NeurCADRecon: Neural Representation for Reconstructing CAD Surfaces by Enforcing Zero Gaussian Curvature
Authors: 
Qiujie Dong, 
Rui Xu, Pengfei Wang, Shuangmin Chen, Shiqing Xin, Xiaohong Jia, Wenping Wang, Changhe TuAuthors Info & Claims
Article No.: 51, Pages 1 - 17
Abstract
Despite recent advances in reconstructing an organic model with the neural signed distance function (SDF), the high-fidelity reconstruction of a CAD model directly from low-quality unoriented point clouds remains a significant challenge. In this paper, we address this challenge based on the prior observation that the surface of a CAD model is generally composed of piecewise surface patches, each approximately developable even around the feature line. Our approach, named NeurCADRecon, is self-supervised, and its loss includes a developability term to encourage the Gaussian curvature toward 0 while ensuring fidelity to the input points (see the teaser figure). Noticing that the Gaussian curvature is non-zero at tip points, we introduce a double-trough curve to tolerate the existence of these tip points. Furthermore, we develop a dynamic sampling strategy to deal with situations where the given points are incomplete or too sparse. Since our resulting neural SDFs can clearly manifest sharp feature points/lines, one can easily extract the feature-aligned triangle mesh from the SDF and then decompose it into smooth surface patches, greatly reducing the difficulty of recovering the parametric CAD design. A comprehensive comparison with existing state-of-the-art methods shows the significant advantage of our approach in reconstructing faithful CAD shapes.
References
[1]
M. Atzmon and Y. Lipman. 2020. SAL: Sign Agnostic Learning of Shapes From Raw Data. In 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). IEEE Computer Society, Los Alamitos, CA, USA, 2562--2571.
[2]
Matan Atzmon and Yaron Lipman. 2021. SALD: Sign Agnostic Learning with Derivatives. In International Conference on Learning Representations (ICLR).
[3]
Yizhak Ben-Shabat, Chamin Hewa Koneputugodage, and Stephen Gould. 2022. DiGS: Divergence guided shape implicit neural representation for unoriented point clouds. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR).
[4]
Alexandre Boulch and Renaud Marlet. 2022. POCO: Point Convolution for Surface Reconstruction. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR).
[5]
Fatih Calakli and Gabriel Taubin. 2011. SSD: Smooth Signed Distance Surface Reconstruction. Computer Graphics Forum 30, 7 (2011), 1993--2002.
[6]
Jonathan C Carr, Richard K Beatson, Jon B Cherrie, Tim J Mitchell, W Richard Fright, Bruce C McCallum, and Tim R Evans. 2001. Reconstruction and representation of 3D objects with radial basis functions. In Proceedings of the 28th annual conference on Computer graphics and interactive techniques.
[7]
Rohan Chabra, Jan E Lenssen, Eddy Ilg, Tanner Schmidt, Julian Straub, Steven Lovegrove, and Richard Newcombe. 2020. Deep Local Shapes: Learning local sdf priors for detailed 3d reconstruction. In Computer Vision-ECCV 2020: 16th European Conference, Glasgow, UK, August 23--28, 2020, Proceedings, Part XXIX 16. Springer, 608--625.
[8]
Angel X. Chang, Thomas Funkhouser, Leonidas Guibas, Pat Hanrahan, Qixing Huang, Zimo Li, Silvio Savarese, Manolis Savva, Shuran Song, Hao Su, Jianxiong Xiao, Li Yi, and Fisher Yu. 2015. ShapeNet: An Information-Rich 3D Model Repository. Technical Report arXiv:1512.03012 [cs.GR].
[9]
Zhiqin Chen, Andrea Tagliasacchi, Thomas Funkhouser, and Hao Zhang. 2022. Neural dual contouring. ACM Trans. Graph. 41, 4 (jul 2022).
[10]
Zhiqin Chen and Hao Zhang. 2021. Neural marching cubes. ACM Trans. Graph. 40, 6 (dec 2021).
[11]
Xingyi Du, Qingnan Zhou, Nathan Carr, and Tao Ju. 2021. Boundary-sampled halfspaces: a new representation for constructive solid modeling. 40, 4 (jul 2021).
[12]
Philipp Erler, Paul Guerrero, Stefan Ohrhallinger, Niloy J Mitra, and Michael Wimmer. 2020. Points2Surf: learning implicit surfaces from point clouds. In Proceedings of the European Conference on Computer Vision (ECCV).
