Accurate and dense mapping in large-scale environments is essential for various robot applications. Recently, implicit neural signed distance fields (SDFs) have shown promising advances in this task. However, most existing approaches employ projective distances from range data as SDF supervision, introducing approximation errors and thus degrading the mapping quality. To address this problem, we introduce N$^{3}$-Mapping, an implicit neural mapping system featuring normal-guided neural non-projective signed distance fields. Specifically, we directly sample points along the surface normal, instead of the ray, to obtain more accurate non-projective distance values from range data. Then these distance values are used as supervision to train the implicit map. For large-scale mapping, we apply a voxel-oriented sliding window mechanism to alleviate the forgetting issue with a bounded memory footprint. Besides, considering the uneven distribution of measured point clouds, a hierarchical sampling strategy is designed to improve training efficiency. Experiments demonstrate that our method effectively mitigates SDF approximation errors and achieves state-of-the-art mapping quality compared to existing approaches.

翻译：准确且稠密的大规模环境建图对于多种机器人应用至关重要。近年来，隐式神经符号距离场在该任务中展现出显著进展。然而，现有方法大多采用来自测距数据的投影距离作为SDF监督，引入近似误差，从而降低了建图质量。为解决此问题，我们提出N$^{3}$-Mapping，一种采用法向引导神经非投影符号距离场的隐式神经建图系统。具体而言，我们沿表面法向（而非射线）直接采样点，以从测距数据中获得更精确的非投影距离值。随后，这些距离值被用作监督信号来训练隐式地图。针对大规模建图，我们应用面向体素的滑动窗口机制，以在有限内存占用下缓解遗忘问题。此外，考虑到测量点云分布不均匀，我们设计了分层采样策略以提高训练效率。实验表明，与现有方法相比，我们的方法有效减轻了SDF近似误差，并实现了最优的建图质量。