Abstract
We present an adaptive deep representation of volumetric fields of 3D shapes and an efficient approach to learn this deep representation for high-quality 3D shape reconstruction and auto-encoding. Our method encodes the volumetric field of a 3D shape with an adaptive feature volume organized by an octree and applies a compact multilayer perceptron network for mapping the features to the field value at each 3D position. An encoder-decoder network is designed to learn the adaptive feature volume based on the graph convolutions over the dual graph of octree nodes. The core of our network is a new graph convolution operator defined over a regular grid of features fused from irregular neighboring octree nodes at different levels, which not only reduces the computational and memory cost of the convolutions over irregular neighboring octree nodes, but also improves the performance of feature learning. Our method effectively encodes shape details, enables fast 3D shape reconstruction, and exhibits good generality for modeling 3D shapes out of training categories. We evaluate our method on a set of reconstruction tasks of 3D shapes and scenes and validate its superiority over other existing approaches. Our code, data, and trained models are available at https://wang-ps.github.io/dualocnn.
Supplemental Material
- Matan Atzmon and Yaron Lipman. 2020. SAL: Sign agnostic learning of shapes from raw data. In CVPR.Google Scholar
- Matan Atzmon and Yaron Lipman. 2021. SALD: Sign Agnostic Learning with Derivatives. In ICLR.Google Scholar
- Peter W Battaglia, Jessica B Hamrick, Victor Bapst, Alvaro Sanchez-Gonzalez, Vinicius Zambaldi, Mateusz Malinowski, Andrea Tacchetti, David Raposo, Adam Santoro, Ryan Faulkner, et al. 2018. Relational inductive biases, deep learning, and graph networks. arXiv preprint arXiv:1806.01261 (2018).Google Scholar
- Matthew Berger, Andrea Tagliasacchi, Lee M. Seversky, Pierre Alliez, Gaël Guennebaud, Joshua A. Levine, Andrei Sharf, and Claudio T. Silva. 2017. A survey of surface reconstruction from point clouds. Comput. Graph. Forum 36, 1 (2017).Google Scholar
- Federica Bogo, Javier Romero, Gerard Pons-Moll, and Michael J Black. 2017. Dynamic FAUST: Registering human bodies in motion. In CVPR.Google Scholar
- Robert Bridson. 2015. Fluid simulation for computer graphics. CRC press.Google Scholar
Digital Library
- Andrew Brock, Theodore Lim, J.M. Ritchie, and Nick Weston. 2016. Generative and discriminative voxel modeling with convolutional neural networks. In 3D deep learning workshop (NeurIPS).Google Scholar
- Rohan Chabra, Jan Eric 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 ECCV.Google Scholar
- 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. arXiv preprint arXiv:1512.03012 (2015).Google Scholar
- Zhiqin Chen and Hao Zhang. 2019. Learning implicit fields for generative shape modeling. In CVPR.Google Scholar
- Julian Chibane, Thiemo Alldieck, and Gerard Pons-Moll. 2020. Implicit functions in feature space for 3d shape reconstruction and completion. In CVPR.Google Scholar
- Christopher Choy, JunYoung Gwak, and Silvio Savarese. 2019. 4D spatio-temporal convnets: Minkowski convolutional neural networks. In CVPR.Google Scholar
- Christopher Choy, Danfei Xu, JunYoung Gwak, Kevin Chen, and Silvio Savarese. 2016. 3D-R2N2: A unified approach for single and multi-view 3D object reconstruction. In ECCV.Google Scholar
- Brian Curless and Marc Levoy. 1996. A Volumetric Method for Building Complex Models from Range Images. In SIGGRAPH.Google Scholar
- Angela Dai, Charles R. Qi, and Matthias Niessner. 2017. Shape completion using 3D-encoder-predictor CNNs and shape synthesis. In CVPR.Google Scholar
