LOGOS: LiDAR-Only Gaussian Elevation Splatting for Unified Tiny Obstacle Segmentation

Abstract: Robust obstacle segmentation is essential for the safety of intelligent robots, where LiDAR-based perception systems play a fundamental role in the robot-environment interaction. While extensive LiDAR-based approaches have demonstrated high performance on common obstacles in urban scenarios, their results on tiny obstacles such as curbs, gravel, and potholes remain unsatisfactory due to the significant similarity between tiny obstacles and inherent road undulations. Moreover, their segmentation accuracy even deteriorates sharply when the LiDAR scans suffer from degradation in challenging off-road scenes. To overcome these bottlenecks, we propose LOGOS, a LiDAR-only unified tiny obstacle segmentation system, which models the road surface as a continuous mixture of 2D Gaussian primitives and distinguishes tiny obstacles via high-presicion elevation estimation. Unlike existing Gaussian splatting methods that rely on iterative RGB training, LOGOS is a backpropagation-free LiDAR-only approach. It directly estimates Gaussian parameters via a freespace-aware initialization by incrementally pruning non-road primitives using smoothness constraints. Subsequently, pointwise signed distances are computed via a novel normal-aware elevation splatting function, ensuring robustness to both flat and sloped terrains. We evaluate LOGOS on a highly heterogeneous benchmark of point cloud frames collected from urban mobility scenarios and mining haulage off-road environments. These data are practically acquired using different LiDAR sensors and exhibit large variations in point density, terrain roughness, and obstacle types. Experiments on the road and off-road scenes demonstrate that LOGOS significantly outperforms other state-of-the-art methods, particularly in degraded point cloud regions and challenging off-road scenarios, while maintaining real-time efficiency.

• The paper introduces a backpropagation-free pipeline that models road surfaces with continuously blended 2D Gaussian primitives, uses smoothness-based pruning, and applies normal-aware elevation splatting to classify positive and negative obstacles.
• LOGOS achieves F1 scores of 0.957 on bumpy road scenes and 0.962 on bumpy off-road scenes, outperforming TA-TOS while running at 31–57 ms per frame on an Apple M1 Pro.
• The method remains robust under severe point sparsity and turning motion, reaching 0.823–0.913 IoU in downsampled scans where grid-based baselines fall below 0.189 IoU, although negative-obstacle detection and cross-domain tuning remain challenges.

LOGOS is a LiDAR-only pipeline for tiny obstacle segmentation that replaces fixed parametric or discrete grid road models with a continuous mixture of 2D Gaussian primitives, and computes pointwise signed distances via a normal-aware elevation splatting function. The work targets obstacles—curbs, gravel, potholes, ruts—that are geometrically indistinguishable from natural terrain undulations, and specifically addresses the accuracy collapse of grid-based methods in degraded scans caused by occlusion, edge sparsity, and rapid turning (2606.21527).

Motivation and positioning

The authors argue that existing approaches fail for two structural reasons. Classification-based methods (semantic segmentation networks such as RangeNet++, SphereFormer, TASeg) assign few points to tiny obstacles and suffer from long-tail category distributions, so low-height objects are absorbed into the ground class. Road-modeling methods reconstruct a reference surface and threshold signed distances, but fixed parametric models (plane, quadric) cannot fit undulating terrain, while discrete grids (Patchwork, Patchwork++, DipG-Seg, TA-TOS) require sufficient inlier density per cell; when RANSAC-based per-cell height estimation becomes unreliable in sparse regions, downstream refinement cannot recover the error. Gaussian splatting offers a continuous representation, but adapting it poses three challenges: no RGB input is available, iterative gradient-based optimization is incompatible with real-time perception, and the objective is elevation estimation rather than photorealistic rendering. LOGOS addresses all three by being backpropagation-free.

Method

The pipeline has two stages. In freespace-aware initialization, a sliding window ($W \times W$ with stride $S < W$) sweeps a BEV ROI; windows with fewer than $N_{\min}$ points are skipped. For valid windows, mean and covariance are estimated by MLE, SVD enforces a rank-2 covariance (smallest eigenvalue set to zero), and the third right-singular vector gives an upward-oriented normal. The ideal selection of road Gaussians is formulated as an $\ell_0$ minimization subject to smoothness constraints, which is NP-hard; instead, an incremental greedy procedure processes windows in spatial order, accepting a candidate only if its deviation from already-accepted neighbors satisfies a smoothness threshold $\epsilon_c$. This yields linear complexity and deterministic behavior.

