Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
166 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
42 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Fast and Globally Consistent Normal Orientation based on the Winding Number Normal Consistency (2405.16634v2)

Published 26 May 2024 in cs.GR

Abstract: Estimating consistently oriented normals for point clouds enables a number of important applications in computer graphics. While local normal estimation is possible with simple techniques like PCA, orienting them to be globally consistent has been a notoriously difficult problem. Some recent methods exploit various properties of the winding number formula to achieve global consistency. Despite their exciting progress, these algorithms either have high space/time complexity, or do not produce accurate and consistently oriented normals for imperfect data. In this paper, we propose a novel property from the winding number formula, termed Winding Number Normal Consistency (WNNC), to tackle this problem. The derived property is based on the simple observation that the normals (negative gradients) sampled from the winding number field should be codirectional to the normals used to compute the winding number field. Since the WNNC property itself does not resolve the inside/outside orientation ambiguity, we further incorporate an objective function from Parametric Gauss Reconstruction (PGR). We propose to iteratively update normals by alternating between WNNC-based normal updates and PGR-based gradient descents, which leads to an embarrassingly simple yet effective iterative algorithm that allows fast and high-quality convergence to globally consistent normals. Furthermore, our proposed algorithm only involves repeatedly evaluating the winding number formula and its derivatives, which can be accelerated and parallelized using a treecode-based approximation algorithm. Our GPU (and even CPU) implementation can be significantly faster than the recent state-of-the-art methods for normal orientation from raw points. Our code is integrated with the popular PyTorch framework to facilitate further research into winding numbers, and is publicly available at https://jsnln.github.io/wnnc/index.html.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (48)
  1. Voronoi-based variational reconstruction of unoriented point sets. In Proceedings of the Fifth Eurographics Symposium on Geometry Processing, Barcelona, Spain, July 4-6, 2007, pages 39–48. Eurographics Association, 2007.
  2. Pytorch 2: Faster machine learning through dynamic python bytecode transformation and graph compilation. In Proceedings of the 29th ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 2, page 929–947, New York, NY, USA, 2024. Association for Computing Machinery.
  3. Fast winding numbers for soups and clouds. ACM Trans. Graph., 37(4), 2018.
  4. A hierarchical O(N log N) force-calculation algorithm. Nature, 324(6096):446–449, 1986.
  5. Nesti-net: Normal estimation for unstructured 3d point clouds using convolutional neural networks. In 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 10104–10112, 2019.
  6. Estimating differential quantities using polynomial fitting of osculating jets. Computer Aided Geometric Design, 22(2):121–146, 2005.
  7. Binary orientation trees for volume and surface reconstruction from unoriented point clouds. Computer Graphics Forum, 29(7):2011–2019, 2010.
  8. A volumetric method for building complex models from range images. In Proceedings of the 23rd Annual Conference on Computer Graphics and Interactive Techniques, page 303–312, New York, NY, USA, 1996. Association for Computing Machinery.
  9. trimesh, 2019.
  10. Provable surface reconstruction from noisy samples. In Proceedings of the Twentieth Annual Symposium on Computational Geometry, page 330–339, New York, NY, USA, 2004. Association for Computing Machinery.
  11. Jean Duchon. Splines minimizing rotation-invariant semi-norms in sobolev spaces. In Constructive Theory of Functions of Several Variables, pages 85–100, Berlin, Heidelberg, 1977. Springer Berlin Heidelberg.
  12. Points2Surf: Learning implicit surfaces from point clouds. In Computer Vision – ECCV 2020, pages 108–124, Cham, 2020. Springer International Publishing.
  13. Linear light source reflectometry. ACM Trans. Graph., 22(3):749–758, 2003.
  14. A fast algorithm for particle simulations. Journal of Computational Physics, 135(2):280–292, 1997.
  15. Implicit geometric regularization for learning shapes. In Proceedings of the 37th International Conference on Machine Learning. JMLR.org, 2020.
  16. PCPNet: Learning local shape properties from raw point clouds. Computer Graphics Forum, 37(2):75–85, 2018.
