这是indexloc提供的服务，不要输入任何密码
Skip to main content
Springer Nature Link
Log in

Learning Meshing from Delaunay Triangulation for 3D Shape Representation

  • Published:
International Journal of Computer Vision Aims and scope Submit manuscript

Abstract

Recently, there has been a growing interest in learning-based explicit methods due to their ability to respect the original input and preserve details. However, the connectivity on complex structures is still difficult to infer due to the limited local shape perception, resulting in artifacts and non-watertight triangles. In this paper, we present a novel learning-based method with Delaunay triangulation to achieve high-precision reconstruction. We model the Delaunay triangulation as a dual graph, extract multi-scale geometric information from the points, and embed it into the structural representation of Delaunay triangulation in an organic way, benefiting fine-grained details reconstruction. To encourage neighborhood information interaction of edges and nodes in the graph, we introduce a Local Graph Iteration algorithm, serving as a variant of graph neural network. Benefiting from its robust local processing for dual graph, a scaling strategy is designed to enable large-scale reconstruction. Moreover, due to the complicated spatial relations between tetrahedrons and the ground truth surface, it is hard to directly generate ground truth labels of tetrahedrons for supervision. Therefore, we propose a multi-label supervision strategy, which is integrated in the loss we design for this task and allows our method to obtain robust labeling without visibility information. Experiments show that our method yields watertight and high-quality meshes. Especially for some thin structures and sharp edges, our method shows better performance than the current state-of-the-art methods. Furthermore, it has a strong adaptability to point clouds of different densities.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+
from $39.99 /Month
  • Starting from 10 chapters or articles per month
  • Access and download chapters and articles from more than 300k books and 2,500 journals
  • Cancel anytime
View plans

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

Explore related subjects

Discover the latest articles, books and news in related subjects, suggested using machine learning.

Data Availability

All the datasets we used are publicly available. The ShapeNet dataset (Chang et al., 2015) can be found in the following link: ShapeNet. The FAMOUSTHINGI (Rakotosaona et al., 2021) dataset can be found in the following link: FAMOUSTHINGI. The DTU dataset (Jensen et al., 2014) can be found in the following link: DTU. Our results and associated data can be found in the following link: Data.

References

  • Alexa, M., et al. (2003). Computing and rendering point set surfaces. IEEE Transactions on visualization and computer graphics, 9, 3–15.

    Article  Google Scholar 

  • Amenta, N., & Bern, M. (1999). Surface reconstruction by Voronoi filtering. Discrete & Computational Geometry, 22, 481–504.

    Article  MathSciNet  Google Scholar 

  • Aumentado-Armstrong, T., Tsogkas, S., Dickinson, S., & Jepson, A. D. (2022). Representing 3d shapes with probabilistic directed distance fields. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition (pp. 19343–19354).

  • Berger, M., et al. (2017). A survey of surface reconstruction from point clouds. Computer Graphics Forum, 36, 301–329.

    Article  Google Scholar 

  • Bernardini, F., Mittleman, J., Rushmeier, H., Silva, C., & Taubin, G. (1999). The ball-pivoting algorithm for surface reconstruction. IEEE Transactions on Visualization and Computer Graphics, 5, 349–359.

    Article  Google Scholar 

  • Boissonnat, J.-D., Devillers, O., Teillaud, M., & Yvinec, M. (2000). Triangulations in cgal. In Proceedings of the sixteenth annual symposium on computational geometry (pp. 11–18).

  • Boissonnat, J.-D., & Geiger, B. (1993). Three-dimensional reconstruction of complex shapes based on the delaunay triangulation. Biomedical Image Processing and Biomedical Visualization, 1905, 964–975.

    Article  Google Scholar 

  • Bolle, R. M., & Vemuri, B. C. (1991). On three-dimensional surface reconstruction methods. IEEE Transactions on Pattern Analysis & Machine Intelligence, 13, 1–13.

    Article  Google Scholar 

  • Boulch, A., & Marlet, R. (2022). Poco: Point convolution for surface reconstruction. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition (pp. 6302–6314).

  • Carr, J. C., et al. (2001). Reconstruction and representation of 3d objects with radial basis functions. In Proceedings of the 28th annual conference on computer graphics and interactive techniques (pp. 67–76).

  • Chang, A. X., et al. (2015). Shapenet: An information-rich 3d model repository. arXiv preprint arXiv:1512.03012.

  • Chen, Z., Tagliasacchi, A., Funkhouser, T., & Zhang, H. (2022). Neural dual contouring. ACM Transactions on Graphics (TOG), 41, 1–13.

