Splat-LOAM: Gaussian Splatting LiDAR Odometry and Mapping¶

Conference: ICCV 2025 arXiv: 2503.17491 Code: GitHub Area: Autonomous Driving Keywords: Gaussian Splatting, LiDAR SLAM, Odometry, Mapping, Spherical Projection

TL;DR¶

The first LiDAR odometry and mapping pipeline built entirely on 2D Gaussian primitives, simultaneously achieving high-accuracy pose estimation and lightweight scene reconstruction via a spherical-projection-driven differentiable rasterizer.

Background & Motivation¶

LiDAR sensors provide precise geometric measurements and are widely used for ego-motion estimation and environment reconstruction in autonomous driving. However, classical approaches face a fundamental trilemma: the trade-off among accuracy, memory, and runtime.

Classical methods (point cloud stacking, surfels, meshes) can incrementally build global maps but typically result in massive point clouds or require compromises between accuracy and memory.
NeRF-based implicit methods (e.g., SHINE-Mapping, N³-Mapping, PIN-SLAM) introduce neural implicit SDF representations, improving accuracy and storage efficiency, but require complex sampling strategies for SDF estimation and suffer from speed bottlenecks in online execution.
3D Gaussian Splatting (3DGS) has achieved impressive results in visual SLAM (e.g., SplatAM, Gaussian-SLAM), yet these methods rely on camera images and color information and cannot be directly applied to pure LiDAR data.

The paper's starting point is that LiDAR naturally provides precise 3D structural information that can directly initialize Gaussian primitives, and the efficiency of Gaussian Splatting—together with its freedom from modeling empty space—is particularly well-suited to LiDAR scenarios. The core idea is to combine 2D Gaussian primitives with a spherical projection model and design a dedicated differentiable rasterizer, enabling an efficient LOAM pipeline driven purely by LiDAR data.

Method¶

Overall Architecture¶

The system employs a keyframe-driven local map strategy. A new Gaussian local model is initialized whenever visibility conditions are satisfied. Incoming frames estimate poses via frame-to-model registration, while the local model is iteratively optimized. The entire pipeline uses only 2D Gaussian primitives as the scene representation.

Key Designs¶

Spherical Projection Model: Since LiDAR provides 360° panoramic input, the pinhole camera projection model is unsuitable. The paper adopts spherical projection \(\phi(\mathbf{p}) = \mathbf{K}\psi(\mathbf{p})\), mapping 3D points to image coordinates defined by azimuth and elevation angles. The camera intrinsic matrix \(\mathbf{K}\) is adaptively computed from the actual angular range of each frame's point cloud, avoiding blank regions caused by hard-coded FoV values.
2D Gaussian Primitive Definition and Rasterization: Each 2D Gaussian is defined by opacity \(o\), center \(\boldsymbol{\mu}\), two tangent vectors \(\mathbf{t}_\alpha, \mathbf{t}_\beta\), and scales \((s_\alpha, s_\beta)\). Rendering uses tile-based α-blending: the image is divided into 16×16 tiles, and within each tile, Gaussians sorted by distance are integrated front-to-back to yield depth \(d\), normal \(\mathbf{n}\), and opacity \(o\).
Explicit Ray–Splat Intersection Computation: The paper abandons the local affine approximation used in the original 3DGS (which introduces numerical instability and distortion under spherical projection), instead computing explicit ray–splat tri-plane intersections by solving a homogeneous linear system to obtain intersection coordinates \((\alpha, \beta)\).
Spherical Bounding Box Handling: Spherical images exhibit coordinate singularities at the horizontal boundaries \(\{0, W\}\). The paper proposes a method that first shifts vertices to the image center, computes the extent, and then maps back, ensuring correct bounding box computation even when a splat lies behind the sensor.
Frame-to-Model Registration: Both geometric and photometric registration are combined. Geometric registration uses PCA-based kd-tree point-to-plane ICP, while photometric registration minimizes projection range errors on the spherical depth map. Pose updates are parameterized locally via the Lie algebra \(\mathfrak{se}(3)\) and solved using second-order Gauss-Newton optimization.

