategy for sparse LiDAR pointclouds. Existing solutions close to our approach fail to identify and preservethe global static LiDAR topology and generate sub-optimal points. We proposeGLiDR, a Graph Generative network that is topologically regularized using0-dimensional Persistent Homology (PH) constraints. This enables GLiDR tointroduce newer static points along a topologically consistent global staticLiDAR backbone. GLiDR generates precise static points using 32x sparser dynamicscans and performs better than the baselines across three datasets. The newlyintroduced static points allow GLiDR to outperform LiDAR-based navigation usingSLAM in several settings. GLiDR generates a valuable byproduct - an accuratebinary segmentation mask of static and dynamic objects that is helpful fornavigation planning and safety in constrained environments.

GLiDR: Topologically Regularized Graph Generative Network for Sparse LiDAR Point Clouds