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

2025-03-11

AI Summary

To address artifacts, sharp distortions, and topological errors in large-scale outdoor LiDAR surface reconstruction, this paper proposes a physics-informed neural implicit reconstruction method. Our approach explicitly incorporates the L₂-norm of the signed distance function (SDF) Hessian into the optimization objective—marking the first such use—to suppress unphysical ridges and enforce intrinsic surface smoothness. We further introduce a joint hierarchical octree encoding and multi-scale MLP framework to enhance geometric fidelity and computational efficiency. Additionally, we propose a CUDA-accelerated, vertex-level feature-preserving smoothing strategy for efficient mesh refinement at inference time. Evaluated on large-scale outdoor LiDAR datasets, our method significantly outperforms state-of-the-art approaches: reconstructed surfaces exhibit superior continuity and geometric accuracy, while effectively eliminating noise-induced edge distortions and topological inconsistencies.

Technology Category

• Computer Vision: Low Level & Physics-based Vision
• Search and Optimization: Learning to Search
• Machine Learning: Learning with Manifolds

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Economics, Online Markets and Human Computation: Architectures and workflows that use LLMs for crowd work

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 exttt{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/}

Problem

• Accurate 3D mapping from LiDAR in large outdoor environments.
• Reducing artifacts in surface reconstructions from noisy LiDAR data.
• Improving smoothness and accuracy in neural-based surface generation.

Innovation

• Physics-informed neural representation for LiDAR reconstruction
• Hierarchical octree encoding and multi-scale neural network
• CUDA-accelerated least-squares optimization for mesh refinement