  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.
