mlsanityData to 14 Oct 2026

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

arXiv 2003.10826 ↗First posted 23 Mar 2020cs.CVcited by 43

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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.

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

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 7; 2022: 9; 2023: 11; 2024: 5; 2025: 7; 2026: 4.

43 papers.

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  1. 2021Shape As Points: A Differentiable Poisson Solvercited by 187
  2. 2021DiGS : Divergence guided shape implicit neural representation for unoriented point cloudscited by 77
  3. 2021SA-ConvONet: Sign-Agnostic Optimization of Convolutional Occupancy Networkscited by 59
  4. 2022CAP-UDF: Learning Unsigned Distance Functions Progressively from Raw Point Clouds with Consistency-Aware Field Optimizationcited by 47
  5. 2022NeAF: Learning Neural Angle Fields for Point Normal Estimationcited by 38
  6. 2023Learning a More Continuous Zero Level Set in Unsigned Distance Fields through Level Set Projectioncited by 36
  7. 2021AdaFit: Rethinking Learning-based Normal Estimation on Point Cloudscited by 29
  8. 2023IterativePFN: True Iterative Point Cloud Filteringcited by 28
  9. 2022Refine-Net: Normal Refinement Neural Network for Noisy Point Cloudscited by 23
  10. 2022HSurf-Net: Normal Estimation for 3D Point Clouds by Learning Hyper Surfacescited by 22
  11. 2022GraphFit: Learning Multi-scale Graph-Convolutional Representation for Point Cloud Normal Estimationcited by 20
  12. 2023Rethinking the Approximation Error in 3D Surface Fitting for Point Cloud Normal Estimationcited by 13
31 more
  1. 2021Improvement of Normal Estimation for PointClouds via Simplifying Surface Fittingcited by 12
  2. 2022Contrastive Learning for Joint Normal Estimation and Point Cloud Filteringcited by 12
  3. 2022DNNR: Differential Nearest Neighbors Regressioncited by 11
  4. 2022PCDNF: Revisiting Learning-based Point Cloud Denoising via Joint Normal Filteringcited by 11
  5. 2023Neural Gradient Learning and Optimization for Oriented Point Normal Estimationcited by 11
  6. 2023Learning Signed Hyper Surfaces for Oriented Point Cloud Normal Estimationcited by 10
  7. 2023NeuralGF: Unsupervised Point Normal Estimation by Learning Neural Gradient Functioncited by 10
  8. 2023Accurate Differential Operators for Hybrid Neural Fieldscited by 9
  9. 2021Fast and Accurate Normal Estimation for Point Cloud via Patch Stitchingcited by 8
  10. 2023MSECNet: Accurate and Robust Normal Estimation for 3D Point Clouds by Multi-Scale Edge Conditioningcited by 6
  11. 2023CMG-Net: Robust Normal Estimation for Point Clouds via Chamfer Normal Distance and Multi-scale Geometrycited by 6
  12. 2021CloudWalker: Random walks for 3D point cloud shape analysiscited by 4
  13. 2025PFF-Net: Patch Feature Fitting for Point Cloud Normal Estimationcited by 3
  14. 2022Normal Transformer: Extracting Surface Geometry from LiDAR Points Enhanced by Visual Semanticscited by 2
  15. 2025CanonNet: Canonical Ordering and Curvature Learning for Point Cloud Analysiscited by 2
  16. 2025Better STEP, a format and dataset for boundary representationcited by 2
  17. 2025Learning Normals of Noisy Points by Local Gradient-Aware Surface Filteringcited by 2
  18. 2023Weighted Point Cloud Normal Estimationcited by 1
  19. 2024Surface Normal Estimation with Transformerscited by 1
  20. 2025LiSu: A Dataset and Method for LiDAR Surface Normal Estimationcited by 1
  21. 2026GLASS: Geometry-aware Local Alignment and Structure Synchronization Network for 2D-3D Registrationcited by 1
  22. 2023PointNorm-Net: Self-Supervised Normal Prediction of 3D Point Clouds via Multi-Modal Distribution Estimationcited by 0
  23. 2024E3-Net: Efficient E(3)-Equivariant Normal Estimation Networkcited by 0
  24. 2024Asymmetrical Siamese Network for Point Clouds Normal Estimationcited by 0
  25. 2024Refining 3D Point Cloud Normal Estimation via Sample Selectioncited by 0
  26. 2024OCMG-Net: Neural Oriented Normal Refinement for Unstructured Point Cloudscited by 0
  27. 2025Graph-based Point Cloud Surface Reconstruction using B-Splinescited by 0
  28. 2025MambaH-Fit: Rethinking Hyper-surface Fitting-based Point Cloud Normal Estimation via State Space Modellingcited by 0
  29. 2026Patch-based Representation and Learning for Efficient Deformation Modelingcited by 0
  30. 2026RAIN-FIT: Learning of Fitting Surfaces and Noise Distribution from Large Data Setscited by 0
  31. 2026Points as Tori: Fast Pointwise Signed Distance for Point Cloudscited by 0