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

arXiv: https://arxiv.org/abs/2503.08929 · HTML: https://mlsanity.com/paper/2503.08929/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 46 references that are in the map.
- First posted on arXiv 11 Mar 2025.

## Builds on (most cited first, 30 of 30)

- [Neuralangelo: High-Fidelity Neural Surface Reconstruction](https://mlsanity.com/paper/2306.03092/) (2023)
- [Gaussian Splatting SLAM](https://mlsanity.com/paper/2312.06741/) (2023)
- [Multipole Graph Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2006.09535/) (2020)
- [Neural RGB-D Surface Reconstruction](https://mlsanity.com/paper/2104.04532/) (2021)
- [Neural Operators for Accelerating Scientific Simulations and Design](https://mlsanity.com/paper/2309.15325/) (2023)
- [NeuSG: Neural Implicit Surface Reconstruction with 3D Gaussian Splatting Guidance](https://mlsanity.com/paper/2312.00846/) (2023)
- [KISS-ICP: In Defense of Point-to-Point ICP -- Simple, Accurate, and Robust Registration If Done the Right Way](https://mlsanity.com/paper/2209.15397/) (2022)
- [Recent Advances in 3D Gaussian Splatting](https://mlsanity.com/paper/2403.11134/) (2024)
- [Neural Kernel Surface Reconstruction](https://mlsanity.com/paper/2305.19590/) (2023)
- [The Newer College Dataset: Handheld LiDAR, Inertial and Vision with Ground Truth](https://mlsanity.com/paper/2003.05691/) (2020)
- [Neural Fields as Learnable Kernels for 3D Reconstruction](https://mlsanity.com/paper/2111.13674/) (2021)
- [Neural Splines: Fitting 3D Surfaces with Infinitely-Wide Neural Networks](https://mlsanity.com/paper/2006.13782/) (2020)
- [SHINE-Mapping: Large-Scale 3D Mapping Using Sparse Hierarchical Implicit Neural Representations](https://mlsanity.com/paper/2210.02299/) (2022)
- [NeRF-LOAM: Neural Implicit Representation for Large-Scale Incremental LiDAR Odometry and Mapping](https://mlsanity.com/paper/2303.10709/) (2023)
- [PET-NeuS: Positional Encoding Tri-Planes for Neural Surfaces](https://mlsanity.com/paper/2305.05594/) (2023)
- [NeuRodin: A Two-stage Framework for High-Fidelity Neural Surface Reconstruction](https://mlsanity.com/paper/2408.10178/) (2024)
- [SLAMesh: Real-time LiDAR Simultaneous Localization and Meshing](https://mlsanity.com/paper/2303.05252/) (2023)
- [ImMesh: An Immediate LiDAR Localization and Meshing Framework](https://mlsanity.com/paper/2301.05206/) (2023)
- [PaCMO: Partner Dependent Human Motion Generation in Dyadic Human Activity using Neural Operators](https://mlsanity.com/paper/2211.16210/) (2022)
- [Neural Operator: Is data all you need to model the world? An insight into the paradigm of data-driven scientific ML](https://mlsanity.com/paper/2301.13331/) (2023)
- [p-Poisson surface reconstruction in curl-free flow from point clouds](https://mlsanity.com/paper/2310.20095/) (2023)
- [Graph-based Decentralized Task Allocation for Multi-Robot Target Localization](https://mlsanity.com/paper/2309.08896/) (2023)
- [Trajectory Prediction for Robot Navigation using Flow-Guided Markov Neural Operator](https://mlsanity.com/paper/2309.09137/) (2023)
- [3QFP: Efficient neural implicit surface reconstruction using Tri-Quadtrees and Fourier feature Positional encoding](https://mlsanity.com/paper/2401.07164/) (2024)
- [CAD-Mesher: A Convenient, Accurate, Dense Mesh-based Mapping Module in SLAM for Dynamic Environments](https://mlsanity.com/paper/2408.05981/) (2024)
- [A Smoothness Energy without Boundary Distortion for Curved Surfaces](https://mlsanity.com/paper/1905.09777/) (2019)
- [AdaFNIO: Adaptive Fourier Neural Interpolation Operator for video frame interpolation](https://mlsanity.com/paper/2211.10791/) (2022)
- [Neural Poisson Surface Reconstruction: Resolution-Agnostic Shape Reconstruction from Point Clouds](https://mlsanity.com/paper/2308.01766/) (2023)
- [ARTEMIS: AI-driven Robotic Triage Labeling and Emergency Medical Information System](https://mlsanity.com/paper/2309.08865/) (2023)
- [Learning Lagrangian Interaction Dynamics with Sampling-Based Model Order Reduction](https://mlsanity.com/paper/2407.03925/) (2024)

## Abstract (arXiv)

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 L2-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 textttCUDA-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 hrefhttps://github.com/HrishikeshVish/HessianForge/https://github.com/HrishikeshVish/HessianForge/