# A Probabilistic Formulation of LiDAR Mapping with Neural Radiance Fields

arXiv: https://arxiv.org/abs/2411.01725 · HTML: https://mlsanity.com/paper/2411.01725/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 32 references that are in the map.
- First posted on arXiv 4 Nov 2024.

## Builds on (most cited first, 21 of 21)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Mip-NeRF 360: Unbounded Anti-Aliased Neural Radiance Fields](https://mlsanity.com/paper/2111.12077/) (2021)
- [NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collections](https://mlsanity.com/paper/2008.02268/) (2020)
- [Open3D: A Modern Library for 3D Data Processing](https://mlsanity.com/paper/1801.09847/) (2018)
- [BARF: Bundle-Adjusting Neural Radiance Fields](https://mlsanity.com/paper/2104.06405/) (2021)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [Mega-NeRF: Scalable Construction of Large-Scale NeRFs for Virtual Fly-Throughs](https://mlsanity.com/paper/2112.10703/) (2021)
- [Neural LiDAR Fields for Novel View Synthesis](https://mlsanity.com/paper/2305.01643/) (2023)
- [The Newer College Dataset: Handheld LiDAR, Inertial and Vision with Ground Truth](https://mlsanity.com/paper/2003.05691/) (2020)
- [LiDAR-NeRF: Novel LiDAR View Synthesis via Neural Radiance Fields](https://mlsanity.com/paper/2304.10406/) (2023)
- [SHINE-Mapping: Large-Scale 3D Mapping Using Sparse Hierarchical Implicit Neural Representations](https://mlsanity.com/paper/2210.02299/) (2022)
- [NeRF-LiDAR: Generating Realistic LiDAR Point Clouds with Neural Radiance Fields](https://mlsanity.com/paper/2304.14811/) (2023)
- [PIN-SLAM: LiDAR SLAM Using a Point-Based Implicit Neural Representation for Achieving Global Map Consistency](https://mlsanity.com/paper/2401.09101/) (2024)
- [NeRF-LOAM: Neural Implicit Representation for Large-Scale Incremental LiDAR Odometry and Mapping](https://mlsanity.com/paper/2303.10709/) (2023)
- [Generative Range Imaging for Learning Scene Priors of 3D LiDAR Data](https://mlsanity.com/paper/2210.11750/) (2022)
- [PC-NeRF: Parent-Child Neural Radiance Fields Using Sparse LiDAR Frames in Autonomous Driving Environments](https://mlsanity.com/paper/2402.09325/) (2024)
- [Neural Elevation Models for Terrain Mapping and Path Planning](https://mlsanity.com/paper/2405.15227/) (2024)
- [Correcting Motion Distortion for LIDAR HD-Map Localization](https://mlsanity.com/paper/2308.13694/) (2023)

## Built on by (most cited first, 1 of 1)

- [Characterizing Lidar Range-Measurement Ambiguity due to Multiple Returns](https://mlsanity.com/paper/2604.09282/) (2026)

## Abstract (arXiv)

In this paper we reexamine the process through which a Neural Radiance Field (NeRF) can be trained to produce novel LiDAR views of a scene. Unlike image applications where camera pixels integrate light over time, LiDAR pulses arrive at specific times. As such, multiple LiDAR returns are possible for any given detector and the classification of these returns is inherently probabilistic. Applying a traditional NeRF training routine can result in the network learning phantom surfaces in free space between conflicting range measurements, similar to how floater aberrations may be produced by an image model. We show that by formulating loss as an integral of probability (rather than as an integral of optical density) the network can learn multiple peaks for a given ray, allowing the sampling of first, nth, or strongest returns from a single output channel. Code is available at https://github.com/mcdermatt/PLINK