“MeshCNN: a network with an edge” by Hanocka, Hertz, Fish, Giryes, Fleishman, et al. …

  • ©Rana Hanocka, Amir Hertz, Noa Fish, Raja Giryes, Shachar Fleishman, and Daniel Cohen-Or




    MeshCNN: a network with an edge

Session/Category Title:   Off the Deep End



    Polygonal meshes provide an efficient representation for 3D shapes. They explicitly captureboth shape surface and topology, and leverage non-uniformity to represent large flat regions as well as sharp, intricate features. This non-uniformity and irregularity, however, inhibits mesh analysis efforts using neural networks that combine convolution and pooling operations. In this paper, we utilize the unique properties of the mesh for a direct analysis of 3D shapes using MeshCNN, a convolutional neural network designed specifically for triangular meshes. Analogous to classic CNNs, MeshCNN combines specialized convolution and pooling layers that operate on the mesh edges, by leveraging their intrinsic geodesic connections. Convolutions are applied on edges and the four edges of their incident triangles, and pooling is applied via an edge collapse operation that retains surface topology, thereby, generating new mesh connectivity for the subsequent convolutions. MeshCNN learns which edges to collapse, thus forming a task-driven process where the network exposes and expands the important features while discarding the redundant ones. We demonstrate the effectiveness of MeshCNN on various learning tasks applied to 3D meshes.


    1. Adobe. 2016. Adobe Fuse 3D Characters. https://www.mixamo.com.Google Scholar
    2. Dragomir Anguelov, Praveen Srinivasan, Daphne Koller, Sebastian Thrun, Jim Rodgers, and James Davis. 2005. SCAPE: Shape Completion and Animation of People. In ACM SIGGRAPH 2005 Papers (SIGGRAPH ’05). ACM, New York, NY, USA, 408–416. Google ScholarDigital Library
    3. James Atwood and Don Towsley. 2016. Diffusion-convolutional Neural Networks. In Proceedings of the 30th International Conference on Neural Information Processing Systems (NIPS’16). Curran Associates Inc., USA, 2001–2009. http://dl.acm.org/citation.cfm?id=3157096.3157320 Google ScholarDigital Library
    4. Matan Atzmon, Haggai Maron, and Yaron Lipman. 2018. Point Convolutional Neural Networks by Extension Operators. ACM Trans. Graph. 37, 4 (July 2018), 71:1–71:12. Google ScholarDigital Library
    5. Mark de Berg, Otfried Cheong, Marc van Kreveld, and Mark Overmars. 2008. Computational Geometry: Algorithms and Applications (3rd ed. ed.). Springer-Verlag TELOS, Santa Clara, CA, USA. Google ScholarDigital Library
    6. Federica Bogo, Javier Romero, Matthew Loper, and Michael J Black. 2014. FAUST: Dataset and evaluation for 3D mesh registration. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. 3794–3801. Google ScholarDigital Library
    7. Davide Boscaini, Jonathan Masci, Simone Melzi, Michael M Bronstein, Umberto Castellani, and Pierre Vandergheynst. 2015. Learning class-specific descriptors for deformable shapes using localized spectral convolutional networks. In Computer Graphics Forum, Vol. 34. Wiley Online Library, 13–23.Google Scholar
    8. Davide Boscaini, Jonathan Masci, Emanuele Rodolà, and Michael Bronstein. 2016. Learning shape correspondence with anisotropic convolutional neural networks. In Advances in Neural Information Processing Systems. 3189–3197. Google ScholarDigital Library
    9. Mario Botsch, Leif Kobbelt, Mark Pauly, Pierre Alliez, and Bruno Lévy. 2010. Polygon mesh processing. AK Peters/CRC Press.Google Scholar
    10. Darko Bozidar and Tomaz Dobravec. 2015. Comparison of parallel sorting algorithms. CoRR abs/1511.03404 (2015).Google Scholar
    11. Andrew Brock, Theodore Lim, J.M. Ritchie, and Nick Weston. 2016. Generative and Discriminative Voxel Modeling with Convolutional Neural Networks. In NIPS 3D Deep Learning Workshop.Google Scholar
