OREN: Octree Residual Network for Real-Time Euclidean Signed Distance Mapping

2026-07-11 · Source: cs.AI updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Robotics & Autonomous Systems · Depth: Expert, extended

Summary

The paper introduces $\nabla$-SDF, a hybrid method for online Euclidean Signed Distance Function (SDF) reconstruction from streaming point cloud data. It combines an explicit prior obtained from gradient-augmented octree interpolation with an implicit neural residual. This approach addresses the limitations of discrete volumetric methods, which lack continuity and differentiability, and neural network methods, which suffer from efficiency issues, catastrophic forgetting, and memory constraints, often being restricted to truncated SDFs. $\nabla$-SDF achieves non-truncated (Euclidean) SDF reconstruction, offering computational and memory efficiency similar to volumetric techniques, alongside differentiability and accuracy comparable to neural networks. Evaluated on the Replica dataset, $\nabla$-SDF demonstrates superior accuracy and efficiency compared to existing methods, operating at 8.51 fps. It utilizes a semi-sparse octree with 9 layers (5 semi-sparse, resolution 10 cm) and a neural residual network featuring a multi-resolution hash grid with 4 levels and 2 features, decoded by a five-layer 64-dimension MLP.

Key takeaway

For robotics engineers and AI scientists developing real-time mapping and navigation systems, $\nabla\$-SDF provides a robust solution for generating accurate, differentiable Euclidean Signed Distance Functions. You should consider this hybrid explicit-implicit approach to overcome the limitations of purely volumetric or neural network methods, especially when requiring both computational efficiency and high-fidelity geometric details across large environments. This method ensures reliable SDF estimates for precise robot interaction and planning.

Key insights

$\nabla$-SDF combines gradient-augmented octree interpolation with a neural residual for accurate, efficient, and differentiable Euclidean SDF reconstruction.

Principles

• Hybrid explicit-implicit models balance efficiency and accuracy.
• Gradient augmentation improves SDF prior accuracy.
• Semi-sparse octrees enhance global SDF representation.

Method

$\nabla$-SDF$ uses a semi-sparse octree for a gradient-augmented SDF prior, then a multi-resolution hash grid and MLP decode a neural residual. Three loss functions (reconstruction, Eikonal, projection) train the hybrid model.

In practice

• Use semi-sparse octrees for global SDF representation.
• Incorporate gradient information into interpolation for better priors.
• Combine explicit priors with neural residuals for detail.

Topics

• Signed Distance Functions
• Octree Mapping
• Neural Implicit Representations
• Robot Autonomy
• Real-time 3D Reconstruction
• Gradient-Augmented Interpolation

Best for: Research Scientist, AI Scientist, Robotics Engineer, Computer Vision Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.AI updates on arXiv.org.