$ abla$-SDF: Learning Euclidean Signed Distance Functions Online with Gradient-Augmented Octree Interpolation and Neural Residual

2025-10-21

AI Summary

This work addresses the challenge of online learning of Euclidean Signed Distance Functions (SDFs) for large-scale point cloud scenes, where accuracy, continuity, differentiability, and computational efficiency are difficult to reconcile. We propose an explicit-implicit hybrid representation: for the first time, gradient-augmented sparse octree interpolation serves as an explicit SDF prior, coupled with a lightweight neural network modeling the residual. This enables non-truncated, differentiable, and memory-efficient online SDF reconstruction. The design avoids catastrophic forgetting and inference latency inherent in purely neural approaches, supporting efficient incremental updates and real-time inference. Evaluated on multiple large real-world scenes, our method outperforms existing online SDF reconstruction techniques in both reconstruction accuracy and computational efficiency. Consequently, it significantly enhances performance and scalability of downstream robotics tasks—including localization, mapping, and motion planning.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Learning with Manifolds
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

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 $ abla$-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.

Problem

• Online reconstruction of Euclidean signed distance functions from point clouds
• Overcoming limitations of discrete volumetric and neural SDF methods
• Achieving accurate differentiable SDFs with computational efficiency for robotics

Innovation

• Hybrid method combining explicit gradient-augmented octree interpolation
• Implicit neural residual for non-truncated Euclidean SDF reconstruction
• Achieves computational efficiency comparable to volumetric methods