# Neural Kernel Surface Reconstruction

arXiv: https://arxiv.org/abs/2305.19590 · HTML: https://mlsanity.com/paper/2305.19590/

## Key facts

- Cited by 104 papers in the map (data through 14 Oct 2026).
- Builds on 64 of its 88 references that are in the map.
- First posted on arXiv 31 May 2023.

## Builds on (most cited first, 30 of 64)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [ScanNet: Richly-annotated 3D Reconstructions of Indoor Scenes](https://mlsanity.com/paper/1702.04405/) (2017)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Scalability in Perception for Autonomous Driving: Waymo Open Dataset](https://mlsanity.com/paper/1912.04838/) (2019)
- [CARLA: An Open Urban Driving Simulator](https://mlsanity.com/paper/1711.03938/) (2017)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Matterport3D: Learning from RGB-D Data in Indoor Environments](https://mlsanity.com/paper/1709.06158/) (2017)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [3D-R2N2: A Unified Approach for Single and Multi-view 3D Object Reconstruction](https://mlsanity.com/paper/1604.00449/) (2016)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [3D Shape Generation and Completion through Point-Voxel Diffusion](https://mlsanity.com/paper/2104.03670/) (2021)
- [Deep Marching Tetrahedra: a Hybrid Representation for High-Resolution 3D Shape Synthesis](https://mlsanity.com/paper/2111.04276/) (2021)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [ABC: A Big CAD Model Dataset For Geometric Deep Learning](https://mlsanity.com/paper/1812.06216/) (2018)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [Submanifold Sparse Convolutional Networks](https://mlsanity.com/paper/1706.01307/) (2017)
- [MetaSDF: Meta-learning Signed Distance Functions](https://mlsanity.com/paper/2006.09662/) (2020)
- [Texture Fields: Learning Texture Representations in Function Space](https://mlsanity.com/paper/1905.07259/) (2019)
- [PU-Net: Point Cloud Upsampling Network](https://mlsanity.com/paper/1801.06761/) (2018)
- [BSP-Net: Generating Compact Meshes via Binary Space Partitioning](https://mlsanity.com/paper/1911.06971/) (2019)
- [Shape As Points: A Differentiable Poisson Solver](https://mlsanity.com/paper/2106.03452/) (2021)
- [Thingi10K: A Dataset of 10,000 3D-Printing Models](https://mlsanity.com/paper/1605.04797/) (2016)
- [Multi-view Supervision for Single-view Reconstruction via Differentiable Ray Consistency](https://mlsanity.com/paper/1704.06254/) (2017)
- [CvxNet: Learnable Convex Decomposition](https://mlsanity.com/paper/1909.05736/) (2019)
- [Learning a Predictable and Generative Vector Representation for Objects](https://mlsanity.com/paper/1603.08637/) (2016)

## Built on by (most cited first, 30 of 104)

- [XCube: Large-Scale 3D Generative Modeling using Sparse Voxel Hierarchies](https://mlsanity.com/paper/2312.03806/) (2023)
- [ViPE: Video Pose Engine for 3D Geometric Perception](https://mlsanity.com/paper/2508.10934/) (2025)
- [Direct3D-S2: Gigascale 3D Generation Made Easy with Spatial Sparse Attention](https://mlsanity.com/paper/2505.17412/) (2025)
- [UniScene: Unified Occupancy-centric Driving Scene Generation](https://mlsanity.com/paper/2412.05435/) (2024)
- [Dora: Sampling and Benchmarking for 3D Shape Variational Auto-Encoders](https://mlsanity.com/paper/2412.17808/) (2024)
- [SparseFlex: High-Resolution and Arbitrary-Topology 3D Shape Modeling](https://mlsanity.com/paper/2503.21732/) (2025)
- [Visual Imitation Enables Contextual Humanoid Control](https://mlsanity.com/paper/2505.03729/) (2025)
- [LidarDM: Generative LiDAR Simulation in a Generated World](https://mlsanity.com/paper/2404.02903/) (2024)
- [4K4DGen: Panoramic 4D Generation at 4K Resolution](https://mlsanity.com/paper/2406.13527/) (2024)
- [PIN-SLAM: LiDAR SLAM Using a Point-Based Implicit Neural Representation for Achieving Global Map Consistency](https://mlsanity.com/paper/2401.09101/) (2024)
- [G3R: Gradient Guided Generalizable Reconstruction](https://mlsanity.com/paper/2409.19405/) (2024)
- [GStex: Per-Primitive Texturing of 2D Gaussian Splatting for Decoupled Appearance and Geometry Modeling](https://mlsanity.com/paper/2409.12954/) (2024)
- [LiDAR4D: Dynamic Neural Fields for Novel Space-time View LiDAR Synthesis](https://mlsanity.com/paper/2404.02742/) (2024)
- [Choose Your Simulator Wisely: A Review on Open-source Simulators for Autonomous Driving](https://mlsanity.com/paper/2311.11056/) (2023)
- [GaussGym: An open-source real-to-sim framework for learning locomotion from pixels](https://mlsanity.com/paper/2510.15352/) (2025)
- [iTACO: Interactable Digital Twins of Articulated Objects from Casually Captured RGBD Videos](https://mlsanity.com/paper/2506.08334/) (2025)
- [ORV: 4D Occupancy-centric Robot Video Generation](https://mlsanity.com/paper/2506.03079/) (2025)
- [Sat2City: 3D City Generation from A Single Satellite Image with Cascaded Latent Diffusion](https://mlsanity.com/paper/2507.04403/) (2025)
- [Unsupervised Occupancy Learning from Sparse Point Cloud](https://mlsanity.com/paper/2404.02759/) (2024)
- [Fast Learning of Signed Distance Functions from Noisy Point Clouds via Noise to Noise Mapping](https://mlsanity.com/paper/2407.14225/) (2024)
- [ZeroGrasp: Zero-Shot Shape Reconstruction Enabled Robotic Grasping](https://mlsanity.com/paper/2504.10857/) (2025)
- [PoNQ: a Neural QEM-based Mesh Representation](https://mlsanity.com/paper/2403.12870/) (2024)
- [Total-Decom: Decomposed 3D Scene Reconstruction with Minimal Interaction](https://mlsanity.com/paper/2403.19314/) (2024)
- [Robustifying Generalizable Implicit Shape Networks with a Tunable Non-Parametric Model](https://mlsanity.com/paper/2311.12967/) (2023)
- [LiDPM: Rethinking Point Diffusion for Lidar Scene Completion](https://mlsanity.com/paper/2504.17791/) (2025)
- [Zero-Shot Multi-Object Scene Completion](https://mlsanity.com/paper/2403.14628/) (2024)
- [DynoSurf: Neural Deformation-based Temporally Consistent Dynamic Surface Reconstruction](https://mlsanity.com/paper/2403.11586/) (2024)
- [3D LiDAR Mapping in Dynamic Environments Using a 4D Implicit Neural Representation](https://mlsanity.com/paper/2405.03388/) (2024)
- [Sparfels: Fast Reconstruction from Sparse Unposed Imagery](https://mlsanity.com/paper/2505.02178/) (2025)
- [Scaling Up Occupancy-centric Driving Scene Generation: Dataset and Method](https://mlsanity.com/paper/2510.22973/) (2025)

## Abstract (arXiv)

We present a novel method for reconstructing a 3D implicit surface from a large-scale, sparse, and noisy point cloud. Our approach builds upon the recently introduced Neural Kernel Fields (NKF) representation. It enjoys similar generalization capabilities to NKF, while simultaneously addressing its main limitations: (a) We can scale to large scenes through compactly supported kernel functions, which enable the use of memory-efficient sparse linear solvers. (b) We are robust to noise, through a gradient fitting solve. (c) We minimize training requirements, enabling us to learn from any dataset of dense oriented points, and even mix training data consisting of objects and scenes at different scales. Our method is capable of reconstructing millions of points in a few seconds, and handling very large scenes in an out-of-core fashion. We achieve state-of-the-art results on reconstruction benchmarks consisting of single objects, indoor scenes, and outdoor scenes.