LF-GICP: Parameter-Free Degeneracy-Aware LiDAR Odometry via a Voxel-Normal Localizability Field

Eunsoo Im

cs.ROAug 20, 2026

LF-GICP: Parameter-Free Degeneracy-Aware LiDAR Odometry via a Voxel-Normal Localizability Field

Authors: Eunsoo Im

Abstract

Scan-to-map LiDAR odometry drifts unboundedly along the unobservable axes of geometrically degenerate environments like tunnels and corridors, and existing degeneracy handling requires environment-specific parameter tuning. This paper presents a parameter-free approach. We show that in voxelized GICP the Gauss--Newton (GN) Hessian masks translational degeneracy, because covariance regularization keeps the translation block artificially well-conditioned. We bypass this with a regularization-free voxel-normal localizability field and two of its statistics: a normalized fraction $f_0$ detecting directional anisotropy, and an absolute per-voxel mass $λ_0$ distinguishing information absence (tunnels) from dilution (dense open scenes). A temporal-median gate combines both to trigger Fisher-information correspondence weighting. Calibrated once by fixed rules on two short sequences and then frozen, LF-GICP achieves the lowest KITTI relative translation error ( $0.865\%$ ) under an identical evaluation protocol against re-run baselines, outperforms them on GEODE tunnels and MulRan, leads the HeLiPR mean, and generalizes across four sensor types without re-tuning. We further demonstrate empirically that straight, uniform tunnels remain unobservable along their axis for LiDAR-only registration.

Figures & tables

Fig. 1: GEODE Urban_Tunnel02 under the same frozen configuration as the KITTI evaluation (Sec. IV-B ). (a) Aligned trajectories (500-frame GT horizon): KISS-ICP drifts laterally while LF-GICP tracks ground truth. (b) $f_{0}$ : the median gate detects the tunnel without an environment flag or site-specific threshold.

Panel of Figure 2 — Fig. 2: LF-GICP overview. From the accumulated voxel map— before covariance regularization—we build the localizability field $\bm{M}$ and its two statistics: the anisotropy fraction $f_{0}$ and the absolute weak-axis mass $\lambda_{0}$ that separates information absence from dilution . A trailing-median gate with hysteresis activates Fisher-information weighting only under genuine absence; diluted or well-conditioned scenes run the loop (top, blue) untouched.

Fig. 3: Sequence medians of $(f_{0},\lambda_{0})$ across five benchmarks and four sensor types. $f_{0}$ alone cannot separate tunnels (absence) from anisotropic but data-rich scenes (dilution); $\lambda_{0}$ bifurcates the classes with a wide margin around the calibrated $\tau_{2}$ . Mitigation triggers only in the shaded region.

Fig. 4: Full-sequence ATE on MulRan and HeLiPR (Table II visualized), including the deskewed vanilla VGICP backend. GenZ-ICP requires 177–185 GB peak RSS on the four large-area HeLiPR sequences.

Seq	frames	LF-GICP	VGICP	KISS-ICP	GenZ-ICP
00	4541	0.692	1.062	0.906	0.924
01	1101	1.822	2.390	2.120	2.238
02	4661	1.084	1.429	1.227	1.133
03	801	1.207	1.165	1.071	1.050
04	271	0.814	1.065	0.928	0.935
05	2761	0.577	0.841	0.778	0.666

TABLE I: KITTI full-sequence relative translation error (%) under a single configuration and identical raw scans (best in bold ): 9/11 wins,

-

17.9%/

-

16.3% average error vs. re-run KISS-ICP/GenZ-ICP, and

-

28% vs. the vanilla VGICP backend [ 15 ] without degeneracy handling. The

\lambda_{0}

condition prevents false triggers on open roads (

\leq

8% of frames). See Sec. IV-A for the KITTI protocol note.

	Seq (frames)	LF-GICP	VGICP	KISS-ICP	GenZ †
MulRan	DCC01 (5409)	11.45	15.43	16.87	13.92
MulRan	KAIST01 (8142)	11.30	13.32	29.32	13.33
HeLiPR	DCC04 (7857)	2.26	3.49	2.19	8.51
	DCC05 (10810)	1.59	1.75	2.03	7.33
	KAIST04 (12613)	2.97	4.22	3.72	5.07
	KAIST05 (12477)	3.20	3.10	4.57	8.22

TABLE II: Full-sequence ATE (m) on MulRan (OS1-64) and HeLiPR (OS2-128), single frozen motion-compensated configuration (best in bold ). VGICP is the deskewed vanilla backend without degeneracy handling.

\dagger

runner without deskewing; the four large-area HeLiPR sequences additionally require 177–185 GB peak RSS due to unbounded map growth.

