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CCNDF: Curvature Constrained Neural Distance Fields from 3D LiDAR Sequences

Akshit Singh, Karan Bhakuni, Rajendra Nagar

TL;DR

This work tackles the supervision gap in learning neural distance fields (NDF) for large-scale outdoor scenes by introducing a curvature-aware, second-order derivative-based supervision strategy. Building on LocNDF, it derives an efficient ROC-based mean-curvature surrogate to estimate signed distances from LiDAR rays, enabling self-supervised training without ground-truth NDFs. The approach demonstrates improved mapping detail and localization accuracy on benchmarks such as Apollo KITTI, surpassing prior geometric supervision methods. By leveraging higher-order NDF properties, the method offers a principled, scalable pathway to robust implicit surface learning for real-world 3D perception tasks.

Abstract

Neural distance fields (NDF) have emerged as a powerful tool for addressing challenges in 3D computer vision and graphics downstream problems. While significant progress has been made to learn NDF from various kind of sensor data, a crucial aspect that demands attention is the supervision of neural fields during training as the ground-truth NDFs are not available for large-scale outdoor scenes. Previous works have utilized various forms of expected signed distance to guide model learning. Yet, these approaches often need to pay more attention to critical considerations of surface geometry and are limited to small-scale implementations. To this end, we propose a novel methodology leveraging second-order derivatives of the signed distance field for improved neural field learning. Our approach addresses limitations by accurately estimating signed distance, offering a more comprehensive understanding of underlying geometry. To assess the efficacy of our methodology, we conducted comparative evaluations against prevalent methods for mapping and localization tasks, which are primary application areas of NDF. Our results demonstrate the superiority of the proposed approach, highlighting its potential for advancing the capabilities of neural distance fields in computer vision and graphics applications.

CCNDF: Curvature Constrained Neural Distance Fields from 3D LiDAR Sequences

TL;DR

This work tackles the supervision gap in learning neural distance fields (NDF) for large-scale outdoor scenes by introducing a curvature-aware, second-order derivative-based supervision strategy. Building on LocNDF, it derives an efficient ROC-based mean-curvature surrogate to estimate signed distances from LiDAR rays, enabling self-supervised training without ground-truth NDFs. The approach demonstrates improved mapping detail and localization accuracy on benchmarks such as Apollo KITTI, surpassing prior geometric supervision methods. By leveraging higher-order NDF properties, the method offers a principled, scalable pathway to robust implicit surface learning for real-world 3D perception tasks.

Abstract

Neural distance fields (NDF) have emerged as a powerful tool for addressing challenges in 3D computer vision and graphics downstream problems. While significant progress has been made to learn NDF from various kind of sensor data, a crucial aspect that demands attention is the supervision of neural fields during training as the ground-truth NDFs are not available for large-scale outdoor scenes. Previous works have utilized various forms of expected signed distance to guide model learning. Yet, these approaches often need to pay more attention to critical considerations of surface geometry and are limited to small-scale implementations. To this end, we propose a novel methodology leveraging second-order derivatives of the signed distance field for improved neural field learning. Our approach addresses limitations by accurately estimating signed distance, offering a more comprehensive understanding of underlying geometry. To assess the efficacy of our methodology, we conducted comparative evaluations against prevalent methods for mapping and localization tasks, which are primary application areas of NDF. Our results demonstrate the superiority of the proposed approach, highlighting its potential for advancing the capabilities of neural distance fields in computer vision and graphics applications.

Paper Structure

This paper contains 8 sections, 9 equations, 6 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methodology
  4. Curvature-Constrained Neural Distance Fields
  5. Geometric Advantages of Proposed Approach
  6. Results and Evaluation
  7. Discussion, Limitations and Future work
  8. Conclusion

Figures (6)

  • Figure 1: Different methods for computing the signed distance to supervise NDF for a point on a ray beam.
  • Figure 2: The figure illustrates the concentric nature of NDF; ROC of points on NDF constantly increase as we move away from the surface
  • Figure 3: Visual comparison of results obtained with various geometrical methods for NDF supervision on the benchmark dataset. (a) Ray Distance, (b) Ray distance along the normal pointing towards the closest surface, and (c) Proposed approach.
  • Figure 4: Results on KITTI dataset.
  • Figure 5: This figure illustrates front-view mappings derived from various geometric methods, with darker colours indicating improved normal estimation. (a) Ray Distance, (b) Ray distance along the normal pointing towards the closest surface, and (c) Proposed approach.
  • ...and 1 more figures