BIEVR-LIO: Robust LiDAR-Inertial Odometry through Bump-Image-Enhanced Voxel Maps (arXiv 2026)

Created on July 09, 2026

2026   ·   lio   slam   terrain   legged   ·   paper-review

Item Details
Authors Patrick Pfreundschuh, Turcan Tuna, Cedric Le Gentil, Roland Siegwart, Cesar Cadena, Helen Oleynikova (ETH Zürich ASL / RSL / MRL)
Venue arXiv preprint 2026 (arXiv:2604.14421, v2 2026-07-02; the formal acceptance venue has not been confirmed)
Links arXiv · Code

One-line Summary

The starting point of BIEVR-LIO is the observation that “LIO dies in geometry-poor environments (straight tunnels, flat fields) not because there are no cues, but because the map resolution is too low to capture the fine bumps”. So instead of collapsing each voxel into a single plane, every voxel stores a high-resolution 2D height image (“bump image”) whose pixels hold the deviation from the dominant plane. The gradient of this image is used as an additional Jacobian direction to constrain directions that point-to-plane could not observe, and combined with map-informed sampling that places more points in high-information voxels, the system shows SOTA robustness across several sensors and platforms with a single parameter set. The code is released under the BSD-3 license and supports ROS1/2.

LIO has become the de facto standard indoors and outdoors, but in geometrically poor environments lacking constraints in certain directions, degeneracy causes accuracy to plummet or the estimate to diverge. Existing paradigms for this problem fall into three broad families.

  1. Degeneracy detection and mitigation: analyze the Hessian/eigenvalues of the registration to find degenerate directions and correct them. X-ICP (T-RO 2023), learning-based localizability (IROS 2022), LA-LIO (2024), LODESTAR (RA-L 2026). Their limitation is that they depend on additional sensor odometry or only survive short degenerate stretches. Interestingly, a co-author of this paper (Tuna) is a principal of this very line, and the perspective has been turned to “do not detect, squeeze out more information in the first place”.
  2. Intensity/reflectivity augmentation: when geometry is lacking, add LiDAR intensity as a photometric cue. RI-LIO (2023), COIN-LIO (ICRA 2024, prior work by this paper’s first author), PG-LIO (2025). Their limitation is the assumption of a dense and regular scan pattern, which makes them unsuitable for sparse/irregular scans such as Livox.
  3. Map representation improvement: the insight that registration quality ultimately depends on the resolution of the map representation. Plane/covariance voxel maps (VoxelMap, iG-LIO) erase detail with one normal/covariance per voxel, and surfel maps (SuMa, SLICT, LIO-MARS) are also planar approximations. Distance-field methods (D-LIO, 2Fast-2Lamaa) are neighbors. The most direct ancestor is CURL-SLAM (T-RO 2025), which compresses the voxel surface with spherical harmonics, approximating the height image by harmonic coefficients. However, harmonic fitting is expensive, so the map cannot be updated at LiDAR frequency, and the approximation is inherently smooth, killing fine cues.

The core shift of BIEVR-LIO is that “uninformative is different from degenerate”. Real-world tunnels and flat fields are, strictly speaking, well-constrained in principle because of fine bumps such as wall cutouts, rail beds, and stone surface irregularities. Existing systems cannot use them because map resolution is insufficient under real-time constraints. So the paper inherits CURL-SLAM’s paradigm of “height image inside a voxel + photometric-style registration” but discards the harmonic-coefficient approximation and stores an explicit high-resolution oriented height image. This choice simultaneously yields constant-time pixel lookup, LiDAR-frequency map updates, and preservation of sharp discontinuities. Also, instead of Hessian-based information sampling (expensive because it needs residuals and correspondences), informative voxels are selected with the MID (Mean Image Distance) metric precomputed in the map.

The formal acceptance venue and citation count have not been confirmed (arXiv only). The comparison baselines themselves form the current LIO SOTA landscape: KISS-ICP, GenZ-ICP, Traj-LO, FAST-LIO2, DLIO, iG-LIO, RESPLE, RKO-LIO, COIN-LIO.

