We present a simple yet efficient algorithm for recognizing simple quadric primitives (plane, sphere, cylinder, cone) from triangular meshes. Our approach is an improved version of a previous hierarchical clustering algorithm, which performs pairwise clustering of triangle patches from bottom to top. The key contributions of our approach include a strategy for priority and fidelity consideration of the detected primitives, and a scheme for boundary smoothness between adjacent clusters. Experimental results demonstrate that the proposed method produces qualitatively and quantitatively better results than representative state-of-the-art methods on a wide range of test data.
Várady, T.; Martin, R. R.; Cox, J. Reverse engineering of geometric models: An introduction. Computer-Aided Design Vol. 29, No. 4, 255–268, 1997.
Petitjean, S. A survey of methods for recovering quadrics in triangle meshes. ACM Computing Surveys Vol. 34, No. 2, 211–262, 2002.
Luo, L.; Baran, I.; Rusinkiewicz, S.; Matusik, W. Chopper: Partitioning models into 3D-printable parts. ACM Transactions on Graphics Vol. 31, No. 6, Article No. 129, 2012.
Hu, R.; Li, H.; Zhang, H.; Cohen-Or, D. Approximate pyramidal shape decomposition. ACM Transactions on Graphics Vol. 33, No. 6, Article No. 213, 2014.
Lien, J. M.; Amato, N. M. Approximate convex decomposition of polyhedra and its applications. Computer Aided Geometric Design Vol. 25, No. 7, 503–522, 2008.
David, C.-S.; Pierre, A.; Mathieu, D. Variational shape approximation. ACM Transactions on Graphics Vol. 23, No. 3, https://doi.org/10.1145/1015706.1015817, 2004.
Wu, J.; Kobbelt, L. Structure recovery via hybrid variational surface approximation. Computer Graphics Forum Vol. 24, No. 3, 277–284, 2005.
Julius, D.; Kraevoy, V.; Sheffer, A. D-charts: Quasi-developable mesh segmentation. Computer Graphics Forum Vol. 24, No. 3, 581–590, 2005.
Simari, P. D.; Singh, K. Extraction and remeshing of ellipsoidal representations from mesh data. In: Proceedings of Graphics Interface, 161–168, 2005.
Lu, L.; Choi, Y. K., Wang, W. P.; Kim, M. S. Variational 3D shape segmentation for bounding volume computation. Computer Graphics Forum Vol. 26, No. 3, 329–338, 2007.
Yan, D. M.; Wang, W. P.; Liu, Y.; Yang, Z. W. Variational mesh segmentation via quadric surface fitting. Computer-Aided Design Vol. 44, No. 11, 1072–1082, 2012.
Kim, Y. M.; Mitra, N. J.; Yan, D. M.; Guibas, L. Acquiring 3D indoor environments with variability and repetition. ACM Transactions on Graphics Vol. 31, No. 6, Article No. 138, 2012.
Katz, S.; Tal, A. Hierarchical mesh decomposition using fuzzy clustering and cuts. ACM Transactions on Graphics Vol. 22, No. 3, 954–961, 2003.
Ji, Z.; Liu, L.; Chen, Z.; Wang, G. Easy mesh cutting. Computer Graphics Forum Vol. 25, No. 3, 283–291, 2006.
Lavoue, G.; Dupont, F.; Baskurt, A. A new CAD mesh segmentation method, based on curvature tensor analysis. Computer-Aided Design Vol. 37, No. 10, 975–987, 2005.
Yan, D. M.; Liu, Y.; Wang, W. P. Quadric surface extraction by variational shape approximation. In: Geometric Modeling and Processing — GMP 2006. Lecture Notes in Computer Science, Vol. 4077. Kim, M. S.; Shimada, K. Eds. Springer Berlin Heidelberg, 73–86, 2006.
Le, T.; Bui, G.; Duan, Y. A multi-view recurrent neural network for 3D mesh segmentation. Computers & Graphics Vol. 66, 103–112, 2017.
Garland, M.; Willmott, A.; Heckbert, P. S. Hierarchical face clustering on polygonal surfaces. In: Proceedings of the Symposium on Interactive 3D Graphics, 49–58, 2001.
