N$^{3}$-Mapping: Normal Guided Neural Non-Projective Signed Distance Fields for Large-scale 3D Mapping

TL;DR

This work addresses the challenge of dense, large-scale 3D mapping with implicit neural SDFs by mitigating errors from projective-distance supervision. It introduces N$^{3}$-Mapping, which employs normal-guided non-projective sampling along surface normals, an octree-based implicit map, a voxel-oriented sliding window for bounded memory, and hierarchical sampling to balance training across regions. The method demonstrates state-of-the-art mapping accuracy and completeness on both synthetic and real-world datasets, while maintaining scalability and robustness to noise and dynamic elements. Collectively, these contributions enable efficient, incremental, high-quality dense mapping suitable for robotics and navigation tasks, with potential extensions to localization and perception pipelines.

Abstract

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.

Figures (10)

• Figure 1: Overview of our approach. With a sequence of range data and corresponding poses, our approach samples non-projective distance values to obtain accurate SDF labels along the normal direction. During training, these labels are used to supervise the learning of our implicit map through the voxel-oriented training strategy.
• Figure 2: Different methods for sampling signed distance values. Both projective distance along the ray and corrected distance with normals lead to large errors on curved surfaces. Our normal-guided sampling method can produce more accurate distance values.
• Figure 3: Illustration of the difference between keyframe-oriented and our proposed voxel-oriented sliding window. For the voxel $\boldsymbol{V_0}$ at the edge of the local window, our strategy preserves all supervisions from various views, while the keyframe-oriented method retains only partial observations, potentially leading to a forgetting issue.
• Figure 4: A qualitative comparison of different methods on the Maicity and the Newer College dataset. The odd rows show the reconstructed mesh colored by surface normals. The even rows present the error map with the ground truth point cloud as a reference where the redder points represent larger errors.
• Figure 5: Ablation study for our contributions and alternative designs on Maicity dataset. Regions are highlighted by colored boxes and circles to distinguish improvements