    Google Scholar 

  • Chen, Z., & Zhang, H. (2019). Learning implicit fields for generative shape modeling. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition (pp. 5939–5948).

  • Chen, Z., & Zhang, H. (2021). Neural marching cubes. ACM Transactions on Graphics (TOG), 40, 1–15.

    Google Scholar 

  • Chibane, J., Pons-Moll, G., et al. (2020). Neural unsigned distance fields for implicit function learning. Advances in Neural Information Processing Systems, 33, 21638–21652.

    Google Scholar 

  • Chou, G., Chugunov, I., & Heide, F. (2022). Gensdf: Two-stage learning of generalizable signed distance functions. Advances in Neural Information Processing Systems, 35, 24905–24919.

    Google Scholar 

  • Cignoni, P., et al. (2008). MeshLab: An open-source mesh processing tool. In V. Scarano, R. D. Chiara, & U. Erra (Eds.), Eurographics Italian chapter conference. The Eurographics Association.

    Google Scholar 

  • Duan, Y., et al. (2020). Curriculum deepsdf (pp. 51–67). Springer.

    Google Scholar 

  • Edelsbrunner, H., & Mücke, E. P. (1994). Three-dimensional alpha shapes. ACM Transactions on Graphics (TOG), 13, 43–72.

    Article  Google Scholar 

  • Erler, P., Guerrero, P., Ohrhallinger, S., Mitra, N. J., & Wimmer, M. (2020). Points2surf learning implicit surfaces from point clouds. In European conference on computer vision (pp. 108–124).

  • Evrard, F., Denner, F., & Van Wachem, B. (2018). Surface reconstruction from discrete indicator functions. IEEE Transactions on Visualization and Computer Graphics, 25, 1629–1635.

    Article  Google Scholar 

  • Gao, J., et al. (2020). Learning deformable tetrahedral meshes for 3d reconstruction. Advances in Neural Information Processing Systems, 33, 9936–9947.

    Google Scholar 

  • Genova, K., Cole, F., Sud, A., Sarna, A., & Funkhouser, T. (2020). Local deep implicit functions for 3d shape. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition (pp. 4857–4866).

  • Genova, K., et al. (2019). Learning shape templates with structured implicit functions. In Proceedings of the IEEE/CVF international conference on computer vision (pp. 7154–7164).

  • Gropp, A., Yariv, L., Haim, N., Atzmon, M., & Lipman, Y. (2020). Implicit geometric regularization for learning shapes. In International conference on machine learning (pp. 3789–3799).

  • Jancosek, M., & Pajdla, T. (2011). Multi-view reconstruction preserving weakly-supported surfaces. In Proceedings of the 2011 IEEE conference on computer vision and pattern recognition (pp. 3121–3128).

  • Jancosek, M., & Pajdla, T. (2014). Exploiting visibility information in surface reconstruction to preserve weakly supported surfaces. International Scholarly Research Notices, 798595, 1–20.

  • Jensen, R., Dahl, A., Vogiatzis, G., Tola, E., & Aanæs, H. (2014). Large scale multi-view stereopsis evaluation. In Proceedings of the IEEE conference on computer vision and pattern recognition (pp. 406–413).

  • Jiang, C., et al. (2020). Local implicit grid representations for 3d scenes. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition (pp. 6001–6010).

  • Kazhdan, M. (2005). Reconstruction of solid models from oriented point sets. In Proceedings of the third Eurographics symposium on Geometry processing (pp. 73–es).

  • Kazhdan, M., Bolitho, M. & Hoppe, H. (2006). Poisson surface reconstruction. In Proceedings of the fourth Eurographics symposium on Geometry processing (Vol. 7).

  • Kazhdan, M., & Hoppe, H. (2013). Screened Poisson surface reconstruction. ACM Transactions on Graphics (ToG), 32, 1–13.

    Article  Google Scholar 

  • Kipf, T. N., & Welling, M. (2017). Semi-supervised classification with graph convolutional networks. In International conference on learning representations.

  • Kolluri, R., Shewchuk, J. R., & O’Brien, J. F. (2004). Spectral surface reconstruction from noisy point clouds. In Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on geometry processing (pp. 11–21).

  • Labatut, P., Pons, J.-P., & Keriven, R. (2007). Efficient multi-view reconstruction of large-scale scenes using interest points, delaunay triangulation and graph cuts. In 2007 IEEE 11th international conference on computer vision (pp. 1–8).

