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NeRF-LOAM: Neural Implicit Representation for Large-Scale Incremental LiDAR Odometry and Mapping

Junyuan Deng, Xieyuanli Chen, Songpengcheng Xia, Zhen Sun, Guoqing Liu, Wenxian Yu, Ling Pei

arXiv:2303.10709v1cs.CV

TL;DR

Simultaneous LiDAR odometry and mapping supports autonomy in large-scale environments, but outdoor mapping poses challenges for SDF-based methods. NeRF-LOAM jointly optimizes poses and neural voxel embeddings, and the paper reports higher-quality mesh maps and generalization without pre-training.

  • Problem

    Simultaneous odometry and mapping supports autonomy in large-scale environments, while SDF approximations can produce inaccurate values for far LiDAR points and weaken outdoor odometry, especially along Z.

    Source: §1 · p. 1, §3 · p. 3

  • Method

    NeRF-LOAM uses a neural SDF with voxel embeddings and jointly optimizes scan poses, embeddings, and network parameters for incremental outdoor LiDAR mapping.

    Source: §1 · p. 2, §3 · p. 3

  • Results

    NeRF-LOAM reconstructs higher-quality 3D mesh maps than other learning-based or non-learning-based methods and estimates accurate poses while generalizing across situations.

    Source: §6 · p. 8

  • Takeaways & Limitations

    The online joint optimization avoids pre-training and supports generalization to different environments.

    Source: §1 · p. 2

    The unoptimized Python implementation cannot currently operate in real time, with ray–map intersection queries identified as the primary bottleneck.

    Source: §6 · p. 8

Abstract

from arXiv · show

Simultaneously odometry and mapping using LiDAR data is an important task for mobile systems to achieve full autonomy in large-scale environments. However, most existing LiDAR-based methods prioritize tracking quality over reconstruction quality. Although the recently developed neural radiance fields (NeRF) have shown promising advances in implicit reconstruction for indoor environments, the problem of simultaneous odometry and mapping for large-scale scenarios using incremental LiDAR data remains unexplored. To bridge this gap, in this paper, we propose a novel NeRF-based LiDAR odometry and mapping approach, NeRF-LOAM, consisting of three modules neural odometry, neural mapping, and mesh reconstruction. All these modules utilize our proposed neural signed distance function, which separates LiDAR points into ground and non-ground points to reduce Z-axis drift, optimizes odometry and voxel embeddings concurrently, and in the end generates dense smooth mesh maps of the environment. Moreover, this joint optimization allows our NeRF-LOAM to be pre-trained free and exhibit strong generalization abilities when applied to different environments. Extensive evaluations on three publicly available datasets demonstrate that our approach achieves state-of-the-art odometry and mapping performance, as well as a strong generalization in large-scale environments utilizing LiDAR data. Furthermore, we perform multiple ablation studies to validate the effectiveness of our network design. The implementation of our approach will be made available at https://github.com/JunyuanDeng/NeRF-LOAM.

1. Introduction

Large-scale LiDAR odometry and mapping matters for autonomy, but existing methods often prioritize tracking over dense reconstruction, while NeRF-based approaches have focused on indoor RGB-D settings. NeRF-LOAM targets incremental outdoor LiDAR with joint neural optimization, dynamic voxel embeddings, and key-scan refinement, and is reported to achieve state-of-the-art odometry and mapping performance.

1. Introduction

  • Existing LiDAR methods often prioritize tracking quality over dense reconstruction, while prior NeRF approaches focus on indoor RGB-D settings that are difficult to extend to sparse outdoor LiDAR.The paper identifies large-scale incremental LiDAR odometry and mapping as an unresolved problem.Source: §1 · p. 1
  • NeRF-LOAM is reported to achieve state-of-the-art odometry and mapping performance in outdoor large-scale environments using LiDAR data.The method was evaluated on three publicly available datasets.Source: §1 · p. 2
  • NeRF-LOAM jointly optimizes poses, voxel embeddings, and a neural implicit decoder by minimizing signed-distance-function errors.Its neural SDF separates ground and non-ground points; ground-point normals support a precise SDF intended to reduce Z-axis drift and smooth the dense map.Source: §1 · p. 2
  • The method combines dynamic voxel-embedding generation with key-scan refinement to allocate embeddings quickly and produce a high-fidelity 3D representation.The key-scan strategy also helps avoid catastrophic forgetting or a pre-training process.Source: §1 · p. 2
  • The authors report that online joint optimization makes NeRF-LOAM pre-training-free and able to generalize across different environments.They describe the method as the first neural implicit odometry-and-mapping method for large-scale environments using LiDAR data.Source: §1 · p. 2