    12. Alexander M Bronstein, Michael M Bronstein, Leonidas J Guibas, and Maks Ovsjanikov. 2011. Shape google: Geometric words and expressions for invariant shape retrieval. ACM Transactions on Graphics (TOG) 30, 1 (2011), 1. Google ScholarDigital Library
    13. Michael M. Bronstein, Joan Bruna, Yann LeCun, Arthur Szlam, and Pierre Vandergheynst. 2017. Geometric Deep Learning: Going beyond Euclidean data. IEEE Signal Process. Mag. 34, 4 (2017), 18–42.Google ScholarCross Ref
    14. Joan Bruna, Wojciech Zaremba, Arthur Szlam, and Yann LeCun. 2014. Spectral Networks and Locally Connected Networks on Graphs. In International Conference on Learning Representations (ICLR).Google Scholar
    15. C. Cangea, P. Velickovic, N. Jovanovic, T. Kipf, and P. Lio. 2018. Towards Sparse Hierarchical Graph Classifiers. In NeurIPS Workshop on Relational Representation Learning.Google Scholar
    16. Liang-Chieh Chen, George Papandreou, Iasonas Kokkinos, Kevin Murphy, and Alan L Yuille. 2018. Deeplab: Semantic image segmentation with deep convolutional nets, atrous convolution, and fully connected crfs. IEEE transactions on pattern analysis and machine intelligence 40, 4 (2018), 834–848.Google Scholar
    17. Michaël Defferrard, Xavier Bresson, and Pierre Vandergheynst. 2016. Convolutional neural networks on graphs with fast localized spectral filtering. In Advances in Neural Information Processing Systems. 3844–3852. Google ScholarDigital Library
    18. Danielle Ezuz, Justin Solomon, Vladimir G. Kim, and Mirela Ben-Chen. 2017. GWCNN: A Metric Alignment Layer for Deep Shape Analysis. Computer Graphics Forum (2017). Google ScholarDigital Library
    19. Xifeng Gao, Daniele Panozzo, Wenping Wang, Zhigang Deng, and Guoning Chen. 2017. Robust structure simplification for hex re-meshing. ACM Transactions on Graphics 36, 6 (2017). Google ScholarDigital Library
    20. Michael Garland and Paul S Heckbert. 1997. Surface simplification using quadric error metrics. In Proceedings of the 24th annual conference on Computer graphics and interactive techniques. ACM Press/Addison-Wesley Publishing Co., 209–216. Google ScholarDigital Library
    21. Daniela Giorgi, Silvia Biasotti, and Laura Paraboschi. 2007. Shape retrieval contest 2007: Watertight models track. SHREC competition 8, 7 (2007).Google Scholar
    22. Francisco Gomez-Donoso, Alberto Garcia-Garcia, J Garcia-Rodriguez, Sergio Orts-Escolano, and Miguel Cazorla. 2017. Lonchanet: A sliced-based cnn architecture for real-time 3d object recognition. In 2017 International Joint Conference on Neural Networks (IJCNN). IEEE, 412–418.Google ScholarCross Ref
    23. Benjamin Graham, Martin Engelcke, and Laurens van der Maaten. 2017. 3D Semantic Segmentation with Submanifold Sparse Convolutional Networks. CoRR abs/1711.10275 (2017).Google Scholar
    24. Paul Guerrero, Yanir Kleiman, Maks Ovsjanikov, and Niloy J. Mitra. 2018. PCPNet: Learning Local Shape Properties from Raw Point Clouds. Computer Graphics ForumGoogle Scholar
    25. 37, 2 (2018), 75–85.Google Scholar
    26. Niv Haim, Nimrod Segol, Heli Ben-Hamu, Haggai Maron, and Yaron Lipman. 2018. Surface Networks via General Covers. CoRR abs/1812.10705 (2018).Google Scholar
    27. Rana Hanocka, Noa Fish, Zhenhua Wang, Raja Giryes, Shachar Fleishman, and Daniel Cohen-Or. 2018. ALIGNet: Partial-Shape Agnostic Alignment via Unsupervised Learning. ACM Trans. Graph. 38, 1, Article 1 (Dec. 2018), 14 pages. Google ScholarDigital Library
    28. Mikael Henaff, Joan Bruna, and Yann LeCun. 2015. Deep Convolutional Networks on Graph-Structured Data. CoRR abs/1506.05163 (2015).Google Scholar
