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

arXiv: https://arxiv.org/abs/2412.15909 · HTML: https://mlsanity.com/paper/2412.15909/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 39 references that are in the map.
- First posted on arXiv 20 Dec 2024.

## Builds on (most cited first, 22 of 22)

- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [KiloNeRF: Speeding up Neural Radiance Fields with Thousands of Tiny MLPs](https://mlsanity.com/paper/2103.13744/) (2021)
- [NICE-SLAM: Neural Implicit Scalable Encoding for SLAM](https://mlsanity.com/paper/2112.12130/) (2021)
- [iMAP: Implicit Mapping and Positioning in Real-Time](https://mlsanity.com/paper/2103.12352/) (2021)
- [Neural RGB-D Surface Reconstruction](https://mlsanity.com/paper/2104.04532/) (2021)
- [Neural Unsigned Distance Fields for Implicit Function Learning](https://mlsanity.com/paper/2010.13938/) (2020)
- [Co-SLAM: Joint Coordinate and Sparse Parametric Encodings for Neural Real-Time SLAM](https://mlsanity.com/paper/2304.14377/) (2023)
- [FAST-LIO2: Fast Direct LiDAR-inertial Odometry](https://mlsanity.com/paper/2107.06829/) (2021)
- [Vision-Only Robot Navigation in a Neural Radiance World](https://mlsanity.com/paper/2110.00168/) (2021)
- [Voxblox: Incremental 3D Euclidean Signed Distance Fields for On-Board MAV Planning](https://mlsanity.com/paper/1611.03631/) (2016)
- [KISS-ICP: In Defense of Point-to-Point ICP -- Simple, Accurate, and Robust Registration If Done the Right Way](https://mlsanity.com/paper/2209.15397/) (2022)
- [iSDF: Real-Time Neural Signed Distance Fields for Robot Perception](https://mlsanity.com/paper/2204.02296/) (2022)
- [Learning Signed Distance Field for Multi-view Surface Reconstruction](https://mlsanity.com/paper/2108.09964/) (2021)
- [FAST-LIO: A Fast, Robust LiDAR-inertial Odometry Package by Tightly-Coupled Iterated Kalman Filter](https://mlsanity.com/paper/2010.08196/) (2020)
- [Neural Splines: Fitting 3D Surfaces with Infinitely-Wide Neural Networks](https://mlsanity.com/paper/2006.13782/) (2020)
- [SHINE-Mapping: Large-Scale 3D Mapping Using Sparse Hierarchical Implicit Neural Representations](https://mlsanity.com/paper/2210.02299/) (2022)
- [Continual Neural Mapping: Learning An Implicit Scene Representation from Sequential Observations](https://mlsanity.com/paper/2108.05851/) (2021)
- [Differentiable Spatial Planning using Transformers](https://mlsanity.com/paper/2112.01010/) (2021)
- [IR-MCL: Implicit Representation-Based Online Global Localization](https://mlsanity.com/paper/2210.03113/) (2022)
- [HIO-SDF: Hierarchical Incremental Online Signed Distance Fields](https://mlsanity.com/paper/2310.09463/) (2023)

## Abstract (arXiv)

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.