# DeepFit: 3D Surface Fitting via Neural Network Weighted Least Squares

arXiv: https://arxiv.org/abs/2003.10826 · HTML: https://mlsanity.com/paper/2003.10826/

## Key facts

- Cited by 43 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Mar 2020.

## Built on by (most cited first, 30 of 43)

- [Shape As Points: A Differentiable Poisson Solver](https://mlsanity.com/paper/2106.03452/) (2021)
- [DiGS : Divergence guided shape implicit neural representation for unoriented point clouds](https://mlsanity.com/paper/2106.10811/) (2021)
- [SA-ConvONet: Sign-Agnostic Optimization of Convolutional Occupancy Networks](https://mlsanity.com/paper/2105.03582/) (2021)
- [CAP-UDF: Learning Unsigned Distance Functions Progressively from Raw Point Clouds with Consistency-Aware Field Optimization](https://mlsanity.com/paper/2210.02757/) (2022)
- [NeAF: Learning Neural Angle Fields for Point Normal Estimation](https://mlsanity.com/paper/2211.16869/) (2022)
- [Learning a More Continuous Zero Level Set in Unsigned Distance Fields through Level Set Projection](https://mlsanity.com/paper/2308.11441/) (2023)
- [AdaFit: Rethinking Learning-based Normal Estimation on Point Clouds](https://mlsanity.com/paper/2108.05836/) (2021)
- [IterativePFN: True Iterative Point Cloud Filtering](https://mlsanity.com/paper/2304.01529/) (2023)
- [Refine-Net: Normal Refinement Neural Network for Noisy Point Clouds](https://mlsanity.com/paper/2203.12514/) (2022)
- [HSurf-Net: Normal Estimation for 3D Point Clouds by Learning Hyper Surfaces](https://mlsanity.com/paper/2210.07158/) (2022)
- [GraphFit: Learning Multi-scale Graph-Convolutional Representation for Point Cloud Normal Estimation](https://mlsanity.com/paper/2207.11484/) (2022)
- [Rethinking the Approximation Error in 3D Surface Fitting for Point Cloud Normal Estimation](https://mlsanity.com/paper/2303.17167/) (2023)
- [Improvement of Normal Estimation for PointClouds via Simplifying Surface Fitting](https://mlsanity.com/paper/2104.10369/) (2021)
- [Contrastive Learning for Joint Normal Estimation and Point Cloud Filtering](https://mlsanity.com/paper/2208.06811/) (2022)
- [DNNR: Differential Nearest Neighbors Regression](https://mlsanity.com/paper/2205.08434/) (2022)
- [PCDNF: Revisiting Learning-based Point Cloud Denoising via Joint Normal Filtering](https://mlsanity.com/paper/2209.00798/) (2022)
- [Neural Gradient Learning and Optimization for Oriented Point Normal Estimation](https://mlsanity.com/paper/2309.09211/) (2023)
- [Learning Signed Hyper Surfaces for Oriented Point Cloud Normal Estimation](https://mlsanity.com/paper/2305.05873/) (2023)
- [NeuralGF: Unsupervised Point Normal Estimation by Learning Neural Gradient Function](https://mlsanity.com/paper/2311.00389/) (2023)
- [Accurate Differential Operators for Hybrid Neural Fields](https://mlsanity.com/paper/2312.05984/) (2023)
- [Fast and Accurate Normal Estimation for Point Cloud via Patch Stitching](https://mlsanity.com/paper/2103.16066/) (2021)
- [MSECNet: Accurate and Robust Normal Estimation for 3D Point Clouds by Multi-Scale Edge Conditioning](https://mlsanity.com/paper/2308.02237/) (2023)
- [CMG-Net: Robust Normal Estimation for Point Clouds via Chamfer Normal Distance and Multi-scale Geometry](https://mlsanity.com/paper/2312.09154/) (2023)
- [CloudWalker: Random walks for 3D point cloud shape analysis](https://mlsanity.com/paper/2112.01050/) (2021)
- [PFF-Net: Patch Feature Fitting for Point Cloud Normal Estimation](https://mlsanity.com/paper/2511.21365/) (2025)
- [Normal Transformer: Extracting Surface Geometry from LiDAR Points Enhanced by Visual Semantics](https://mlsanity.com/paper/2211.10580/) (2022)
- [CanonNet: Canonical Ordering and Curvature Learning for Point Cloud Analysis](https://mlsanity.com/paper/2504.02763/) (2025)
- [Better STEP, a format and dataset for boundary representation](https://mlsanity.com/paper/2506.05417/) (2025)
- [Learning Normals of Noisy Points by Local Gradient-Aware Surface Filtering](https://mlsanity.com/paper/2507.03394/) (2025)
- [Weighted Point Cloud Normal Estimation](https://mlsanity.com/paper/2305.04007/) (2023)

## Abstract (arXiv)

We propose a surface fitting method for unstructured 3D point clouds. This method, called DeepFit, incorporates a neural network to learn point-wise weights for weighted least squares polynomial surface fitting. The learned weights act as a soft selection for the neighborhood of surface points thus avoiding the scale selection required of previous methods. To train the network we propose a novel surface consistency loss that improves point weight estimation. The method enables extracting normal vectors and other geometrical properties, such as principal curvatures, the latter were not presented as ground truth during training. We achieve state-of-the-art results on a benchmark normal and curvature estimation dataset, demonstrate robustness to noise, outliers and density variations, and show its application on noise removal.