[13]
Ron Goldman. 2005. Curvature formulas for implicit curves and surfaces. Computer Aided Geometric Design 22, 7 (2005), 632--658.
[14]
Amos Gropp, Lior Yariv, Niv Haim, Matan Atzmon, and Yaron Lipman. 2020. Implicit Geometric Regularization for Learning Shapes. In Proceedings of the International Conference on Machine Learning (ICML).
[15]
Fei Hou, Chiyu Wang, Wencheng Wang, Hong Qin, Chen Qian, and Ying He. 2022. Iterative Poisson Surface Reconstruction (IPSR) for Unoriented Points. ACM Trans. Graph. 41, 4 (2022), 13 pages.
[16]
Jiahui Huang, Hao-Xiang Chen, and Shi-Min Hu. 2022. A Neural Galerkin Solver for Accurate Surface Reconstruction. ACM Trans. Graph. 41, 6 (2022), 16 pages.
[17]
Zhiyang Huang, Nathan Carr, and Tao Ju. 2019. Variational Implicit Point Set Surfaces. ACM Trans. Graph. 38, 4 (2019), 13 pages.
[18]
Chiyu Jiang, Avneesh Sud, Ameesh Makadia, Jingwei Huang, Matthias Nießner, Thomas Funkhouser, et al. 2020. Local implicit grid representations for 3d scenes. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR).
[19]
Tao Ju, Frank Losasso, Scott Schaefer, and Joe Warren. 2002. Dual Contouring of Hermite Data. ACM Trans. Graph. 21, 3 (jul 2002), 339--346.
[20]
Dan Julius, Vladislav Kraevoy, and Alla Sheffer. 2005. D-charts: Quasi-developable mesh segmentation. In Computer Graphics Forum, Vol. 24. Citeseer, 581--590.
[21]
Kacper Kania, Maciej Zieba, and Tomasz Kajdanowicz. 2020. UCSG-NET-unsupervised discovering of constructive solid geometry tree. Advances in Neural Information Processing Systems 33 (2020), 8776--8786.
[22]
Misha Kazhdan, Ming Chuang, Szymon M. Rusinkiewicz, and Hugues Hoppe. 2020. Poisson Surface Reconstruction with Envelope Constraints. Computer Graphics Forum 30, 7 (2020), 1993--2002.
[23]
Michael Kazhdan and Hugues Hoppe. 2013. Screened Poisson surface reconstruction. ACM Transactions on Graphics (ToG) 32, 3 (2013), 1--13.
[24]
Michael M. Kazhdan, Matthew Bolitho, and Hugues Hoppe. 2006. Poisson surface reconstruction. In Eurographics Symposium on Geometry Processing.
[25]
Diederik P. Kingma and Jimmy Ba. 2014. Adam: A Method for Stochastic Optimization.
[26]
Johannes Knoblauch. 1913. Grundlagen der differentialgeometrie. BG Teubner. 89--94 pages.
[27]
Sebastian Koch, Albert Matveev, Zhongshi Jiang, Francis Williams, Alexey Artemov, Evgeny Burnaev, Marc Alexa, Denis Zorin, and Daniele Panozzo. 2019. ABC: A Big CAD Model Dataset For Geometric Deep Learning. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR).
[28]
Ravikrishna Kolluri. 2008. Provably good moving least squares. ACM Transactions on Algorithms (TALG) (2008).
[29]
John M. Lee. 2018. The Gauss-Bonnet Theorem. Springer International Publishing, Cham, 263--282.
[30]
Thomas Lewiner, Hélio Lopes, Antônio Wilson Vieira, and Geovan Tavares. 2003. Efficient implementation of marching cubes' cases with topological guarantees. Journal of Graphics Tools 8, 2 (2003), 1--15.
[31]
Lingxiao Li, Minhyuk Sung, Anastasia Dubrovina, Li Yi, and Leonidas J Guibas. 2019. Supervised fitting of geometric primitives to 3d point clouds. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2652--2660.
[32]
Manyi Li, Falai Chen, Wenping Wang, and Changhe Tu. 2016. Sparse RBF surface representations. Computer Aided Geometric Design 48 (2016), 49--59.