Problem and Motivation

  • What was unsolved: in environments without geometric constraints in certain directions, such as straight tunnels and wide flat fields, LIO drifts or diverges. As LIO spreads into consumer products such as robotic lawn mowers, robustness on low-cost sparse sensors (Livox) has become urgent.
  • Why existing solutions fall short: degeneracy detection handles only short stretches or depends on extra sensors, intensity augmentation presupposes dense sensors, and representation improvements (planes, surfels, harmonic compression) erase fine geometry through approximation.
  • Key observation: even seemingly uninformative environments are actually constrained by fine bumps, so geometry-only registration is possible if the representation resolution is sufficient. The question is how cheaply high resolution can be maintained and queried under real-time constraints.

Key Ideas and Method

In one sentence: each voxel holds a high-resolution oriented height image of deviations from the dominant plane, enabling direct scan-to-map registration without computing intermediate geometric primitives; the gradient of that height image constrains directions that point-to-plane misses; and the MID metric concentrates point sampling in informative regions. The pipeline is loosely coupled. The pose is produced solely by registration, and the IMU is used only for undistortion, the prior, and bias estimation.

BIEVR representation: voxel = plane + bump image

The iterative plane estimation borrows the voxel update strategy of iG-LIO. As points accumulate in a 0.5m voxel, the sum \(\mathbf{s}\), the outer-product sum \(\mathbf{C}\), and the count \(n\) are updated in parallel to obtain the centroid \(\boldsymbol{\mu}\) and covariance \(\boldsymbol{\Sigma}\). The eigenvector of the smallest eigenvalue of \(\boldsymbol{\Sigma}\) becomes the voxel normal, and a voxel frame is defined with it as the z-axis.

The bump image is initialized once 4 or more points have accumulated. The 8 corners of the voxel are projected onto the plane (x-y) to determine the required image size W, H (pixel resolution \(r = 0.05\)m), and each input point is projected to pixel \((u,v)\) with its height above the plane \(z\) accumulated as a weighted average pixel value. Points closer to the LiDAR receive a larger confidence weight.

\[w_i = \min\left(0.5,\ \frac{1}{d_i}\right)\]

A 1-pixel Gaussian filter is applied to mitigate noise, and if the normal changes by more than 3°, the frame is updated and the points are re-projected. Intuitively, it is a “terrain relief stamp” of the voxel viewed head-on. The plane is the stamp base, and the bump image is the fine undulation on it. Information that the planar approximation throws away is captured as pixels.

The implementation is a Morton-code hash map (O(1) lookup), storing per voxel the transform, the image, pixel weights, statistics, and MID. Updates are parallel, and an LRU cache bounds memory.

Map-informed dual-resolution sampling

MID (Mean Image Distance) is the mean of \(\lvert I(u,v)\rvert\) over the observed pixels. It is small when flat and large when bumpy, so it serves as a non-planarity metric and an indicator of informative Jacobian potential. Because it is precomputed during map updates, no extra computation is needed during sampling. This is a major advantage over Hessian-based methods.

Sampling is two-stage. The input scan is downsampled to 0.1m, the voxel of each point is looked up, and all points in the top-300 MID voxels are kept. The rest are coarsely downsampled to 0.5m. Points are used densely in informative regions and sparsely elsewhere, reducing the point count by roughly 4 times as a result.

Loosely-coupled state estimation

The state is \(\mathbf{x} = [\mathbf{R}_{GI}, \mathbf{t}, \mathbf{v}, \mathbf{b}_a, \mathbf{b}_g, \mathbf{g}]\), living on \(SO(3)\times\mathbb{R}^{12}\times S^2\).

Why loosely coupled: tight coupling requires tuning the modality weights, and in low-structure segments the inertial residual dominates the optimization and overwhelms the subtle registration cues. Since the goal of this paper is to preserve fine geometry, the pose is produced solely by registration and only the remaining states are optimized separately.

IMU prediction and undistortion use Le Gentil’s piecewise-linear continuous-time preintegration to obtain \(\Delta\mathbf{R}\) and \(\Delta\mathbf{p}\), which are used for per-point undistortion and the registration prior.

Registration is CURL-SLAM-style “virtual image photometric minimization”. The residual of each point is the difference between its height above the plane and the bilinearly interpolated image value.

\[r_i = z_i - I(u_i, v_i)\]

If all four surrounding pixels are unobserved, the point is excluded. Levenberg-Marquardt is used with a Huber loss (\(\delta = 0.1\)m). The key is the two-component Jacobian. The first component is along the plane normal and is identical to classical point-to-plane. The second component consists of two directions derived from the height-image gradient \(\partial I/\partial \boldsymbol{\xi}\), capturing how the pixel value changes when the point moves parallel to the plane. This second component injects information into directions that point-to-plane could not observe, and is the source of robustness in uninformative regions. The ablation proves that this term is decisive.

