# Implicit Geometric Regularization for Learning Shapes

arXiv: https://arxiv.org/abs/2002.10099 · HTML: https://mlsanity.com/paper/2002.10099/

## Key facts

- Cited by 710 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Feb 2020.

## Built on by (most cited first, 30 of 710)

- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [Efficient Geometry-aware 3D Generative Adversarial Networks](https://mlsanity.com/paper/2112.07945/) (2021)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [PlenOctrees for Real-time Rendering of Neural Radiance Fields](https://mlsanity.com/paper/2103.14024/) (2021)
- [UNISURF: Unifying Neural Implicit Surfaces and Radiance Fields for Multi-View Reconstruction](https://mlsanity.com/paper/2104.10078/) (2021)
- [RegNeRF: Regularizing Neural Radiance Fields for View Synthesis from Sparse Inputs](https://mlsanity.com/paper/2112.00724/) (2021)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [MonoSDF: Exploring Monocular Geometric Cues for Neural Implicit Surface Reconstruction](https://mlsanity.com/paper/2206.00665/) (2022)
- [Neuralangelo: High-Fidelity Neural Surface Reconstruction](https://mlsanity.com/paper/2306.03092/) (2023)
- [FoundationPose: Unified 6D Pose Estimation and Tracking of Novel Objects](https://mlsanity.com/paper/2312.08344/) (2023)
- [Advances in Neural Rendering](https://mlsanity.com/paper/2111.05849/) (2021)
- [PhySG: Inverse Rendering with Spherical Gaussians for Physics-based Material Editing and Relighting](https://mlsanity.com/paper/2104.00674/) (2021)
- [NeuS2: Fast Learning of Neural Implicit Surfaces for Multi-view Reconstruction](https://mlsanity.com/paper/2212.05231/) (2022)
- [UniSim: A Neural Closed-Loop Sensor Simulator](https://mlsanity.com/paper/2308.01898/) (2023)
- [StyleSDF: High-Resolution 3D-Consistent Image and Geometry Generation](https://mlsanity.com/paper/2112.11427/) (2021)
- [3D Neural Field Generation using Triplane Diffusion](https://mlsanity.com/paper/2211.16677/) (2022)
- [I M Avatar: Implicit Morphable Head Avatars from Videos](https://mlsanity.com/paper/2112.07471/) (2021)
- [SNARF: Differentiable Forward Skinning for Animating Non-Rigid Neural Implicit Shapes](https://mlsanity.com/paper/2104.03953/) (2021)
- [BakedSDF: Meshing Neural SDFs for Real-Time View Synthesis](https://mlsanity.com/paper/2302.14859/) (2023)
- [Geo-Neus: Geometry-Consistent Neural Implicit Surfaces Learning for Multi-view Reconstruction](https://mlsanity.com/paper/2205.15848/) (2022)
- [Shape As Points: A Differentiable Poisson Solver](https://mlsanity.com/paper/2106.03452/) (2021)
- [PointAvatar: Deformable Point-based Head Avatars from Videos](https://mlsanity.com/paper/2212.08377/) (2022)
- [SCANimate: Weakly Supervised Learning of Skinned Clothed Avatar Networks](https://mlsanity.com/paper/2104.03313/) (2021)
- [SparseNeuS: Fast Generalizable Neural Surface Reconstruction from Sparse Views](https://mlsanity.com/paper/2206.05737/) (2022)
- [NICER-SLAM: Neural Implicit Scene Encoding for RGB SLAM](https://mlsanity.com/paper/2302.03594/) (2023)
- [NeRO: Neural Geometry and BRDF Reconstruction of Reflective Objects from Multiview Images](https://mlsanity.com/paper/2305.17398/) (2023)
- [H-NeRF: Neural Radiance Fields for Rendering and Temporal Reconstruction of Humans in Motion](https://mlsanity.com/paper/2110.13746/) (2021)
- [DreamEditor: Text-Driven 3D Scene Editing with Neural Fields](https://mlsanity.com/paper/2306.13455/) (2023)
- [Panoptic NeRF: 3D-to-2D Label Transfer for Panoptic Urban Scene Segmentation](https://mlsanity.com/paper/2203.15224/) (2022)
- [BundleSDF: Neural 6-DoF Tracking and 3D Reconstruction of Unknown Objects](https://mlsanity.com/paper/2303.14158/) (2023)

## Abstract (arXiv)

Representing shapes as level sets of neural networks has been recently proved to be useful for different shape analysis and reconstruction tasks. So far, such representations were computed using either: (i) pre-computed implicit shape representations; or (ii) loss functions explicitly defined over the neural level sets. In this paper we offer a new paradigm for computing high fidelity implicit neural representations directly from raw data (i.e., point clouds, with or without normal information). We observe that a rather simple loss function, encouraging the neural network to vanish on the input point cloud and to have a unit norm gradient, possesses an implicit geometric regularization property that favors smooth and natural zero level set surfaces, avoiding bad zero-loss solutions. We provide a theoretical analysis of this property for the linear case, and show that, in practice, our method leads to state of the art implicit neural representations with higher level-of-details and fidelity compared to previous methods.