"PINGS" is a novel LiDAR-visual SLAM system that unifies continuous Signed Distance Fields (SDFs) and Gaussian Splatting (3DGS) radiance fields within an elastic, compact, point-based implicit neural map. By enforcing geometric consistency and leveraging mutual supervision between these fields, PINGS achieves robust and accurate 3D reconstruction for large-scale environments. The system incrementally builds globally consistent maps, enabling superior photorealistic and geometric rendering at novel views, more accurate distance fields for improved localization and mesh reconstruction, and greater map compactness compared to state-of-the-art methods. An open-source implementation is provided.
PINGS: Gaussian Splatting Meets Distance Fields within a Point-Based Implicit Neural Map
0:00 - Introduction to PINGS: Unifying Geometric & Photorealistic Mapping
Problem: Autonomous robots require high-fidelity environmental maps that are both geometrically accurate and photorealistic. Existing methods typically excel at one (e.g., LiDAR for geometry/SDFs, cameras for photorealism/NeRF/3DGS) but struggle with scalable, incremental, and consistent mapping of both simultaneously.
PINGS Solution: This paper proposes PINGS, a novel LiDAR-visual SLAM system that unifies continuous Signed Distance Fields (SDFs) and Gaussian Splatting (3DGS) radiance fields using an elastic, compact, point-based implicit neural map.
Core Innovation: Enforcing geometric consistency between these fields leads to mutual improvements.
Key Claims: (i) Improved RGB and geometric rendering at novel views by constraining the radiance field with the SDF; (ii) More accurate SDF for better localization and surface reconstruction by leveraging dense photometric cues; (iii) Large-scale globally consistent mapping via loop closures; (iv) More compact map representation.
Availability: The open-source implementation is publicly available on GitHub.
III.A - Novel Point-Based Implicit Neural Map Representation
The map M is represented as a set of neural points, each defined by its 3D position, orientation, optimizable geometric features (fg), appearance features (fa), and timestamps for creation and last update.
A voxel hashing structure (with a 0.3m voxel resolution) is maintained for fast neural point indexing and neighbor search.
To prevent odometry drift from accumulating inconsistent observations, map optimization and odometry estimation are performed only within a local map Ml centered at the current LiDAR position.
III.B - Neural Signed Distance Field (SDF) Modeling
The continuous SDF value at any query position is predicted by a globally shared SDF decoder, taking as input the geometric features and relative coordinates of nearby neural points, and then interpolated.
The neural SDF is incrementally trained using a weighted sum of binary cross-entropy loss and Eikonal loss, by sampling points along LiDAR rays to generate pseudo SDF labels.
This incrementally built SDF map is then used for LiDAR odometry estimation and surface mesh extraction.
III.C - Neural Gaussian Splatting Radiance Field
Gaussian Spawning: Neural points within the current camera frustum serve as anchor points to spawn multiple (e.g., K=8) Gaussian primitives. Dedicated MLP decoders use the neural point's features to predict each Gaussian's position, rotation, scale, opacity, and RGB color.
Gaussian Surfels: For accurate and multi-view consistent geometry, 3D Gaussian ellipsoids are flattened into 2D disks (surfels), enabling the rendering of depth and normal maps.
Training Loss: A combined loss (Lgs) is used, integrating photometric rendering loss, depth rendering loss (supervised by sparse depth maps projected from LiDAR data), and an area regularization term to encourage minimal surfel overlap.
Camera poses and per-frame exposure parameters are jointly optimized during radiance field training to account for imperfect sensor synchronization.
III.D - Joint Optimization with Geometric Consistency
To enforce mutual alignment between the surfaces described by the SDF and the Gaussian splatting radiance field, a joint optimization approach is proposed. This resolves geometric ambiguities in the radiance field and refines SDF accuracy in regions with sparse LiDAR measurements.
A two-part geometric consistency loss (Lcons) is introduced: it enforces SDF values to match sampled offsets along surfel normals and aligns SDF gradients with surfel normals.
The total loss (sum of SDF loss, Gaussian splatting loss, and geometric consistency loss) is minimized to jointly optimize neural point features, decoder parameters, camera poses, and exposure correction parameters.
III.E - PINGS LiDAR-Visual SLAM System Workflow
PINGS alternates between two main steps: (i) incremental learning of the local neural point map (mapping), and (ii) odometry estimation using the learned SDF (localization).
Loop Closure: The system detects loop closures using features from the local neural point map. Upon detection, pose graph optimization is performed to correct odometry drift, and neural points associated with corrected LiDAR frames are updated, maintaining global map consistency.
