A Probabilistic Formulation of LiDAR Mapping With Neural Radiance Fields

In this letter 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, $\text{n}^{\text{th}}$, or strongest returns from a single output channel.