Attene, M.; Falcidieno, B.; Spagnuolo, M. Hierarchical mesh segmentation based on fitting primitives. The Visual Computer Vol. 22, No. 3, 181–193, 2006.
Zhuang, Y. X.; Dou, H.; Carr, N., Ju, T. Feature-aligned segmentation using correlation clustering. Computational Visual Media Vol. 3, No. 2, 147–160, 2017.
Shamir, A. A survey on mesh segmentation techniques. Computer Graphics Forum Vol. 27, No. 6, 1539–1556, 2008.
Kaiser, A.; Ybanez Zepeda, J. A.; Boubekeur, T. A survey of simple geometric primitives detection methods for captured 3D data. Computer Graphics Forum Vol. 38, No. 1, 167–196, 2019.
Fitzgibbon, A. W.; Eggert, D. W.; Fisher, R. B. High-level cad model acquisition from range images. Computer-Aided Design Vol. 29, No. 4, 321–330, 1997.
Vieira, M.; Shimada, K. Surface mesh segmentation and smooth surface extraction through region growing. Computer Aided Geometric Design Vol. 22, No. 8, 771–792, 2005.
Lloyd, S. Least squares quantization in PCM. IEEE Transactions on Information Theory Vol. 28, No. 2, 129–137, 1982.
Schnabel, R.; Wahl, R.; Klein, R. Efficient RANSAC for point-cloud shape detection. Computer Graphics Forum Vol. 26, No. 2, 214–226, 2007.
Li, H.; Wan, G. W.; Li, H. H.; Sharf, A.; Xu, K.; Chen, B. Q. Mobility fitting using 4D ransac. Computer Graphics Forum Vol. 35, No. 5, 79–88, 2016.
Lee, Y.; Lee, S.; Shamir, A.; Cohen-Or, D.; Seidel, H. P. Mesh scissoring with minima rule and part salience. Computer Aided Geometric Design Vol. 22, No. 5, 444–465, 2005.
Rodrigues, R. S. V.; Morgado, J. F. M.; Gomes, A. J. P. Part-based mesh segmentation: A survey. Computer Graphics Forum Vol. 37, No. 6, 235–274, 2018.
Lai, Y. K.; Hu, S. M.; Martin, R. R., Rosin, P. L. Rapid and effective segmentation of 3D models using random walks. Computer Aided Geometric Design Vol. 26, No. 6, 665–679, 2009.
Lafarge, F.; Keriven, R.; Brédif, M. Insertion of 3-D-primitives in mesh-based representations: Towards compact models preserving the details. IEEE Transactions on Image Processing Vol. 19, No. 7, 1683–1694, 2010.
Chen, X. B.; Golovinskiy, A., Funkhouser, T. A benchmark for 3D mesh segmentation. In: Proceedings of the ACM SIGGRAPH 2009 papers, Article No. 73, 2009.
Zheng, Y. Y.; Tai, C. L., Au, O. K. C. Dot scissor: A single-click interface for mesh segmentation. IEEE Transactions on Visualization and Computer Graphics Vol. 18, No. 8, 1304–1312, 2012.
Au, O. K.-C.; Zheng, Y.; Chen, M.; Xu, P.; Tai, C.-L. Mesh segmentation with concavity-aware fields. IEEE Transactions on Visualization and Computer Graphics Vol. 18, No. 7, 1125–1134, 2012.
Liu, R.; Zhang, H. Mesh segmentation via spectral embedding and contour analysis. Computer Graphics Forum Vol. 26, No. 3, 385–394, 2007.
Theologou, P.; Pratikakis, I.; Theoharis, T. Unsupervised spectral mesh segmentation driven by heterogeneous graphs. IEEE Transactions on Pattern Analysis and Machine Intelligence Vol. 39, No. 2, 397–410, 2017.
Ohtake, Y., Belyaev, A., Seidel, H. P. Ridge-valley lines on meshes via implicit surface fitting. ACM Transactions on Graphics Vol. 23, No. 3, 609–612, 2004.
Cao, Y. H.; Yan, D. M.; Wonka, P. Patch layout generation by detecting feature networks. Computers & Graphics Vol. 46, 275–282, 2015.