    29. Hugues Hoppe. 1997. View-dependent refinement of progressive meshes. In Proceedings of the 24th annual conference on Computer graphics and interactive techniques. ACM Press/Addison-Wesley Publishing Co., 189–198. Google ScholarDigital Library
    30. Hugues Hoppe. 1999. New quadric metric for simplifying meshes with appearance attributes. In Visualization’99. Proceedings. IEEE, 59–510. Google ScholarDigital Library
    31. Hugues Hoppe, Tony DeRose, Tom Duchamp, John McDonald, and Werner Stuetzle. 1993. Mesh optimization., 19–26 pages. Google ScholarDigital Library
    32. Yangqing Jia. 2014. Learning Semantic Image Representations at a Large Scale. (2014).Google Scholar
    33. Chiyu Max Jiang, Jingwei Huang, Karthik Kashinath, Prabhat, Philip Marcus, and Matthias Niessner. 2019. Spherical CNNs on Unstructured Grids. In International Conference on Learning Representations. https://openreview.net/forum?id=Bkl-43C9FQGoogle Scholar
    34. Evangelos Kalogerakis, Melinos Averkiou, Subhransu Maji, and Siddhartha Chaudhuri. 2017. 3D shape segmentation with projective convolutional networks. In Proc. CVPR, Vol. 1. 8.Google Scholar
    35. Evangelos Kalogerakis, Aaron Hertzmann, and Karan Singh. 2010. Learning 3D mesh segmentation and labeling. ACM Transactions on Graphics (TOG) 29, 4 (2010), 102. Google ScholarDigital Library
    36. I. Kokkinos, M. M. Bronstein, R. Litman, and A. M. Bronstein. 2012. Intrinsic shape context descriptors for deformable shapes. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR). 159–166. Google ScholarDigital Library
    37. Ilya Kostrikov, Zhongshi Jiang, Daniele Panozzo, Denis Zorin, and Burna Joan. 2018. Surface Networks. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR).Google Scholar
    38. Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton. 2012. Imagenet classification with deep convolutional neural networks. In Advances in neural information processing systems. 1097–1105. Google ScholarDigital Library
    39. Longin Jan Latecki and Rolf Lakamper. 2000. Shape similarity measure based on correspondence of visual parts. IEEE Transactions on Pattern Analysis and Machine Google ScholarDigital Library
    40. Intelligence 22, 10 (2000), 1185–1190. Google ScholarDigital Library
    41. Yann LeCun. 2012. Learning invariant feature hierarchies. In European conference on computer vision. Springer, 496–505. Google ScholarDigital Library
    42. Yangyan Li, Rui Bu, Mingchao Sun, and Baoquan Chen. 2018. PointCNN. CoRR abs/1801.07791 (2018).Google Scholar
    43. Yangyan Li, Soren Pirk, Hao Su, Charles R Qi, and Leonidas J Guibas. 2016. FPNN: Field probing neural networks for 3D data. In Advances in Neural Information Processing Systems (NIPS). 307–315. Google ScholarDigital Library
    44. Z Lian, A Godil, B Bustos, M Daoudi, J Hermans, S Kawamura, Y Kurita, G Lavoua, and P Dp Suetens. 2011. Shape retrieval on non-rigid 3D watertight meshes. In Eurographics Workshop on 3D Object Retrieval (3DOR). Google ScholarDigital Library
    45. Or Litany, Alexander M. Bronstein, Michael M. Bronstein, and Ameesh Makadia. 2018. Deformable Shape Completion With Graph Convolutional Autoencoders. In CVPR.Google Scholar
    46. Haggai Maron, Meirav Galun, Noam Aigerman, Miri Trope, Nadav Dym, Ersin Yumer, Vladimir G Kim, and Yaron Lipman. 2017. Convolutional neural networks on surfaces via seamless toric covers. ACM Trans. Graph 36, 4 (2017), 71. Google ScholarDigital Library
    47. Jonathan Masci, Davide Boscaini, Michael Bronstein, and Pierre Vandergheynst. 2015. Geodesic convolutional neural networks on riemannian manifolds. In Proceedings of the IEEE international conference on computer vision workshops. 37–45. Google ScholarDigital Library
    48. Federico Monti, Davide Boscaini, Jonathan Masci, Emanuele Rodola, Jan Svoboda, and Michael M Bronstein. 2017. Geometric deep learning on graphs and manifolds using mixture model CNNs. In Proc. CVPR, Vol. 1. 3.Google ScholarCross Ref
