# Deep Geometric Prior for Surface Reconstruction

arXiv: https://arxiv.org/abs/1811.10943 · HTML: https://mlsanity.com/paper/1811.10943/

## Key facts

- Cited by 110 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Nov 2018.

## Built on by (most cited first, 30 of 110)

- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Shape As Points: A Differentiable Poisson Solver](https://mlsanity.com/paper/2106.03452/) (2021)
- [Neural Kernel Surface Reconstruction](https://mlsanity.com/paper/2305.19590/) (2023)
- [POCO: Point Convolution for Surface Reconstruction](https://mlsanity.com/paper/2201.01831/) (2022)
- [Learning Smooth Neural Functions via Lipschitz Regularization](https://mlsanity.com/paper/2202.08345/) (2022)
- [DiGS : Divergence guided shape implicit neural representation for unoriented point clouds](https://mlsanity.com/paper/2106.10811/) (2021)
- [SCALE: Modeling Clothed Humans with a Surface Codec of Articulated Local Elements](https://mlsanity.com/paper/2104.07660/) (2021)
- [Neural Dual Contouring](https://mlsanity.com/paper/2202.01999/) (2022)
- [Deep Implicit Moving Least-Squares Functions for 3D Reconstruction](https://mlsanity.com/paper/2103.12266/) (2021)
- [Reconstructing Surfaces for Sparse Point Clouds with On-Surface Priors](https://mlsanity.com/paper/2204.10603/) (2022)
- [Neural Fields as Learnable Kernels for 3D Reconstruction](https://mlsanity.com/paper/2111.13674/) (2021)
- [Surface Reconstruction from Point Clouds by Learning Predictive Context Priors](https://mlsanity.com/paper/2204.11015/) (2022)
- [Neural Signed Distance Function Inference through Splatting 3D Gaussians Pulled on Zero-Level Set](https://mlsanity.com/paper/2410.14189/) (2024)
- [CAP-UDF: Learning Unsigned Distance Functions Progressively from Raw Point Clouds with Consistency-Aware Field Optimization](https://mlsanity.com/paper/2210.02757/) (2022)
- [Early Stopping for Deep Image Prior](https://mlsanity.com/paper/2112.06074/) (2021)
- [Surface Reconstruction from Point Clouds: A Survey and a Benchmark](https://mlsanity.com/paper/2205.02413/) (2022)
- [Controllable Mesh Generation Through Sparse Latent Point Diffusion Models](https://mlsanity.com/paper/2303.07938/) (2023)
- [D2CSG: Unsupervised Learning of Compact CSG Trees with Dual Complements and Dropouts](https://mlsanity.com/paper/2301.11497/) (2023)
- [Towards Better Gradient Consistency for Neural Signed Distance Functions via Level Set Alignment](https://mlsanity.com/paper/2305.11601/) (2023)
- [Phase Transitions, Distance Functions, and Implicit Neural Representations](https://mlsanity.com/paper/2106.07689/) (2021)
- [Learning a More Continuous Zero Level Set in Unsigned Distance Fields through Level Set Projection](https://mlsanity.com/paper/2308.11441/) (2023)
- [Neural-Singular-Hessian: Implicit Neural Representation of Unoriented Point Clouds by Enforcing Singular Hessian](https://mlsanity.com/paper/2309.01793/) (2023)
- [Neural Surface Maps](https://mlsanity.com/paper/2103.16942/) (2021)
- [An Object is Worth 64x64 Pixels: Generating 3D Object via Image Diffusion](https://mlsanity.com/paper/2408.03178/) (2024)
- [MedShapeNet -- A Large-Scale Dataset of 3D Medical Shapes for Computer Vision](https://mlsanity.com/paper/2308.16139/) (2023)
- [Orienting Point Clouds with Dipole Propagation](https://mlsanity.com/paper/2105.01604/) (2021)
- [Neural Jacobian Fields: Learning Intrinsic Mappings of Arbitrary Meshes](https://mlsanity.com/paper/2205.02904/) (2022)
- [Unsupervised Inference of Signed Distance Functions from Single Sparse Point Clouds without Learning Priors](https://mlsanity.com/paper/2303.14505/) (2023)
- [Learning Signed Distance Functions from Noisy 3D Point Clouds via Noise to Noise Mapping](https://mlsanity.com/paper/2306.01405/) (2023)
- [SurfGen: Adversarial 3D Shape Synthesis with Explicit Surface Discriminators](https://mlsanity.com/paper/2201.00112/) (2022)

## Abstract (arXiv)

The reconstruction of a discrete surface from a point cloud is a fundamental geometry processing problem that has been studied for decades, with many methods developed. We propose the use of a deep neural network as a geometric prior for surface reconstruction. Specifically, we overfit a neural network representing a local chart parameterization to part of an input point cloud using the Wasserstein distance as a measure of approximation. By jointly fitting many such networks to overlapping parts of the point cloud, while enforcing a consistency condition, we compute a manifold atlas. By sampling this atlas, we can produce a dense reconstruction of the surface approximating the input cloud. The entire procedure does not require any training data or explicit regularization, yet, we show that it is able to perform remarkably well: not introducing typical overfitting artifacts, and approximating sharp features closely at the same time. We experimentally show that this geometric prior produces good results for both man-made objects containing sharp features and smoother organic objects, as well as noisy inputs. We compare our method with a number of well-known reconstruction methods on a standard surface reconstruction benchmark.