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.

翻译：本研究提出神经高程模型，将神经辐射场技术扩展至2.5维连续可微地形建模领域。相较于数字高程模型等传统地形表示方法，NEMos能够直接通过低成本影像数据生成，并通过隐式连续可微高程场实现轻量级地形表征。我们提出一种在NeRF框架内联合训练高程场与辐射场的新方法，该方法采用分位数回归技术。此外，我们开发了一种路径规划算法，该算法通过对连续成本函数进行梯度优化来最小化路径距离、坡度变化及控制能耗，其实现得益于高程场的可微特性。我们在仿真与真实地形影像数据上开展实验，结果表明NEMos能够生成高质量地形重建结果，且相较于离散路径规划方法能产生更平滑的路径。未来研究将探索在高程场中融入特征与语义信息，以构建广义地形模型。