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.

翻译：神经距离场已成为解决三维计算机视觉与图形学下游问题挑战的有力工具。尽管从各类传感器数据学习神经距离场已取得显著进展，但训练过程中神经场的监督机制仍需重点关注，因为大规模户外场景缺乏真实神经距离场数据。先前研究采用多种形式的期望符号距离来指导模型学习，然而这些方法往往忽视曲面几何的关键特性，且仅限于小规模场景应用。为此，我们提出一种创新方法，利用符号距离场的二阶导数改进神经场学习。该方法通过精确估计符号距离克服现有局限，为底层几何结构提供更全面的理解。为评估方法效能，我们在神经距离场主要应用领域——建图与定位任务中，与主流方法进行了对比实验。结果表明所提方法具有显著优势，展现了其在提升计算机视觉与图形学应用中神经距离场性能方面的潜力。