PLS-GS: Probabilistic Lidar Scaffolds for Compact, Surface-Aligned Gaussian Splatting

While 3D Gaussian Splatting (3DGS) is typically optimized from images only, many robotics and mapping applications provide both camera and high-definition LiDAR data, combining rich visual appearance with accurate geometric structure. We introduce PLS-GS, a probabilistic LiDAR scaffold for Gaussian Splatting that exploits this complementary sensing setting to construct a compact 3DGS representation aligned to the measured surface. PLS-GS fits a Hierarchical Gaussian Mixture Model jointly over position and color, yielding a continuous and adaptive scaffold that eliminates the need for discrete scene partitioning such as voxel grids or octrees. The fitted mixture then guides the renderable 3DGS Gaussians: each rendering Gaussian is associated with a GMM component and constrained in the local surface frame induced by that component's covariance. A Mahalanobis support loss bounds the deviation of the rendering Gaussians from the corresponding LiDAR-derived surface. Across five large outdoor scenes, PLS-GS places primitives markedly closer to the LiDAR measurements than both image- and LiDAR-initialized baselines, while employing substantially fewer primitives, yielding a considerably more compact model and faster rendering. At matched capacity, PLS-GS places primitives closer to the LiDAR measurements, with comparable rendering quality. Code is available at https://github.com/k-harikumar/PLS-GS.