2. Related Work

Prior outdoor LiDAR work includes odometry-focused methods and scene representations, while dense reconstruction from incremental LiDAR and outdoor neural implicit mapping remain open challenges. NeRF-LOAM contrasts with earlier approaches by using local voxel embeddings, dynamic allocation, and key-scan refinement for incremental large-scale LiDAR.

2. Related Work

  • ICP-based methods align consecutive point clouds for relative scan motion, but these and related geometry-driven approaches mainly target odometry and yield coarse maps.Learning-based LiDAR odometry methods learn features from points or projected 2D images.Source: §2 · p. 2
  • Learned LiDAR odometry methods may require large training datasets and generalize poorly to other environments.This contrasts with the paper's reported ability to generalize across environments without pre-training.Source: §2 · p. 2
  • Prior reconstruction work spans surfels, occupancy grids, meshes, polynomial representations, and learning-based approaches, but dense reconstruction from incremental 3D LiDAR remains unexplored.The cited approaches include Poisson surface reconstruction and TSDF-based volumetric integration.Source: §2 · p. 2
  • Neural SLAM methods largely target images or indoor RGB-D, while outdoor LiDAR sparsity and octree allocation or search constraints hinder extension to large areas.Some octree-based methods use pre-allocated embeddings or time-consuming voxel search.Source: §2 · p. 2
  • NeRF-LOAM instead uses local voxel embeddings with an MLP decoder, dynamic embedding generation, and key-scan refinement for incremental large-scale LiDAR mapping.The authors state that these design choices support generalization, reduce processing time, and improve reconstruction quality.Source: §2 · p. 2

3. Our Neural SDF

NeRF-LOAM represents outdoor geometry with an octree-based neural SDF whose voxel embeddings, decoder, and scan poses can be optimized jointly. Ground separation and ray-based sampling adapt the SDF supervision to sparse LiDAR and support pose optimization.

  • The neural SDF decodes shared vertex embeddings on octree voxels into a continuous field, with embeddings and network parameters optimized jointly through back-projection.The field is queried by trilinearly interpolating neighboring voxel embeddings at sampled points.Source: §3 · p. 3
  • Sampling rays through currently allocated voxels and points along their voxel intersections lets scan pose and voxel embeddings be optimized simultaneously.A voxel hit threshold excludes samples influenced by unseen surfaces.Source: §3 · p. 3
  • Ground and non-ground points receive different SDF targets, using ground normals to rectify distances and address inaccurate estimates that can worsen Z-axis drift.The paper identifies far LiDAR points and near-grazing rays as cases where endpoint-distance approximations can be inaccurate.Source: §3 · p. 3
  • Training combines a free-space loss toward truncation distance with an SDF supervision loss inside the truncation region.The negative truncation region is omitted to avoid surface-intersection ambiguities; the authors also describe this loss as important for removing dynamic objects.Source: §3 · p. 3
  • Points within the truncation region are treated equally, and an Eikonal loss is added because SDF values are differentiable and equal to one there.This differs from approaches [27] [50] that increase weighting around LiDAR points.Source: §3 · p. 4

4. NeRF-LOAM Framework

NeRF-LOAM processes an incremental LiDAR stream through parallel neural odometry and mapping, followed by key-scan refinement and mesh reconstruction. The framework estimates scan poses and a global mesh map while dynamically extending and jointly optimizing its voxel map.