  • Labatut, P., Pons, J.-P., & Keriven, R. (2009). Robust and efficient surface reconstruction from range data. Computer Graphics Forum, 28, 2275–2290.

    Article  Google Scholar 

  • Li, S., Yao, Y., Fang, T., & Quan, L. (2018). Reconstructing thin structures of manifold surfaces by integrating spatial curves. In Proceedings of the IEEE conference on computer vision and pattern recognition (pp. 2887–2896).

  • Li, S., Zhou, J., Ma, B., Liu, Y.-S., & Han, Z. (2023). Neaf: Learning neural angle fields for point normal estimation. Proceedings of the AAAI Conference on Artificial Intelligence, 37, 1396–1404.

    Article  Google Scholar 

  • Lim, S. P., & Haron, H. (2014). Surface reconstruction techniques: A review. Artificial Intelligence Review, 42, 59–78.

    Article  Google Scholar 

  • Liu, M., Zhang, X., & Su, H. (2020). Meshing point clouds with predicted intrinsic-extrinsic ratio guidance. In European conference on computer vision (pp. 68–84).

  • Liu, S.-L., et al. (2021). Deep implicit moving least-squares functions for 3d reconstruction. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition (pp. 1788–1797).

  • Lorensen, W. E., & Cline, H. E. (1987). Marching cubes: A high resolution 3d surface construction algorithm. ACM Siggraph Computer Graphics, 21, 163–169.

    Article  Google Scholar 

  • Luo, Y., Mi, Z., & Tao, W. (2021). Deepdt: Learning geometry from delaunay triangulation for surface reconstruction. Proceedings of the AAAI Conference on Artificial Intelligence, 35, 2277–2285.

    Article  Google Scholar 

  • Ma, B., Han, Z., Liu, Y.-S., & Zwicker, M. (2021). Neural-pull: Learning signed distance function from point clouds by learning to pull space onto surface. In International conference on machine learning (pp. 7246–7257).

  • Ma, B., Liu, Y.-S., Zwicker, M., & Han, Z. (2022). Surface reconstruction from point clouds by learning predictive context priors. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition (pp. 6326–6337).

  • Manson, J., Petrova, G., & Schaefer, S. (2008). Streaming surface reconstruction using wavelets. Computer Graphics Forum, 27, 1411–1420.

    Article  Google Scholar 

  • Mescheder, L., Oechsle, M., Niemeyer, M., Nowozin, S., & Geiger, A. (2019). Occupancy networks: Learning 3d reconstruction in function space. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition (pp. 4460–4470).

  • Mi, Z., Luo, Y., & Tao, W. (2020). Ssrnet: Scalable 3d surface reconstruction network. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition (pp. 970–979).

  • Mostegel, C., & Rumpler, M. (2012). Robust surface reconstruction from noisy point clouds using graph cuts. Technical report .

  • Nagai, Y., Ohtake, Y., & Suzuki, H. (2009). Smoothing of partition of unity implicit surfaces for noise robust surface reconstruction. Computer Graphics Forum, 28, 1339–1348.

    Article  Google Scholar 

  • Ohtake, Y., Belyaev, A., & Seidel, H.-P. (2005). 3d scattered data interpolation and approximation with multilevel compactly supported rbfs. Graphical Models, 67, 150–165.

    Article  Google Scholar 

  • Öztireli, A. C., Guennebaud, G., & Gross, M. (2009). Feature preserving point set surfaces based on non-linear kernel regression. Computer Graphics Forum, 28, 493–501.

    Article  Google Scholar 

  • Park, J. J., Florence, P., Straub, J., Newcombe, R., & Lovegrove, S. (2019). Deepsdf: Learning continuous signed distance functions for shape representation. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition (pp. 165–174).

  • Peng, S., Niemeyer, M., Mescheder, L., Pollefeys, M., & Geiger, A. (2020). Convolutional occupancy networks. In European conference on computer vision (pp. 523–540).

  • Peng, S., et al. (2021). Shape as points: A differentiable Poisson solver. Advances in Neural Information Processing Systems, 34, 13032–13044.

    Google Scholar 

  • Qi, C. R., Su, H., Mo, K., & Guibas, L. J. (2017). Pointnet: Deep learning on point sets for 3d classification and segmentation. In Proceedings of the IEEE conference on computer vision and pattern recognition (pp. 652–660).

  • Rakotosaona, M.-J., Guerrero, P., Aigerman, N., Mitra, N. J., & Ovsjanikov, M. (2021). Learning delaunay surface elements for mesh reconstruction. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition (pp. 22–31).