In the sliding-window inertial optimization, the poses are fixed (anchored) and only velocity, gravity, and biases are optimized within a 10-second window (gravity and biases are constant within the window). Inertial consistency is maintained without covariance tuning.

Experiments and Results

Compute is an Intel i7-11800H CPU only (no GPU needed), and per-frame time is around 12.8 to 29.8ms (varying with sensor and environment), i.e. real time. A single parameter set was used for all experiments: voxel 0.5m, bump resolution 0.05m, coarse/fine downsample 0.5/0.1m, 300 fine voxels, Huber \(\delta = 0.1\)m, IMU window 10s. The absence of per-scene or per-dataset tuning is the key basis for the generalization claim.

Sensors and platforms cover dense, sparse, and low-resolution cases: Ouster OS0-128 (handheld), Livox Avia (handheld/UGV/UAV), Livox Mid-360 (quadruped), and Hesai XT32 + Honeywell IMU (quadruped). The datasets are five: Newer College (rich structure + narrow stairs), ENWIDE (weak structure, the authors’ prior work), GEODE (tunnel/off-road degeneracy benchmark), MARS-LVIG (high-altitude sparse UAV), and GrandTour (low-resolution quadruped). The metrics are ATE RMSE (m) and 10m-segment relative error RE (%), with RE above 20% counted as failure.

The three key results are as follows.

  1. Sole survivor on degenerate benchmarks. On ENWIDE and GEODE, BIEVR is the only geometry-only method stable on all sequences, with the lowest error on most. There is no noticeable drift over 700m of GEODE Shield (a straight subway tunnel). FAST-LIO2, iG-LIO, DLIO, and others diverge.
  2. Beats COIN-LIO without intensity. On ENWIDE it is more accurate than the intensity-based prior work COIN-LIO on all sequences except RunwayD (gyroscope saturation). On GEODE Tunneling2 (a segment staring straight at a wall) it achieves the lowest ATE thanks to stone surface irregularities.
  3. SOTA in well-constrained environments too, with a single parameter set. Lowest on Newer College Cloister at 0.053m and Stairs at 0.056m (FAST-LIO2 diverges on Stairs). In the narrow sections of GrandTour ARC-4 and LEE-1, FAST-LIO2 and iG-LIO drift while BIEVR is the lowest.
Dataset / Sequence ATE (m) RE (%) Note
Newer College Cloister 0.053 0.2 Lowest
Newer College Stairs 0.056 0.6 Lowest, FAST-LIO2 diverges
Newer College Park 0.798 0.6 FAST-LIO2 0.31, COIN-LIO 0.287 are better
ENWIDE FieldS 0.159 0.3 Lowest
ENWIDE RunwayD 4.35 10.8 Gyroscope saturation, RE consistent
GEODE Shield1 0.256 - Most competitors fail
GEODE Tunneling2 0.096 - Lowest
MARS-LVIG FeaturelessGNSS02 4.93 12.9 Sole survivor

Weaker cases are honestly reported as well. On Newer College Park, MARS-LVIG AMtown02, and HKisland it is similar to or slightly behind the baselines; sparse high-altitude flight is not the sweet spot of this method.

The ablation supports the design claims. On Shield1, the Plane map diverges; even the BIEVR map diverges without the \(\partial I/\partial \boldsymbol{\xi}\) term; enabling this term gives 0.401m, and adding map-informed sampling gives 0.256m. That is, the height-image gradient term is the decisive factor for surviving degeneracy. In the sampling comparison, map-informed (ID) reduced the point count by about 4 times versus fixed high-resolution (HR) (13907 to 5039) and reduced runtime (15.7 to 12.8ms) while improving accuracy. Random (RD) was the worst, so selection “based on map structure” is the essence. In the sensitivity experiment in the appendix, Shield1 diverged at a bump resolution of \(r = 0.15\)m, survived at 0.1m, and was optimal at 0.05m. This empirically shows that high resolution is decisive for extracting fine constraints.

