Self-supervised Geometry Reasoning for LiDAR Simultaneous Localization and Mapping

We present a real-time LiDAR-based framework for Gaussian Splatting SLAM that tightly couples fast G-ICP registration with spherical rasterization-based dense mapping for large-scale sequences. Leveraging LiDAR geometry rather than appearance, we reuse tracking-estimated local covariances to initialize Gaussians with range-aware scales and to derive surface normals for geometry-aware map optimization. We further introduce a covariance-derived geometry score that measures local complexity and drives pruning in planar regions and selective densification in structurally rich areas, while optimized Gaussians and LiDAR-specific confidence cues are fed back to improve tracking robustness. On the Newer College dataset, our method achieves an F-score of 86.78% using purely online trajectories at real-time speed ($>$20 FPS), and additional experiments on other datasets confirm its stability and scalability.

High-quality maps are fundamental for robotics tasks such as navigation and planning. Although modern graph-based LiDAR SLAM systems achieve good trajectory accuracies, a low trajectory error alone does not guarantee geometrically consistent maps, particularly at revisit locations where missed loop closures and residual drift can produce local misalignments. In this work, we address the problem of jointly improving global trajectory estimation and local map quality in 3D LiDAR SLAM. We first propose a framework to efficiently estimate geometry-dependent information matrices for ICP, enabling principled weighting of odometry constraints in a pose graph. We then introduce a hierarchical loop-closure module that decouples place recognition from geometric registration, together with a retroactive loop-closure module that exploits the optimized pose graph to recover missed loop closures. We also propose an evaluation protocol to measure map consistency at revisit locations. We evaluate our SLAM system on several datasets against state-of-the-art LiDAR SLAM systems. Experimental results demonstrate global trajectory accuracies on par with or better than existing methods while consistently improving local geometric map consistency at revisit locations. These results suggest that coupling uncertainty-aware odometry with geometry-guided loop-closure refinement leads to more accurate trajectories and higher-quality maps.

Point clouds are a fundamental representation for robotic perception tasks such as localization, mapping, and object pose estimation. However, LiDAR-acquired point clouds are inherently sparse and non-uniform, providing incomplete observations of the underlying scene geometry. This makes reliable geometric reasoning challenging and degrades downstream perception performance. Existing approaches attempt to compensate for these limitations by estimating local geometry, but often rely on hand-crafted statistics or end-to-end supervised learning, which can suffer from limited scalability or require large amounts of accurately labeled data. To address these challenges, we explicitly model point cloud geometry under a principled mathematical formulation. We represent local geometry as a statistical manifold induced by a family of Gaussian distributions, where each point is associated with a Gaussian capturing its local geometric structure. Based on this formulation, we introduce Point-to-Ellipsoid (POLI), a deep neural estimator that predicts per-point Gaussian geometry. POLI learns a mapping from point cloud observations to their underlying geometry in a self-supervised manner, removing the need for labeled data while preserving strong geometric inductive biases. The resulting representation integrates seamlessly into existing robotic perception pipelines without architectural modifications. Extensive experiments show that POLI enables accurate and robust geometry estimation and consistently improves performance across diverse robotic perception tasks.