Dynamic Object Filtering: Neural points likely representing dynamic objects (identified by large SDF values in free space) are disabled from spawning Gaussian primitives, preventing them from being rendered and causing artifacts.
IV.A - Experimental Setup
PINGS was evaluated on custom-collected in-house car datasets (including a challenging 5 km urban sequence with ~10,000 LiDAR scans and ~40,000 images, providing 360-degree visual coverage) and the Oxford Spires dataset, which includes millimeter-accurate reference maps from a terrestrial laser scanner.
Experiments were conducted on a single NVIDIA A6000 GPU.
IV.B - Superior Novel View Rendering (Photorealistic & Geometric)
Results: PINGS consistently outperforms state-of-the-art baselines (3DGS, GSS, and Neural Point variants) in quantitative metrics (PSNR, SSIM, LPIPS) for photorealistic rendering quality and Depth-L1 error for geometric accuracy. This superiority holds for both in-sequence and challenging out-of-sequence test views.
Key takeaway: The point-based neural representation, joint training with the distance field, and the geometric consistency constraints lead to better optimization control, fewer "floating Gaussians," and smoother, more accurate normal maps.
IV.C - Enhanced Surface Reconstruction Quality
Results: PINGS achieves superior surface reconstruction quality, particularly in terms of Chamfer distance and F-score, on the Oxford Spires dataset. It outperforms methods like OpenMVS, Nerfacto, GSS (with TSDF fusion), VDB-Fusion, and PIN-SLAM.
Key takeaway: The incorporation of dense photometric cues and multi-view consistency from the radiance field significantly improves the accuracy of the SDF, leading to higher quality mesh reconstructions.
IV.D - Improved SLAM Localization Accuracy
Results: PINGS demonstrates both lower odometry drift (Average Relative Translation Error - ARTE) and superior global localization accuracy (Absolute Trajectory Error - ATE) compared to state-of-the-art LiDAR odometry/SLAM systems (F-LOAM, KISS-ICP, SuMa, MULLS, PIN-SLAM).
Key takeaway: The refined SDF obtained through joint optimization with the radiance field directly contributes to more accurate LiDAR odometry and more robust relocalization during loop closure corrections.
IV.E - Large-Scale Globally Consistent Mapping
Demonstration: Figures 1 and 7 visually demonstrate PINGS's ability to build globally consistent maps over challenging large-scale environments (e.g., a 5 km urban sequence).
Loop Closure Effect: Without loop closure correction, odometry drift accumulates, leading to visual artifacts like duplicate objects or misplaced features when revisiting previously mapped regions. Applying loop closure corrections and updating the map resolves these inconsistencies.
Key takeaway: The inherent elasticity of the neural point map is crucial for maintaining global consistency after applying pose graph optimization corrections from loop closures.
IV.F - High Map Memory Efficiency
Results: Experimental analysis shows that PINGS's approach of storing neural points and decoder MLPs is more memory-efficient than directly storing Gaussian primitives (as in GSS) or discrete SDFs in voxels (as in VDB-Fusion).
Efficiency Source: This efficiency stems from using globally-shared decoder MLPs that learn common patterns, and locally-defined neural points that compactly encode multiple Gaussian primitives and continuous SDF values through feature vectors.
Key takeaway: PINGS achieves a better quality-memory trade-off for both radiance and distance fields compared to methods that model only a single field type.
V. - Current Limitations
Processing Speed: The radiance field mapping component is computationally intensive, resulting in an overall processing time of approximately five seconds per frame, which currently limits real-time operation.
No Pre-trained Priors: PINGS relies solely on online, per-scene optimization, potentially affecting mapping quality and convergence speed compared to systems that incorporate pre-trained priors.
Dynamic Object Modeling: While PINGS can filter dynamic objects using the distance field, it lacks explicit 4D modeling capabilities, which is a limitation in highly dynamic environments or when objects transition between static and dynamic states.
VI. - Conclusion & Future Work
PINGS successfully unifies SDF and Gaussian splatting representations within an elastic, compact neural point map, achieving mutual improvements through enforced geometric consistency.
The system demonstrates superior performance in novel view rendering fidelity, surface reconstruction quality, odometry estimation accuracy, and map memory efficiency on challenging large-scale datasets.
Future work aims to address the real-time performance bottleneck, incorporate pre-trained priors, and enable accurate 4D modeling for dynamic environments.