In normal-aware elevation splatting, each point's signed distance is a Mahalanobis-weighted average over Gaussians of the projection $(\mathbf{p} - \mathbf{g}_j)^\top \mathbf{n}_j$. The paper motivates this against two alternatives: perspective projection requires an arbitrary virtual center (LiDAR has none), producing unbalanced near/far-field resolution, and BEV Z-difference splatting assumes locally horizontal roads, introducing systematic error on slopes. Thresholding $h(\mathbf{p})$ at $\pm\epsilon_d$ yields road / positive obstacle / negative obstacle labels.

Experimental results

Evaluation uses TOSeg-Road (Livox Avia, urban) and TOSeg-Offroad (Falcon-K 310-line, mining), totaling 1,270 manually annotated keyframes from 55 sequences, split into flat and bumpy subsets. Against eight baselines, LOGOS achieves the best results everywhere: on TOSeg-Road bumpy, F1 0.957 / IoU 0.918 vs. TA-TOS 0.948 / 0.902; on TOSeg-Offroad bumpy, F1 0.962 / IoU 0.926 vs. TA-TOS 0.939 / 0.885. Parametric baselines degrade severely off-road (Plane-modeling F1 drops to 0.225 on bumpy off-road).

The most consequential results concern robustness:

Condition	TA-TOS IoU	LOGOS IoU
Offroad turning frames	0.720	0.887
Road downsampled to 0.639 pts/m²	0.048	0.823
Offroad downsampled to 0.253 pts/m²	0.189	0.913

On turning frames TA-TOS loses 17% IoU relative to its full-dataset score while LOGOS loses 3%; notably, LOGOS on turning frames (0.887) exceeds TA-TOS on the full off-road dataset (0.870). Under extreme downsampling, TA-TOS collapses catastrophically below roughly 1 pt/m², whereas LOGOS degrades gracefully—at 0.253 pts/m² off-road it still surpasses TA-TOS's full-density performance. The implication is that continuous Gaussian blending effectively interpolates elevation from neighboring point-rich regions, removing the per-cell density dependency that fundamentally limits grid methods.

On mid-road tiny obstacles, gains are real but smaller: positive-obstacle F1 improves from 0.593 to 0.676 (IoU 0.421 → 0.511); negative-obstacle F1 improves from 0.302 to 0.345 (IoU 0.178 → 0.209). Negative obstacle detection remains weak in absolute terms across all methods—the paper concedes this task is intrinsically hard because subtle depressions are smoothed out by surface models—and the reported gain, while consistent, is modest.

Ablations isolate module contributions. Without pruning, performance collapses (off-road F1 0.580 with Z-projection), confirming that obstacle-contaminated Gaussians distort the reference surface. A notable negative interaction emerges: without pruning, normal-aware projection performs worse than Z-difference (off-road F1 0.176 vs. 0.580), because obstacle Gaussians produce arbitrary normals that make the projection physically meaningless. Normal-awareness helps only atop a pruned, clean Gaussian set (IoU 0.891 → 0.914 off-road). Runtime on an Apple M1 Pro is 57 ms (road) and 31 ms (offroad) per frame, slightly faster than TA-TOS despite a costlier segmentation stage (33 ms vs. 1 ms on road data), because joint initialization-plus-pruning (24/16 ms) undercuts TA-TOS's separate RANSAC initialization plus MRF refinement (62/34 ms).

Limitations and open questions

Several constraints are explicit or evident. The method depends on hand-tuned parameters ($W$, $S$, $S < W$0, $S < W$1) that differ substantially between datasets (e.g., thresholds 0.05 m road vs. 0.15 m offroad), so cross-domain generalization without retuning is untested. The incremental pruning assumes spatial continuity of the road surface and processes windows in a fixed order; behavior on discontinuous or strongly non-smooth terrain is not analyzed. The segmentation stage scales with point count and Gaussian count, and the evaluation hardware is a laptop-class CPU rather than an embedded platform typical of mining or mobile robots. Evaluation is confined to two datasets from one research group's collection pipeline; independent benchmarking is absent. Open questions include whether the smoothness threshold can be adapted online to varying terrain roughness, and how the approach behaves under sensor noise, dust, or precipitation common in mining environments.

Conclusion

LOGOS demonstrates that a backpropagation-free Gaussian mixture representation of the road surface, obtained through sliding-window MLE with incremental smoothness-based pruning and rendered via normal-aware BEV splatting, outperforms state-of-the-art grid-based tiny obstacle segmentation while running faster than the strongest baseline. Its principal contribution is robustness: accuracy is preserved under point densities and edge-degraded conditions where discrete-grid methods fail outright. The remaining weaknesses—manual parameter tuning per domain, reliance on terrain smoothness assumptions, and still-modest negative obstacle detection—define the concrete boundaries of the claimed improvement.