    49. Federico Monti, Oleksandr Shchur, Aleksandar Bojchevski, Or Litany, Stephan Gunnemann, and Michael M. Bronstein. 2018. Dual-Primal Graph Convolutional Networks. CoRR abs/1806.00770 (2018).Google Scholar
    50. Mathias Niepert, Mohamed Ahmed, and Konstantin Kutzkov. 2016. Learning Convolutional Neural Networks for Graphs. In International Conference on Machine Learning (ICML). Google ScholarDigital Library
    51. Adam Paszke, Sam Gross, Soumith Chintala, Gregory Chanan, Edward Yang, Zachary DeVito, Zeming Lin, Alban Desmaison, Luca Antiga, and Adam Lerer. 2017. Automatic differentiation in PyTorch. In NIPS-W.Google Scholar
    52. Adrien Poulenard and Maks Ovsjanikov. 2018. Multi-directional Geodesic Neural Networks via Equivariant Convolution. In SIGGRAPH Asia 2018 Technical Papers (SIGGRAPH Asia ’18). ACM, New York, NY, USA, Article 236, 14 pages. Google ScholarDigital Library
    53. Charles R Qi, Hao Su, Kaichun Mo, and Leonidas J Guibas. 2017a. Pointnet: Deep learning on point sets for 3d classification and segmentation. Proc. Computer Vision and Pattern Recognition (CVPR), IEEE 1, 2 (2017), 4.Google Scholar
    54. Charles R. Qi, Hao Su, Matthias Niessner, Angela Dai, Mengyuan Yan, and Leonidas J. Guibas. 2016. Volumetric and multi-view CNNs for object classification on 3d data. In Computer Vision and Pattern Recognition (CVPR). 5648–5656.Google Scholar
    55. Charles R. Qi, Li Yi, Hao Su, and Leonidas J Guibas. 2017b. PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space. In Advances in Neural Information Processing Systems (NIPS). 5105–5114. Google ScholarDigital Library
    56. Anurag Ranjan, Timo Bolkart, Soubhik Sanyal, and Michael J. Black. 2018. Generating 3D faces using Convolutional Mesh Autoencoders. In European Conference on Computer Vision (ECCV). Springer International Publishing, 725–741.Google Scholar
    57. Gernot Riegler, Ali Osman Ulusoy, and Andreas Geiger. 2017. OctNet: Learning deep 3D representations at high resolutions. In Computer Vision and Pattern Recognition (CVPR).Google Scholar
    58. Olaf Ronneberger, Philipp Fischer, and Thomas Brox. 2015. U-net: Convolutional networks for biomedical image segmentation. In International Conference on Medical image computing and computer-assisted intervention. Springer, 234–241.Google ScholarCross Ref
    59. Szymon Rusinkiewicz and Marc Levoy. 2000. QSplat: A Multiresolution Point Rendering System for Large Meshes. In Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH ’00). ACM Press/Addison-Wesley Publishing Co., New York, NY, USA, 343–352. Google ScholarDigital Library
    60. Kripasindhu Sarkar, Basavaraj Hampiholi, Kiran Varanasi, and Didier Stricker. 2018. Learning 3D Shapes as Multi-Layered Height-maps using 2D Convolutional Networks. In Proceedings of the European Conference on Computer Vision (ECCV). 71–86.Google ScholarCross Ref
    61. Pierre Sermanet, David Eigen, Xiang Zhang, Michaël Mathieu, Rob Fergus, and Yann LeCun. 2013. Overfeat: Integrated recognition, localization and detection using convolutional networks. arXiv preprint arXiv:1312.6229 (2013).Google Scholar
    62. Karen Simonyan and Andrew Zisserman. 2014. Very deep convolutional networks for large-scale image recognition. arXiv preprint arXiv:1409.1556 (2014).Google Scholar
    63. Ayan Sinha, Jing Bai, and Karthik Ramani. 2016. Deep learning 3D shape surfaces using geometry images. In European Conference on Computer Vision. Springer, 223–240.Google ScholarCross Ref
    64. Hang Su, Subhransu Maji, Evangelos Kalogerakis, and Erik Learned-Millers. 2015. Multi-view Convolutional Neural Networks for 3D Shape Recognition. In International Conference on Computer Vision (ICCV). Google ScholarDigital Library
