HessianForge: Scalable LiDAR reconstruction with Physics-Informed Neural Representation and Smoothness Energy Constraints

• URL: http://arxiv.org/abs/2503.08929v1
• Date: Tue, 11 Mar 2025 22:18:51 GMT
• Title: HessianForge: Scalable LiDAR reconstruction with Physics-Informed Neural Representation and Smoothness Energy Constraints
• Authors: Hrishikesh Viswanath, Md Ashiqur Rahman, Chi Lin, Damon Conover, Aniket Bera,
• Abstract summary: Deep learning approach learns signed distance field from raw LiDAR point clouds.<n>Test-time refinement strategy to correct topological inconsistencies and edge distortions.<n>textttCUDA-accelerated least-squares optimization.
• Score: 18.858320397002277
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Accurate and efficient 3D mapping of large-scale outdoor environments from LiDAR measurements is a fundamental challenge in robotics, particularly towards ensuring smooth and artifact-free surface reconstructions. Although the state-of-the-art methods focus on memory-efficient neural representations for high-fidelity surface generation, they often fail to produce artifact-free manifolds, with artifacts arising due to noisy and sparse inputs. To address this issue, we frame surface mapping as a physics-informed energy optimization problem, enforcing surface smoothness by optimizing an energy functional that penalizes sharp surface ridges. Specifically, we propose a deep learning based approach that learns the signed distance field (SDF) of the surface manifold from raw LiDAR point clouds using a physics-informed loss function that optimizes the $L_2$-Hessian energy of the surface. Our learning framework includes a hierarchical octree based input feature encoding and a multi-scale neural network to iteratively refine the signed distance field at different scales of resolution. Lastly, we introduce a test-time refinement strategy to correct topological inconsistencies and edge distortions that can arise in the generated mesh. We propose a \texttt{CUDA}-accelerated least-squares optimization that locally adjusts vertex positions to enforce feature-preserving smoothing. We evaluate our approach on large-scale outdoor datasets and demonstrate that our approach outperforms current state-of-the-art methods in terms of improved accuracy and smoothness. Our code is available at \href{https://github.com/HrishikeshVish/HessianForge/}{https://github.com/HrishikeshVish/HessianForge/}

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