Reviewing the claimed contributions: the effect of the BIEVR representation and MID sampling is sufficiently supported by ablation. The single-parameter generalization is also highly convincing; since the baselines used per-sensor tuning it is not a perfectly symmetric comparison, but the setting is unfavorable to BIEVR, which makes it fairer if anything. “Surpassing COIN-LIO without intensity” is conditional. For ENWIDE Tunnel, which lacks even fine geometry, the authors themselves admit that geometry alone is insufficient. The weak points are that the justification of the loosely-coupled choice is qualitative (tight vs loose was not ablated in the same pipeline), and that CURL-SLAM’s code is not public so only the paper’s numbers were cited.

Conclusion and Significance

The core message of BIEVR-LIO is a shift in perspective: “robustness in uninformative environments is not a matter of detecting and correcting degeneracy, but of squeezing out the fine geometry that already exists through the resolution of the map representation”. With the representation of a high-resolution oriented height image per voxel, it preserves the fine undulations that planes, surfels, and harmonic compression erased, while keeping constant-time lookup and LiDAR-frequency updates, and it uses the height-image gradient as an additional Jacobian direction to constrain directions that point-to-plane could not observe. Achieving this geometry-only, without an additional modality such as intensity, so that it applies to sparse/irregular low-cost sensors, is significant for the field. As a by-product, it shows on a real robot that this high-resolution map replaces a separate depth-camera elevation map and can be used directly for quadruped foothold planning, suggesting the possibility of unifying the odometry map and the locomotion terrain representation.

From a robotics practice perspective, the takeaways are as follows.

  • Where it can be used: in autonomous mobile-robot navigation in multi-floor indoor buildings with poor structure such as corridors, lobbies, and elevator halls, there is room to reduce drift compared to existing planar-voxel methods (FAST-LIO2 and others). The GrandTour narrow-section results, where FAST-LIO2 and iG-LIO drift and BIEVR survives, correspond directly. The GEODE Offroad and MARS-LVIG Featureless results relate to degeneracy in unstructured outdoor terrain driving.
  • Integration with terrain representation: with a Livox Mid-360, an elevation map for quadruped footholds was extracted from the odometry map in about 1ms, replacing the depth camera. Unifying traversability/elevation map generation for unstructured outdoor terrain driving with the LIO map in one representation could reduce the burden of a separate elevation pipeline.
  • A LiDAR-only version of the direct philosophy: it reproduces the FAST-LIVO family’s idea of “direct (photometric) registration without intermediate primitives” without a camera, via photometric-style registration on LiDAR height images. This is attractive to teams that want the benefits of direct methods without dependence on cameras and lighting. Note, however, that it uses loosely-coupled LM+Huber, so its structure differs from the FAST-LIO2/ikd-Tree stack.
  • Adoption difficulty: the official repo v1.0.0 (BSD-3, ROS1/2, Docker, per-dataset preset configs) is complete, and being CPU-only and tuning-free, reproduction difficulty is on the low side. Extrinsic and time-sync calibration of one’s own sensors is the main work. As a first attempt, it is reasonable to run an indoor narrow-section rosbag based on the GEODE Shield preset and compare ATE/drift against FAST-LIO2.
  • Limitations: there is no infilling, so empty pixels cannot be used, and performance degrades with low-resolution LiDAR or fast motion due to unfilled pixels (the authors propose a multi-scale image pyramid). For pixel residuals to be meaningful, the IMU prior must be good enough, making it vulnerable to initialization failure or large gyroscope saturation. Completely featureless environments lacking even fine geometry are impossible geometry-only and require intensity. There is no degeneracy detection, so there is no safety judgment about “when not to trust it”, and dynamic objects are not modeled, so the downstream elevation map can be contaminated.

References

  • Paper: arXiv:2604.14421
  • Code: ethz-asl/bievr-lio (BSD-3-Clause, ROS1/2, v1.0.0)
  • CURL-SLAM (T-RO 2025) — the direct predecessor of the “height image inside a voxel + photometric-style registration” paradigm
  • iG-LIO (RA-L 2024) — source of the iterative voxel plane/normal update strategy, and a baseline
  • COIN-LIO (ICRA 2024) — the first author’s intensity-based prior work
  • X-ICP (T-RO 2023) — localizability-aware registration, representative of the degeneracy-detection family
  • GEODE Dataset (IJRR 2026) — tunnel/off-road degeneracy benchmark