    65. F. P. Such, S. Sah, M. A. Dominguez, S. Pillai, C. Zhang, A. Michael, N. D. Cahill, and R. Ptucha. 2017. Robust Spatial Filtering With Graph Convolutional Neural Networks. IEEE Journal of Selected Topics in Signal Processing 11, 6 (Sept 2017), 884–896.Google ScholarCross Ref
    66. Marco Tarini, Nico Pietroni, Paolo Cignoni, Daniele Panozzo, and Enrico Puppo. 2010. Practical quad mesh simplification. In Computer Graphics Forum, Vol. 29. Wiley Online Library, 407–418.Google Scholar
    67. Maxim Tatarchenko, Jaesik Park, Vladlen Koltun, and Qian-Yi Zhou. 2018. Tangent Convolutions for Dense Prediction in 3D. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. 3887–3896.Google ScholarCross Ref
    68. Lyne P. Tchapmi, Christopher B. Choy, Iro Armeni, JunYoung Gwak, and Silvio Savarese. 2017. SEGCloud: Semantic Segmentation of 3D Point Clouds. In 3DV.Google Scholar
    69. Petar Velickovic, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Lio, and Yoshua Bengio. 2018. Graph Attention Networks. In International Conference on Learning Representations.Google Scholar
    70. Nitika Verma, E. Boyer, and Jakob Verbeek. 2018. FeaStNet: Feature-Steered Graph Convolutions for 3D Shape Analysis. In CVPR.Google Scholar
    71. Daniel Vlasic, Ilya Baran, Wojciech Matusik, and Jovan Popović. 2008. Articulated mesh animation from multi-view silhouettes. In ACM Transactions on Graphics (TOG), Vol. 27. ACM, 97. Google ScholarDigital Library
    72. Peng-Shuai Wang, Yang Liu, Yu-Xiao Guo, Chun-Yu Sun, and Xin Tong. 2017. OCNN: Octree-based Convolutional Neural Networks for 3D Shape Analysis. ACM Trans. Graph. 36, 4, Article 72 (July 2017), 11 pages. Google ScholarDigital Library
    73. Yunhai Wang, Shmulik Asafi, Oliver van Kaick, Hao Zhang, Daniel Cohen-Or, and Baoquan Chen. 2012. Active co-analysis of a set of shapes. ACM Transactions on Graphics (TOG) 31, 6 (2012), 165. Google ScholarDigital Library
    74. Yue Wang, Yongbin Sun, Ziwei Liu, Sanjay E Sarma, Michael M Bronstein, and Justin M Solomon. 2018a. Dynamic graph CNN for learning on point clouds. arXiv preprint arXiv:1801.07829 (2018).Google Scholar
    75. Yue Wang, Yongbin Sun, Ziwei Liu, Sanjay E Sarma, Michael M Bronstein, and Justin M Solomon. 2018b. Dynamic Graph CNN for Learning on Point Clouds. arXiv preprint arXiv:1801.07829 (2018).Google Scholar
    76. Francis Williams, Teseo Schneider, Claudio Silva, Denis Zorin, Joan Bruna, and Daniele Panozzo. 2018. Deep Geometric Prior for Surface Reconstruction. arXiv preprint arXiv:1811.10943 (2018).Google Scholar
    77. Zhirong Wu, Shuran Song, Aditya Khosla, Fisher Yu, Linguang Zhang, Xiaoou Tang, and Jianxiong Xiao. 2015. 3D shapenets: A deep representation for volumetric shapes. In Computer Vision and Pattern Recognition (CVPR). 1912–1920.Google Scholar
    78. Haotian Xu, Ming Dong, and Zichun Zhong. 2017. Directionally Convolutional Networks for 3D Shape Segmentation. In Proceedings of the IEEE International Conference on Computer Vision. 2698–2707.Google ScholarCross Ref
    79. Li Yi, Hao Su, Xingwen Guo, and Leonidas Guibas. 2017. SyncSpecCNN: Synchronized Spectral CNN for 3D Shape Segmentation. In Computer Vision and Pattern Recognition (CVPR).Google Scholar
    80. Zhitao Ying, Jiaxuan You, Christopher Morris, Xiang Ren, Will Hamilton, and Jure Leskovec. 2018. Hierarchical Graph Representation Learning with Differentiable Pooling. In Advances in Neural Information Processing Systems. 4805–4815. Google ScholarDigital Library
    81. Tinghui Zhou, Richard Tucker, John Flynn, Graham Fyffe, and Noah Snavely. 2018. Stereo Magnification: Learning View Synthesis Using Multiplane Images. ACM Trans. Graph. 37, 4 (July 2018), 65:1–65:12. Google ScholarDigital Library

ACM Digital Library Publication:

Overview Page: