# 3D Reconstruction with Fast Dipole Sums

arXiv: https://arxiv.org/abs/2405.16788 · HTML: https://mlsanity.com/paper/2405.16788/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 118 references that are in the map.
- First posted on arXiv 27 May 2024.

## Builds on (most cited first, 30 of 41)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [2D Gaussian Splatting for Geometrically Accurate Radiance Fields](https://mlsanity.com/paper/2403.17888/) (2024)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [NeRF++: Analyzing and Improving Neural Radiance Fields](https://mlsanity.com/paper/2010.07492/) (2020)
- [Depth-supervised NeRF: Fewer Views and Faster Training for Free](https://mlsanity.com/paper/2107.02791/) (2021)
- [UNISURF: Unifying Neural Implicit Surfaces and Radiance Fields for Multi-View Reconstruction](https://mlsanity.com/paper/2104.10078/) (2021)
- [SuGaR: Surface-Aligned Gaussian Splatting for Efficient 3D Mesh Reconstruction and High-Quality Mesh Rendering](https://mlsanity.com/paper/2311.12775/) (2023)
- [Ref-NeRF: Structured View-Dependent Appearance for Neural Radiance Fields](https://mlsanity.com/paper/2112.03907/) (2021)
- [Point-NeRF: Point-based Neural Radiance Fields](https://mlsanity.com/paper/2201.08845/) (2022)
- [BlendedMVS: A Large-scale Dataset for Generalized Multi-view Stereo Networks](https://mlsanity.com/paper/1911.10127/) (2019)
- [Neuralangelo: High-Fidelity Neural Surface Reconstruction](https://mlsanity.com/paper/2306.03092/) (2023)
- [Advances in Neural Rendering](https://mlsanity.com/paper/2111.05849/) (2021)
- [NeuS2: Fast Learning of Neural Implicit Surfaces for Multi-view Reconstruction](https://mlsanity.com/paper/2212.05231/) (2022)
- [Geo-Neus: Geometry-Consistent Neural Implicit Surfaces Learning for Multi-view Reconstruction](https://mlsanity.com/paper/2205.15848/) (2022)
- [Neural Reflectance Fields for Appearance Acquisition](https://mlsanity.com/paper/2008.03824/) (2020)
- [Shape As Points: A Differentiable Poisson Solver](https://mlsanity.com/paper/2106.03452/) (2021)
- [Shape, Light, and Material Decomposition from Images using Monte Carlo Rendering and Denoising](https://mlsanity.com/paper/2206.03380/) (2022)
- [High-quality Surface Reconstruction using Gaussian Surfels](https://mlsanity.com/paper/2404.17774/) (2024)
- [A Survey of Structure from Motion](https://mlsanity.com/paper/1701.08493/) (2017)
- [Improving neural implicit surfaces geometry with patch warping](https://mlsanity.com/paper/2112.09648/) (2021)
- [Deep Reflectance Volumes: Relightable Reconstructions from Multi-View Photometric Images](https://mlsanity.com/paper/2007.09892/) (2020)
- [Voxurf: Voxel-based Efficient and Accurate Neural Surface Reconstruction](https://mlsanity.com/paper/2208.12697/) (2022)
- [ReLU Fields: The Little Non-linearity That Could](https://mlsanity.com/paper/2205.10824/) (2022)
- [Learning Smooth Neural Functions via Lipschitz Regularization](https://mlsanity.com/paper/2202.08345/) (2022)
- [Unified Shape and SVBRDF Recovery using Differentiable Monte Carlo Rendering](https://mlsanity.com/paper/2103.15208/) (2021)

## Built on by (most cited first, 12 of 12)

- [Geometry Field Splatting with Gaussian Surfels](https://mlsanity.com/paper/2411.17067/) (2024)
- [SOF: Sorted Opacity Fields for Fast Unbounded Surface Reconstruction](https://mlsanity.com/paper/2506.19139/) (2025)
- [ProbeSDF: Light Field Probes for Neural Surface Reconstruction](https://mlsanity.com/paper/2412.10084/) (2024)
- [Radiance Surfaces: Optimizing Surface Representations with a 5D Radiance Field Loss](https://mlsanity.com/paper/2501.18627/) (2025)
- [Differentiable Light Transport with Gaussian Surfels via Adapted Radiosity for Efficient Relighting and Geometry Reconstruction](https://mlsanity.com/paper/2509.18497/) (2025)
- [Nexels: Neurally-Textured Surfels for Real-Time Novel View Synthesis with Sparse Geometries](https://mlsanity.com/paper/2512.13796/) (2025)
- [Confidence-Based Mesh Extraction from 3D Gaussians](https://mlsanity.com/paper/2603.24725/) (2026)
- [Stochastic Poisson Surface Reconstruction with One Solve using Geometric Gaussian Processes](https://mlsanity.com/paper/2503.19136/) (2025)
- [RayletDF: Raylet Distance Fields for Generalizable 3D Surface Reconstruction from Point Clouds or Gaussians](https://mlsanity.com/paper/2508.09830/) (2025)
- [Points as Tori: Fast Pointwise Signed Distance for Point Clouds](https://mlsanity.com/paper/2607.16946/) (2026)
- [Differentiable Voxelization of Surface Representations](https://mlsanity.com/paper/2608.15934/) (2026)
- [TopoSurfel: Closing the Loop between Gaussian Surfels and Meshes for Surface Reconstruction](https://mlsanity.com/paper/2608.20687/) (2026)

## Abstract (arXiv)

We introduce a method for high-quality 3D reconstruction from multi-view images. Our method uses a new point-based representation, the regularized dipole sum, which generalizes the winding number to allow for interpolation of per-point attributes in point clouds with noisy or outlier points. Using regularized dipole sums, we represent implicit geometry and radiance fields as per-point attributes of a dense point cloud, which we initialize from structure from motion. We additionally derive Barnes-Hut fast summation schemes for accelerated forward and adjoint dipole sum queries. These queries facilitate the use of ray tracing to efficiently and differentiably render images with our point-based representations, and thus update their point attributes to optimize scene geometry and appearance. We evaluate our method in inverse rendering applications against state-of-the-art alternatives, based on ray tracing of neural representations or rasterization of Gaussian point-based representations. Our method significantly improves 3D reconstruction quality and robustness at equal runtimes, while also supporting more general rendering methods such as shadow rays for direct illumination.