[33]
Guying Lin, Lei Yang, Congyi Zhang, Hao Pan, Yuhan Ping, Guodong Wei, Taku Komura, John Keyser, and Wenping Wang. 2023. Patch-Grid: An Efficient and Feature-Preserving Neural Implicit Surface Representation. arXiv:2308.13934 [cs.GR]
[34]
Siyou Lin, Dong Xiao, Zuoqiang Shi, and Bin Wang. 2022. Surface Reconstruction from Point Clouds without Normals by Parametrizing the Gauss Formula. ACM Trans. Graph. 42, 2 (2022), 19 pages.
[35]
Yaron Lipman. 2021. Phase Transitions, Distance Functions, and Implicit Neural Representations. In Proceedings of the International Conference on Machine Learning (ICML).
[36]
Baorui Ma, Zhizhong Han, Yu-Shen Liu, and Matthias Zwicker. 2021. Neural-Pull: Learning Signed Distance Functions from Point Clouds by Learning to Pull Space onto Surfaces. In Proceedings of the International Conference on Machine Learning (ICML).
[37]
Baorui Ma, Liu Yu-Shen, Zwicker Matthias, and Han Zhizhong. 2022. Surface Reconstruction from Point Clouds by Learning Predictive Context Priors. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR).
[38]
Lars Mescheder, Michael Oechsle, Michael Niemeyer, Sebastian Nowozin, and Andreas Geiger. 2019. Occupancy Networks: Learning 3D Reconstruction in Function Space. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR).
[39]
G.M. Nielson. 2004. Dual marching cubes. In IEEE Visualization 2004. 489--496.
[40]
Yutaka Ohtake, Alexander G. Belyaev, Marc Alexa, Greg Turk, and Hans-Peter Seidel. 2003. Multi-level partition of unity implicits. ACM SIGGRAPH 2005 Courses (2003).
[41]
A Cengiz Öztireli, Gael Guennebaud, and Markus Gross. 2009. Feature preserving point set surfaces based on non-linear kernel regression. In Computer Graphics Forum.
[42]
Jeong Joon Park, Peter Florence, Julian Straub, Richard Newcombe, and Steven Love-grove. 2019. DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR).
[43]
Songyou Peng, Chiyu "Max" Jiang, and Yiyi Liao. 2021. Shape As Points: A Differentiable Poisson Solver. In Advances in Neural Information Processing Systems (NeurIPS).
[44]
Songyou Peng, Michael Niemeyer, Lars Mescheder, Marc Pollefeys, and Andreas Geiger. 2020. Convolutional Occupancy Networks. In Computer Vision - ECCV 2020: 16th European Conference, Glasgow, UK, August 23--28, 2020, Proceedings, Part III (Glasgow, United Kingdom). Springer-Verlag, Berlin, Heidelberg, 523--540.
[45]
C. Schroers, S. Setzer, and J. Weickert. 2014. A Variational Taxonomy for Surface Reconstruction from Oriented Points. Computer Graphics Forum 33, 5 (2014), 195--204.
[46]
Silvia Sellán, Noam Aigerman, and Alec Jacobson. 2020. Developability of Heightfields via Rank Minimization. ACM Trans. Graph. 39, 4 (aug 2020).
[47]
Gopal Sharma, Rishabh Goyal, Difan Liu, Evangelos Kalogerakis, and Subhransu Maji. 2018. CSGNet: Neural Shape Parser for Constructive Solid Geometry. In The IEEE Conference on Computer Vision and Pattern Recognition (CVPR).
[48]
Gopal Sharma, Difan Liu, Subhransu Maji, Evangelos Kalogerakis, Siddhartha Chaudhuri, and Radomír Měch. 2020. ParSeNet: A parametric surface fitting network for 3d point clouds. In Computer Vision-ECCV 2020: 16th European Conference, Glasgow, UK, August 23--28, 2020, Proceedings, Part VII 16. Springer, 261--276.
[49]
Chen Shen, James F. O'Brien, and Jonathan R. Shewchuk. 2004. Interpolating and Approximating Implicit Surfaces from Polygon Soup. In ACM SIGGRAPH 2004 Papers.
[50]
Vincent Sitzmann, Julien N.P. Martel, Alexander W. Bergman, David B. Lindell, and Gordon Wetzstein. 2020. Implicit Neural Representations with Periodic Activation Functions. In Advances in Neural Information Processing Systems (NeurIPS).
[51]
Michael David Spivak. 1975. A comprehensive introduction to differential geometry, Vol. 3. 204.
[52]
Oded Stein, Eitan Grinspun, and Keenan Crane. 2018. Developability of Triangle Meshes. ACM Trans. Graph. 37, 4 (jul 2018).