Fig. 5: Full-sequence trajectories, single frozen configuration (Umeyama-aligned; ATE in parentheses; $\blacktriangle$ = start). (a) MulRan KAIST01 (8142 frames, OS1-64): KISS-ICP accumulates heading drift over repeated campus loops. (b) HeLiPR RIVER04 (6114 frames, OS2-128); GenZ-ICP (15.9 m) omitted for clarity.

Sequence	LF-GICP	VGICP ‡	KISS-ICP	GenZ-ICP
Urban_Tunnel01	0.83	0.99	1.91	1.36
Urban_Tunnel02	1.93	2.66	13.70	10.90
Urban_Tunnel03	5.20	3.65	5.45	5.37

TABLE III: GEODE Urban Tunnel ATE (m) at a 500-frame horizon under a single configuration (best in bold ).

\ddagger

vanilla VGICP diverges by 182–502 m over the full sequences.

Regularization $\beta$	0.1	0.5	1.0	2.0
Tunnel03 Hessian $\lambda_{\min}/\mathrm{tr}$	0.316	0.314	0.316	0.324
Tunnel03 $f_{0}$ (Ours)	0.157	0.138	0.128	0.125
KITTI seq00 ATE (m)	0.401	0.374	0.349	0.318

TABLE IV: Regularization sweep: the Hessian fraction stays flat while

f_{0}

exposes the tunnel degeneracy throughout.

Strategy	KITTI (%)	Tunnel03 (m)
$\gamma{=}1$ , $\lambda_{0}$ gate (Ours)	0.865	5.20
$\gamma{=}1$ , $f_{0}$ -only gate	0.922	5.20
Blend ( $\gamma{<}1$ ), $f_{0}$ -only	$\approx$ 0.88	6.83

TABLE V: Mitigation strength ablation on KITTI (avg. relative error) and GEODE Tunnel03. Best results are in bold .

Class	Parameter	Value / rule
Auto	mitigation on/off	$\mathrm{med}_{W}(f_{0}),\mathrm{med}_{W}(\lambda_{0})$ gate, Alg. S1
	degenerate axis $\bm{u}$	null eigenvector of $\bm{M}$ ( 5 )
	deskew motion	constant-velocity prediction
Global	anisotropy enter $\tau_{\text{on}}$	$0.165$
	anisotropy exit $\tau_{\text{off}}$	$0.185$ (robust preset: $0.30$ )
	absence threshold $\tau_{2}$	$0.0143$

TABLE SI: Complete parameter set. Auto = data-driven per frame; Global = one value frozen across all datasets/sensors (derived from the two calibration traces); Sensor = per sensor class.

Fig. S1: Motion compensation on MulRan (azimuth-reconstructed per-point times): deskewing is the dominant correction for the point-to-distribution backend, independent of degeneracy handling.

Fig. S2: KITTI full-sequence relative translation error per sequence (main-paper Table I visualized), including the vanilla VGICP backend without degeneracy handling.

Fig. S3: SubT rock mine failure case. Top: the gate triggers accurately on tunnel entry. Bottom: LF-GICP error growth stems from the representation limit of Gaussian voxel maps, not a detection failure.

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Sep 15, 2026J/K move · Enter open · S save

LiLi: Lie Theory Based 3D LiDAR Scan Alignment Degeneracy Detection

Vsevolod Hulchuk, Jan Bayer, Jan Faigl

Faculty of Electrical Engineering, Czech Technical University, Technická 2, 166 27, Prague, Czech Republic

LiDAR Odometry Lie Group Methods Point Cloud Registration LiDAR Localization

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In this paper, we study 3D LiDAR scan alignment in challenging scenarios with degeneracies, such as straight corridors or flat fields, where the alignment solution is not unique and compromises localization and mapping accuracy. Existing degeneracy detection methods that neglect the potential for reassociating data points are prone to being sensitive to noise and complex degeneracies. Therefore, we propose LiLi - a novel method that leverages Lie theory to identify the full set of degenerate transformations within the SE(3) Lie group of rigid transformations. The method employs perturbations of the optimized solution and compares the resulting optimized poses to ensure robust detection of degeneracies. By leveraging generators from the Lie algebra se(3), the method provides a systematic approach to describing the set of degenerate transformations. Quantitative evaluations on synthetic data show significant improvement over the state-of-the-art Hessian-based method, reducing alignment error by 50%, with more significant improvements for datasets featuring noise. In the real-world degenerate datasets, the proposed method integrated into LiDAR-based odometry yields superior localization performance compared to the reference solution based on the Hessian-based degeneracy detector on a 260 m long trajectory, and succeeds on a 430 m long round-trip tunnel trajectory where the reference fails.

Abstract

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