  • Sharp, N., & Ovsjanikov, M. (2020). Pointtrinet: Learned triangulation of 3d point sets. In European conference on computer vision (pp. 762–778).

  • Shen, T., Gao, J., Yin, K., Liu, M.-Y., & Fidler, S. (2021). Deep marching tetrahedra: A hybrid representation for high-resolution 3d shape synthesis. Advances in Neural Information Processing Systems, 34, 6087–6101.

  • Sitzmann, V., Martel, J., Bergman, A., Lindell, D., & Wetzstein, G. (2020). Implicit neural representations with periodic activation functions. Advances in Neural Information Processing Systems, 33, 7462–7473.

    Google Scholar 

  • Sulzer, R., Landrieu, L., Marlet, R., & Vallet, B. (2021). Scalable surface reconstruction with delaunay-graph neural networks. Computer Graphics Forum, 40, 157–167.

    Article  Google Scholar 

  • Tancik, M., et al. (2020). Fourier features let networks learn high frequency functions in low dimensional domains. Advances in Neural Information Processing Systems, 33, 7537–7547.

    Google Scholar 

  • Taubin, G. (1995). A signal processing approach to fair surface design. In Proceedings of the 22nd annual conference on computer graphics and interactive techniques (pp. 351–358).

  • Turk, G., & Levoy, M. (1994). Zippered polygon meshes from range images. In Proceedings of the 21st annual conference on computer graphics and interactive techniques (pp. 311–318).

  • Turk, G., & Obrien, J. F. (2002). Modelling with implicit surfaces that interpolate. ACM Transactions on Graphics (TOG), 21, 855–873.

    Article  Google Scholar 

  • Wang, Z., Wang, P., Wang, P., Dong, Q., Gao, J., Chen, S., Xin, S., Tu, C., & Wang, W. (2023). Neural-imls: Self-supervised implicit moving least-squares network for surface reconstruction. IEEE Transactions on Visualization and Computer Graphics, 30, 5018–5033.

  • Williams, F., Gojcic, Z., Khamis, S., Zorin, D., Bruna, J., Fidler, S., & Litany, O. (2022). Neural fields as learnable kernels for 3d reconstruction. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (pp. 18500–18510).

  • Williams, F., Trager, M., Bruna, J., & Zorin, D. (2021). Neural splines: Fitting 3d surfaces with infinitely-wide neural networks, In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (pp. 9949–9958).

  • Wu, J., Zhang, C., Xue, T., Freeman, B., & Tenenbaum, J. (2016). Learning a probabilistic latent space of object shapes via 3d generative-adversarial modeling. Advances in Neural Information Processing Systems, 29.

  • You, C. C., et al. (2020). A survey on surface reconstruction techniques for structured and unstructured data. In 2020 IEEE conference on open systems (ICOS) (pp. 37–42).

  • Yuan, G., Fu, Q., Mi, Z., Luo, Y., & Tao, W. (2023). Ssrnet: Scalable 3d surface reconstruction network. IEEE Transactions on Visualization and Computer Graphics, 29, 4906–4919.

    Article  Google Scholar 

  • Zhang, C., Yuan, G., & Tao, W. (2023). Dmnet: Delaunay meshing network for 3d shape representation. In 2023 IEEE/CVF international conference on computer vision (ICCV) (pp. 14372–14382).

  • Zhou, Y., Shen, S., & Hu, Z. (2019). Detail preserved surface reconstruction from point cloud. Sensors, 19, 1278.

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grants 62176096.

Author information

Authors and Affiliations

  1. National Key Laboratory of Science and Technology on Multi-spectral Information Processing, Huazhong University of Science and Technology, Wuhan, 430074, China

    Chen Zhang & Wenbing Tao

Authors
  1. Chen Zhang
    View author publications

    Search author on:PubMed Google Scholar

  2. Wenbing Tao
    View author publications

    Search author on:PubMed Google Scholar

Corresponding author

Correspondence to Wenbing Tao.

Additional information

Communicated by Xiaowei Zhou.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary file 1 (mp4 22337 KB)

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, C., Tao, W. Learning Meshing from Delaunay Triangulation for 3D Shape Representation. Int J Comput Vis 133, 3413–3436 (2025). https://doi.org/10.1007/s11263-024-02344-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Version of record:

  • Issue date:

  • DOI: https://doi.org/10.1007/s11263-024-02344-9

Keywords