[53]
Jiapeng Tang, Jiabao Lei, Dan Xu, Feiying Ma, Kui Jia, and Lei Zhang. 2021b. SAConvONet: Sign-Agnostic Optimization of Convolutional Occupancy Networks. In Proceedings of the IEEE/CVF International Conference on Computer Vision.
[54]
Jia-Heng Tang, Weikai Chen, jie Yang, Bo Wang, Songrun Liu, Bo Yang, and Lin Gao. 2021a. OctField: Hierarchical Implicit Functions for 3D Modeling. In Advances in Neural Information Processing Systems (NeurIPS).
[55]
Mikaela Angelina Uy, Yen-Yu Chang, Minhyuk Sung, Purvi Goel, J. Lambourne, Tolga Birdal, and Leonidas J. Guibas. 2021. Point2Cyl: Reverse Engineering 3D Objects from Point Clouds to Extrusion Cylinders. 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) (2021), 11840--11850.
[56]
Peng-Shuai Wang, Yang Liu, and Xin Tong. 2022a. Dual Octree Graph Networks for Learning Adaptive Volumetric Shape Representations. ACM Trans. Graph. 41, 4 (2022), 15 pages.
[57]
Yifan Wang, Lukas Rahmann, and Olga Sorkine-Hornung. 2022b. Geometry-consistent neural shape representation with implicit displacement fields. In The Tenth International Conference on Learning Representations. OpenReview.
[58]
Yifan Wang, Shihao Wu, Cengiz Oztireli, and Olga Sorkine-Hornung. 2021. Iso-points: Optimizing neural implicit surfaces with hybrid representations. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 374--383.
[59]
Zixiong Wang, Yunxiao Zhang, Rui Xu, Fan Zhang, Peng-Shuai Wang, Shuangmin Chen, Shiqing Xin, Wenping Wang, and Changhe Tu. 2023. Neural-Singular-Hessian: Implicit Neural Representation of Unoriented Point Clouds by Enforcing Singular Hessian. ACM Trans. Graph. 42, 6 (dec 2023).
[60]
Karl DD Willis, Yewen Pu, Jieliang Luo, Hang Chu, Tao Du, Joseph G Lambourne, Armando Solar-Lezama, and Wojciech Matusik. 2021. Fusion 360 gallery: A dataset and environment for programmatic cad construction from human design sequences. ACM Transactions on Graphics (TOG) 40, 4 (2021), 1--24.
[61]
Rundi Wu, Chang Xiao, and Changxi Zheng. 2021. DeepCAD: A deep generative network for computer-aided design models. In Proceedings of the IEEE/CVF International Conference on Computer Vision. 6772--6782.
[62]
Rui Xu, Zhiyang Dou, Ningna Wang, Shiqing Xin, Shuangmin Chen, Mingyan Jiang, Xiaohu Guo, Wenping Wang, and Changhe Tu. 2023. Globally consistent normal orientation for point clouds by regularizing the winding-number field. ACM Transactions on Graphics (TOG) 42, 4 (2023), 1--15.
[63]
Rui Xu, Zixiong Wang, Zhiyang Dou, Chen Zong, Shiqing Xin, Mingyan Jiang, Tao Ju, and Changhe Tu. 2022. RFEPS: Reconstructing Feature-line Equipped Polygonal Surface. ACM Transactions on Graphics (TOG) (2022), 15 pages.
[64]
Fenggen Yu, Zhiqin Chen, Manyi Li, Aditya Sanghi, Hooman Shayani, Ali Mahdavi-Amiri, and Hao Zhang. 2022. CAPRI-Net: learning compact CAD shapes with adaptive primitive assembly. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 11768--11778.
[65]
Jingyang Zhang, Yao Yao, Shiwei Li, Tian Fang, David McKinnon, Yanghai Tsin, and Long Quan. 2022. Critical regularizations for neural surface reconstruction in the wild. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 6270--6279.
[66]
Junsheng Zhou, Baorui Ma, Liu Yu-Shen, Fang Yi, and Han Zhizhong. 2022. Learning Consistency-Aware Unsigned Distance Functions Progressively from Raw Point Clouds. In Advances in Neural Information Processing Systems (NeurIPS).
Index Terms
- NeurCADRecon: Neural Representation for Reconstructing CAD Surfaces by Enforcing Zero Gaussian Curvature
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Published: 19 July 2024
Published in TOG Volume 43, Issue 4
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- National Natural Science Foundation of China
- NSF of Shandong Province
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