4.1. Overview

  • Three modules turn incremental LiDAR scans into scan poses and a reconstructed mesh: neural odometry and mapping run in parallel, while mesh reconstruction separately produces a global map and refined poses.Mapping uses key scans to refine the odometry and map; marching cubes converts predicted SDF values into the mesh.Source: §4.1 · p. 4

4.2. Neural Odometry

  • Neural odometry estimates each scan’s 6-DoF pose by back-projecting SDF loss gradients, using the previous mapping network and voxel embeddings.A constant-move model initializes the pose; after K scans, network parameters are frozen to address catastrophic forgetting, with early poses and embeddings refined later.Source: §4.2 · p. 4

4.3. Neural Mapping

  • Neural mapping adds newly encountered voxels and embeddings to an octree, then jointly optimizes map embeddings while fine-tuning poses.A lookup table indexed by Morton codes is designed for dynamic embedding access; key scans are selected by newly added voxel count or distance and later refine the map and poses.Source: §4.3 · pp. 4–5, §4.4 · p. 5

4.4. Mesh Reconstruction

  • After key-scan refinement, the continuous SDF is queried at fixed voxel-size intervals and marching cubes generates the final mesh.Refinement includes only rays or LiDAR points within a truncation distance based on point density.Source: §4.4 · p. 5

5. Experiments

Experiments compare NeRF-LOAM with existing methods on three outdoor LiDAR datasets, evaluating odometry and mesh reconstruction. Results include competitive or superior benchmark performance and ablations of ground separation, key-scan refinement, and voxel size.

5.1. Experimental Setup

  • Evaluation uses MaiCity, Newer College, and KITTI, with trajectory RMSE for odometry and four mesh-reconstruction metrics for mapping.KITTI lacks ground-truth maps, so mapping results there are qualitative; Newer College scans are sampled at one in five for greater challenge and distinction.Source: §5.1 · p. 5

5.2. Simultaneously Odometry & Mapping Results

  • On MaiCity, NeRF-LOAM mapping with KissICP poses outperforms all baselines, while Newer College quality is comparable; against Puma, it performs better in almost all metrics.Qualitative results also show smoother maps with most artifacts removed; Table 1 covers map accuracy, completion, Chamfer-L1 distance, and F-scores.Source: §5.2 · pp. 5–6, Table 1 · p. 6, Figure 5 · p. 6

5.3. Mapping Quality

  • With ground-truth poses, NeRF-LOAM outperforms mapping baselines across almost all metrics, with especially complete ground reconstruction even from sparse, noisy Newer College observations.Error maps against ground-truth meshes indicate greater reconstruction accuracy.Source: §5.3 · p. 6, Figure 6 · p. 7, Figure 7 · p. 7

5.4. Odometry Evaluation

  • Odometry is comparable on MaiCity and KITTI, and best on Newer College; pre-trained DeLORA and PWC-LONet perform worse on other datasets, with PWC-LONet nearly failing on Newer College.NeRF-LOAM requires no pre-training and generalizes across datasets.Source: §5.4 · pp. 6–7, Table 3 · p. 8

5.5. Ablation Study

  • Ground separation improves odometry and mapping accuracy, with the approach failing on Newer College without it; key-scan refinement produces smoother, more complete maps of roads, walls, and vehicles.Source: §5.5 · p. 7

6. Conclusion

NeRF-LOAM jointly estimates poses and reconstructs outdoor maps from incremental LiDAR without offline pre-training. Experiments report higher-quality mesh maps and accurate poses, while runtime and long-term loop consistency remain limitations.

  • Experiments on simulated and real-world datasets found higher-quality 3D mesh maps than learning-based and non-learning-based methods.Source: §6 · p. 8
  • NeRF-LOAM jointly estimates poses and records geometry in voxel embeddings without offline pre-training, generalizing across different situations.Source: §6 · p. 8
  • The unoptimized Python implementation cannot run in real time, and loop closures remain future work for addressing long-term tracking and mapping drift.The primary runtime bottleneck is the ray-map intersection query.Source: §6 · p. 8
  • The authors identify accurate trajectories and dense environmental maps as important for safety-critical applications such as autonomous cars.Source: §6 · p. 8

A. Simultaneously Odometry & Mapping Results

The qualitative comparisons show NeRF-LOAM producing detailed, complete, smooth maps, including in large-scale KITTI sequences. The method does not maintain a consistent global map on trajectories with loops.