  17. Methods of conjugate gradients for solving linear systems. Journal of research of the National Bureau of Standards, 49:409–435, 1952.
  18. Surface reconstruction from unorganized points. In Proceedings of the 19th Annual Conference on Computer Graphics and Interactive Techniques, page 71–78, New York, NY, USA, 1992. Association for Computing Machinery.
  19. Iterative poisson surface reconstruction (ipsr) for unoriented points. ACM Trans. Graph., 41(4), 2022.
  20. Variational implicit point set surfaces. ACM Trans. Graph., 38(4), 2019.
  21. Surface reconstruction from point clouds: A survey and a benchmark, 2022.
  22. Parallel globally consistent normal orientation of raw unorganized point clouds. Computer Graphics Forum, 38(5):163–173, 2019.
  23. Screened poisson surface reconstruction. ACM Trans. Graph., 32(3), 2013.
  24. Poisson surface reconstruction. In Proceedings of the Fourth Eurographics Symposium on Geometry Processing, page 61–70, Goslar, DEU, 2006. Eurographics Association.
  25. Poisson surface reconstruction with envelope constraints. Computer Graphics Forum, 39(5):173–182, 2020.
  26. Abc: A big cad model dataset for geometric deep learning. In The IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2019.
  27. Consistent propagation of normal orientations in point clouds. In International Symposium on Vision, Modeling, and Visualization, 2009.
  28. Fitting smooth surfaces to dense polygon meshes. In Proceedings of the 23rd Annual Conference on Computer Graphics and Interactive Techniques, page 313–324, New York, NY, USA, 1996. Association for Computing Machinery.
  29. David Levin. Mesh-independent surface interpolation. In Geometric Modeling for Scientific Visualization, pages 37–49, Berlin, Heidelberg, 2004. Springer Berlin Heidelberg.
  30. Neaf: Learning neural angle fields for point normal estimation. In Proceedings of the AAAI Conference on Artificial Intelligence, 2023.
  31. Surface reconstruction from point clouds without normals by parametrizing the gauss formula. ACM Trans. Graph., 42(2), 2022.
  32. Surface reconstruction based on the modified gauss formula. ACM Trans. Graph., 38(1), 2018.
  33. Estimating the in/out function of a surface represented by points. In Proceedings of the Eighth ACM Symposium on Solid Modeling and Applications, page 108–114, New York, NY, USA, 2003. Association for Computing Machinery.
  34. Orienting point clouds with dipole propagation. ACM Trans. Graph., 40(4), 2021.
  35. PyTorch: an imperative style, high-performance deep learning library. Curran Associates Inc., Red Hook, NY, USA, 2019.
  36. Shape as points: A differentiable poisson solver. In Advances in Neural Information Processing Systems, pages 13032–13044. Curran Associates, Inc., 2021.
  37. Harmonic point cloud orientation. Computers & Graphics, 35(3):492–499, 2011. Shape Modeling International (SMI) Conference 2011.
  38. Consistently orienting facets in polygon meshes by minimizing the dirichlet energy of generalized winding numbers. CoRR, abs/1406.5431, 2014.
  39. Zippered polygon meshes from range images. In Proceedings of the 21st Annual Conference on Computer Graphics and Interactive Techniques, page 311–318, New York, NY, USA, 1994. Association for Computing Machinery.
  40. Implicit surface modelling as an eigenvalue problem. In Proceedings of the 22nd International Conference on Machine Learning, page 936–939, New York, NY, USA, 2005. Association for Computing Machinery.
  41. Learning modified indicator functions for surface reconstruction. Comput. Graph., 102(C):309–319, 2022.
  42. Piecewise c1 continuous surface reconstruction of noisy point clouds via local implicit quadric regression. In Proceedings of the 14th IEEE Visualization 2003 (VIS’03), page 13, USA, 2003. IEEE Computer Society.
  43. Surface reconstruction of noisy and defective data sets. In Proceedings of the Conference on Visualization ’04, page 259–266, USA, 2004. IEEE Computer Society.
  44. Globally consistent normal orientation for point clouds by regularizing the winding-number field. ACM Trans. Graph., 42(4), 2023.
  45. Chapter 9 - treecode and fast multipole method for n-body simulation with cuda. In GPU Computing Gems Emerald Edition, pages 113–132. Morgan Kaufmann, Boston, 2011.
  46. Fast surface reconstruction using the level set method. In Proceedings IEEE Workshop on Variational and Level Set Methods in Computer Vision, pages 194–201, 2001.
  47. Thingi10k: A dataset of 10, 000 3d-printing models. ArXiv, abs/1605.04797, 2016.
  48. Adafit: Rethinking learning-based normal estimation on point clouds. In 2021 IEEE/CVF International Conference on Computer Vision (ICCV), pages 6098–6107, 2021.
Citations (1)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
X Twitter Logo Streamline Icon: https://streamlinehq.com

Tweets