# Neural Elevation Models for Terrain Mapping and Path Planning

arXiv: https://arxiv.org/abs/2405.15227 · HTML: https://mlsanity.com/paper/2405.15227/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 May 2024.

## Built on by (most cited first, 3 of 3)

- [A Probabilistic Formulation of LiDAR Mapping with Neural Radiance Fields](https://mlsanity.com/paper/2411.01725/) (2024)
- [Construction of Digital Terrain Maps from Multi-view Satellite Imagery using Neural Volume Rendering](https://mlsanity.com/paper/2508.01386/) (2025)
- [Neural 3D Reconstruction of Planetary Surfaces from Descent-Phase Wide-Angle Imagery](https://mlsanity.com/paper/2604.13235/) (2026)

## Abstract (arXiv)

This work introduces Neural Elevations Models (NEMos), which adapt Neural Radiance Fields to a 2.5D continuous and differentiable terrain model. In contrast to traditional terrain representations such as digital elevation models, NEMos can be readily generated from imagery, a low-cost data source, and provide a lightweight representation of terrain through an implicit continuous and differentiable height field. We propose a novel method for jointly training a height field and radiance field within a NeRF framework, leveraging quantile regression. Additionally, we introduce a path planning algorithm that performs gradient-based optimization of a continuous cost function for minimizing distance, slope changes, and control effort, enabled by differentiability of the height field. We perform experiments on simulated and real-world terrain imagery, demonstrating NEMos ability to generate high-quality reconstructions and produce smoother paths compared to discrete path planning methods. Future work will explore the incorporation of features and semantics into the height field, creating a generalized terrain model.