Loss & Training¶

The total mapping loss is:

\[\mathcal{L}_{\text{map}} = \mathcal{L}_d + \lambda_o \mathcal{L}_o + \lambda_n \mathcal{L}_n + \lambda_s \sum_{i=1}^{N} \mathcal{L}_{s_i}\]

\(\mathcal{L}_d\): L1 depth map error computed only on valid pixels, with distance weighting
\(\mathcal{L}_o\): Opacity coverage loss, encouraging splats to cover valid measurement regions
\(\mathcal{L}_n\): Normal self-regularization, aligning splat normals with surface normals estimated from rendered depth map gradients
\(\mathcal{L}_s\): Scale regularization, penalizing splat extent only beyond threshold \(\tau_s\), supporting anisotropic splats

The odometry loss is the sum of geometric and photometric terms: \(\mathcal{L}_{\text{odom}} = \mathcal{L}_{\text{geo}} + \mathcal{L}_{\text{photo}}\).

Keyframes are sampled according to a geometric distribution, ensuring the most recent keyframe has a ≥40% probability of being selected. Opacity reset is not performed to avoid catastrophic forgetting.

Key Experimental Results¶

Main Results¶

Mapping quality is evaluated on the Newer College and Oxford Spires datasets using ground-truth poses:

Method	Acc↓	Com↓	C-l1↓	F-score↑
OpenVDB	11.45	4.38	7.92	88.85
VoxBlox	20.36	12.64	16.50	64.63
N³-Mapping	6.32	9.75	8.04	94.54
PIN-SLAM	15.28	10.50	12.89	88.05
Splat-LOAM	6.64	4.09	5.37	96.74

For odometry evaluation across four datasets (NC, VBR, Oxford Spires, Mai City), Splat-LOAM with combined geometric and photometric registration achieves competitive performance compared to state-of-the-art methods such as MAD-ICP.

Ablation Study¶

Mesh Extraction	Acc↓	Com↓	C-l1↓	F-score↑
Marching Cubes	16.76	5.53	11.14	76.76
Poisson (centers)	10.15	6.70	8.43	92.33
Ours (rendered)	6.64	4.09	5.37	96.74

Registration ablation shows that jointly using geometric and photometric factors outperforms any single method (Point-to-Point / Point-to-Plane / photometric only), validating the hybrid registration design.

Key Findings¶

Mapping FPS stabilizes when the number of active primitives is in the range of 200K–300K (limited by rasterizer saturation).
The system is sensitive to LiDAR motion distortion; joint velocity and pose estimation is an important direction for improvement.
Compared to N³-Mapping, Splat-LOAM achieves superior detail fidelity, as the latter tends to over-smooth surfaces.

Highlights & Insights¶

The first pure-LiDAR Gaussian Splatting LOAM system, filling a gap in this research direction.
The bounding box computation scheme for handling coordinate singularities under spherical projection is particularly elegant.
The threshold design of the scale regularization loss \(\mathcal{L}_s\) permits anisotropic splats and is more flexible than directly minimizing mean deviation.
Extremely low GPU memory requirements make the system suitable for real-time robotic perception.

Limitations & Future Work¶

Sensitivity to LiDAR motion distortion necessitates simultaneous velocity estimation.
No loop closure module is included, leading to accumulated drift over long trajectories.
LiDAR intensity/reflectance information is not exploited for appearance modeling.
The compact bounding box computation for the spherical projection rasterizer is an approximation, leaving room for improvement.

PIN-SLAM's neural point cloud approach offers good global consistency but is unsatisfactory in terms of memory and speed.
The paradigm of visual Gaussian SLAM (SplatAM, Splat-SLAM) can be adapted in reverse for LiDAR.
GS-LiDAR's periodic oscillation Gaussian design targets dynamic objects and is complementary to this paper's static scene mapping approach.

Rating¶

Novelty: ⭐⭐⭐⭐ First pure-LiDAR GS LOAM
Technical Depth: ⭐⭐⭐⭐ Complete spherical rasterizer design
Experimental Thoroughness: ⭐⭐⭐⭐ Multi-dataset, multi-metric evaluation
Value: ⭐⭐⭐⭐ Low GPU requirements, suitable for robotics
Overall Recommendation: ⭐⭐⭐⭐