Estimation of signed distance functions (SDFs) from point cloud data has been shown to benefit many robot autonomy capabilities, including localization, mapping, motion planning, and control. Methods that support online and large-scale SDF reconstruction tend to rely on discrete volumetric data structures, which affect the continuity and differentiability of the SDF estimates. Recently, using implicit features, neural network methods have demonstrated high-fidelity and differentiable SDF reconstruction but they tend to be less efficient, can experience catastrophic forgetting and memory limitations in large environments, and are often restricted to truncated SDFs. This work proposes $\nabla$-SDF, a hybrid method that combines an explicit prior obtained from gradient-augmented octree interpolation with an implicit neural residual. Our method achieves non-truncated (Euclidean) SDF reconstruction with computational and memory efficiency comparable to volumetric methods and differentiability and accuracy comparable to neural network methods. Extensive experiments demonstrate that \methodname{} outperforms the state of the art in terms of accuracy and efficiency, providing a scalable solution for downstream tasks in robotics and computer vision.

翻译：从点云数据中估计有符号距离函数已被证明有益于许多机器人自主能力，包括定位、建图、运动规划与控制。支持在线、大规模SDF重建的方法通常依赖于离散的体素数据结构，这影响了SDF估计的连续性与可微性。最近，基于隐式特征的神经网络方法展示了高保真且可微的SDF重建能力，但它们往往效率较低，在大规模环境中可能遭遇灾难性遗忘与内存限制，且通常仅限于截断SDF。本文提出$\nabla$-SDF，一种将梯度增强八叉树插值获得的显式先验与隐式神经残差相结合的混合方法。我们的方法实现了非截断（欧几里得）SDF重建，其计算与内存效率可与体素方法相媲美，而可微性与精度则与神经网络方法相当。大量实验表明，\methodname{} 在精度与效率方面均优于现有技术，为机器人学与计算机视觉中的下游任务提供了一个可扩展的解决方案。