Dai, C.; Wang, C. C. L.; Wu, C.; Lefebvre, S.; Fang, G.; Liu, Y.-J. Support-free volume printing by multi-axis motion. ACM Transactions on Graphics Vol. 37, No. 4, Article No. 134, 2018.
Chen, X.; Li, H.; Fu, C.-W.; Zhang, H.; Daniel, C.-O.; Chen, B. 3D fabrication with universal building blocks and pyramidal shells. ACM Transactions on Graphics Vol. 37, No. 6, Article No. 189, 2018.
Kalogerakis, E.; Averkiou, M.; Maji, S.; Chaudhuri, S. 3D shape segmentation with projective convolutional networks. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 6630–6639, 2017.
Shu, Z. Y.; Qi, C. W.; Xin, S. Q.; Hu, C.; Wang, L.; Zhang, Y.; Liu, L. G. Unsupervised 3D shape segmentation and co-segmentation via deep learning. Computer Aided Geometric Design Vol. 43, 39–52, 2016.
Guo, K.; Zou, D. Q.; Chen, X. W. 3D mesh labeling via deep convolutional neural networks. ACM Transactions on Graphics Vol. 35, No. 1, Article No. 3, 2015.
Charles, R. Q.; Su, H.; Kaichun, M.; Guibas, L. J. Pointnet: Deep learning on point sets for 3D classification and segmentation. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 77–85, 2017.
Xu, H.; Dong, M.; Zhong, Z. Directionally convolutional networks for 3D shape segmentation. In: Proceedings of the IEEE International Conference on Computer Vision, 2698–2707, 2017.
Nan, L. L.; Xie, K.; Sharf, A. A search-classify approach for cluttered indoor scene understanding. ACM Transactions on Graphics Vol. 31, No. 6, Article No. 137, 2012.
Dai, A.; Chang, A. X.; Savva, M.; Halber, M.; Funkhouser, T.; Niefiner, M. ScanNet: Richlyannotated 3D reconstructions of indoor scenes. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2432–2443, 2017.
Nguyen, D. T.; Hua, B. S.; Yu, L. F.; Yeung, S. K. A robust 3D-2D interactive tool for scene segmentation and annotation. IEEE Transactions on Visualization and Computer Graphics Vol. 24, No. 12, 3005–3018, 2018.
Taubin, G. Estimation of planar curves, surfaces, and nonplanar space curves defined by implicit equations with applications to edge and range image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence Vol. 13, No. 11, 1115–1138, 1991.
Huang, H. B.; Kalogerakis, E.; Chaudhuri, S.; Ceylan, D.; Kim, V. G.; Yumer, E. Learning local shape descriptors from part correspondences with multiview convolutional networks. ACM Transactions on Graphics Vol. 37, No. 1, Article No. 6, 2018.
Maron, H.; Galun, M.; Aigerman, N.; Trope, M.; Dym, N.; Yumer, E.; Kim, V.G.; Lipman. Convolutional neural networks on surfaces via seamless toric covers. ACM Transactions on Graphics Vol. 36, No. 4, Article No. 71, 2017.
Mitra, N. J.; Guibas, L. J.; Pauly, M. Partial and approximate symmetry detection for 3D geometry. ACM Transactions on Graphics Vol. 25, No. 3, 560–568, 2006.
This work was supported by the National Natural Science of Foundation for Outstanding Young Scholars (12022117), the National Natural Science Foundation of China (61872354), the Beijing Natural Science Foundation (Z190004), and the Intelligent Science and Technology Advanced subject project of University of Chinese Academy of Sciences (115200S001).
Xiaolong Yang received his B.S. degree in information and computing science from Northwestern Polytechnical University in 2017 and is currently pursuing his M.S. and Ph.D. degrees at the Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences. His research interests are in computer graphics and computer vision.
Xiaohong Jia is an associate professor at the Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences. She received her Ph.D. and bachelor degrees from the University of Science and Technology of China in 2009 and 2004, respectively. Her research interests include computer graphics, computer aided geometric design, and computational algebraic geometry.
About this article
Cite this article
Yang, X., Jia, X. Simple primitive recognition via hierarchical face clustering. Comp. Visual Media 6, 431–443 (2020). https://doi.org/10.1007/s41095-020-0192-6
- quadric primitive extraction
- hierarchical clustering