A. Simultaneously Odometry & Mapping Results

B. Mapping Quality

With ground-truth poses on MaiCity, NeRF-LOAM produces the most complete and smooth map among the compared methods. The ablation study covers ground separation, key-scan refinement, and ground-truth pose use.

B. Mapping Quality

  • SHINE-Mapping produces a relatively complete but insufficiently smooth map, while Vdbfusion is smoothest but incomplete.Source: B. Mapping Quality · p. 12
  • NeRF-LOAM provides the most complete and smooth reconstruction in the MaiCity comparison using ground-truth poses.Figure 16 presents a bird's-eye view of the reconstruction.Source: B. Mapping Quality · p. 12
  • The MaiCity and Newer College ablation study examines ground separation, key-scan refinement, and use of ground-truth poses.Source: Table 6 · p. 12

C. Odometry Evaluation on KITTI Dataset

On KITTI, NeRF-LOAM has comparative odometry performance against non-learning methods and outperforms them on some sequences. It requires no pre-training on numerous labeled data and is reported to generalize across sequences and large-scale environments.

C. Odometry Evaluation on KITTI Dataset

  • NeRF-LOAM shows comparative KITTI odometry performance against non-learning methods and outperforms them on some sequences.Source: C. Odometry Evaluation on KITTI Dataset · p. 12
  • Unlike learning-based methods that require numerous labeled data for pre-training, NeRF-LOAM can be directly employed in other environments.The authors identify this as important when adequate data or ground-truth labels are lacking, or when exploring unknown environments.Source: C. Odometry Evaluation on KITTI Dataset · p. 12
  • The paper presents qualitative odometry-mapping results on the KITTI [11] dataset, with visual outputs shown across sequences 00, 01, 03, 04, 05, 09, and 10.Source: Figure 15 · p. 13

D. Additional Ablation Study

The ablations examine ground separation, key-scan refinement, voxel size, and network design, identifying choices that balance odometry and mapping quality with efficiency. They also flag loop detection as future work.

D. Additional Ablation Study

  • Ground separation improves odometry, especially along the z-axis, as also illustrated by the trajectory comparison.The study compares trajectories with and without ground separation against ground truth.Source: D. Additional Ablation Study · p. 13, Figure 18 · p. 14
  • Key-scan refinement greatly improves mapping without ground-truth poses, while ground-truth poses significantly affect mapping, especially around loops.With ground-truth poses, refinement's improvement is slight, but it is retained to help produce smooth, complete maps.Source: D. Additional Ablation Study · p. 13
  • Loop detection remains future work; loops are associated with overlapping meshes.The authors identify loop detection as an important task for future work.Source: D. Additional Ablation Study · pp. 13–14
  • The qualitative odometry results compare NeRF-LOAM trajectories with ground truth across eight KITTI sequences.The sequences shown are 00, 01, 03, 04, 05, 07, 09, and 10.Source: Figure 17 · p. 14
  • At a 20 cm voxel size, processing time decreases while accuracy remains; the processing-time and accuracy trends cross between 15 and 20 cm.The voxel-size study also considers memory consumption on Maicity.Source: D. Additional Ablation Study · p. 14, Figure 19 · p. 14
  • With larger voxels, completion distance decreases while Chamfer-L1 distance stays almost invariant, motivating the 20 cm choice.The authors note that smaller voxels yield finer reconstruction, while larger voxels can make it more complete.Source: D. Additional Ablation Study · p. 14, Figure 20 · p. 14
  • A 16-dimensional embedding and a 2-layer, 256-hidden-unit network are chosen for generalization, tracking and mapping performance, and time efficiency.Deeper networks with more hidden units consume more time; shorter embeddings can be unstable across network choices.Source: D. Additional Ablation Study · pp. 14–15, Figure 21 · p. 15
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