- Matthias Fey and Jan Eric Lenssen. 2019. Fast Graph Representation Learning with PyTorch Geometric. In ICLR Workshop.Google Scholar
- Matthias Fey, Jan Eric Lenssen, Frank Weichert, and Heinrich Müller. 2018. SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernels. In CVPR.Google Scholar
- Kyle Genova, Forrester Cole, Avneesh Sud, Aaron Sarna, and Thomas Funkhouser. 2020. Local Deep Implicit Functions for 3D Shape. In CVPR.Google Scholar
- Justin Gilmer, Samuel S Schoenholz, Patrick F Riley, Oriol Vinyals, and George E Dahl. 2017. Neural message passing for quantum chemistry. In ICML.Google Scholar
- Benjamin Graham, Martin Engelcke, and Laurens van der Maaten. 2018. 3D semantic segmentation with submanifold sparse convolutional networks. In CVPR.Google Scholar
- Amos Gropp, Lior Yariv, Niv Haim, Matan Atzmon, and Yaron Lipman. 2020. Implicit geometric regularization for learning shapes. In ICML.Google Scholar
- Thibault Groueix, Matthew Fisher, Vladimir G. Kim, Bryan C. Russell, and Mathieu Aubry. 2018. AtlasNet: A Papier-Mâché approach to learning 3D surface generation. In CVPR.Google Scholar
- Meng-Hao Guo, Jun-Xiong Cai, Zheng-Ning Liu, Tai-Jiang Mu, Ralph R Martin, and Shi-Min Hu. 2021. PCT: Point cloud transformer. Computational Visual Media 7, 2 (2021).Google Scholar
- Ankur Handa, Viorica Patraucean, Vijay Badrinarayanan, Simon Stent, and Roberto Cipolla. 2016. SceneNet: Understanding Real World Indoor Scenes With Synthetic Data. In CVPR.Google Scholar
- Christian Häne, Shubham Tulsiani, and Jitendra Malik. 2017. Hierarchical surface prediction for 3D object reconstruction. In 3DV.Google Scholar
- Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. 2016. Deep residual learning for image recognition. In CVPR.Google Scholar
- Chiyu Jiang, Avneesh Sud, Ameesh Makadia, Jingwei Huang, Matthias Nießner, and Thomas Funkhouser. 2020. Local implicit grid representations for 3D scenes. In CVPR.Google Scholar
- Tao Ju, Frank Losasso, Scott Schaefer, and Joe Warren. 2002. Dual contouring of hermite data. ACM Trans. Graph. (SIGGRAPH) (2002).Google Scholar
- Michael Kazhdan, Matthew Bolitho, and Hugues Hoppe. 2006. Poisson surface reconstruction. In Symp. Geom. Proc.Google Scholar
Digital Library
- Diederik P. Kingma and Jimmy Ba. 2014. Adam: A method for stochastic optimization. In ICLR.Google Scholar
- Alejandro León, Juan Carlos Torres, and Francisco Velasco. 2008. Volume octree with an implicitly defined dual grid. Computers & Graphics 32, 4 (2008).Google Scholar
- Thomas Lewiner, Vinícius Mello, Adelailson Peixoto, Sinésio Pesco, and Hélio Lopes. 2010. Fast Generation of Pointerless Octree Duals. Computer Graphics Forum 29, 5 (2010).Google Scholar
- Yangyan Li, Rui Bu, Mingchao Sun, Wei Wu, Xinhan Di, and Baoquan Chen. 2018. PointCNN: Convolution on X-transformed points. In NeurIPS.Google Scholar
- Shi-Lin Liu, Hao-Xiang Guo, Hao Pan, Peng-Shuai Wang, Xin Tong, and Yang Liu. 2021. Deep Implicit Moving Least-Squares Functions for 3D Reconstruction. In CVPR.Google Scholar
- William E. Lorensen and Harvey E. Cline. 1987. Marching Cubes: A High Resolution 3D Surface Construction Algorithm. In SIGGRAPH.Google Scholar
Digital Library
- Julien N. P. Martel, David B. Lindell, Connor Z. Lin, Eric R. Chan, Marco Monteiro, and Gordon Wetzstein. 2021. ACORN: Adaptive coordinate networks for neural scene representation. ACM Trans. Graph. (SIGGRAPH) 40, 4 (2021).Google Scholar
Digital Library
- Daniel Maturana and Sebastian Scherer. 2015. VoxNet: A 3D convolutional neural network for real-time object recognition. In IROS.Google Scholar
- Lars Mescheder, Michael Oechsle, Michael Niemeyer, Sebastian Nowozin, and Andreas Geiger. 2019. Occupancy networks: Learning 3D reconstruction in function space. In CVPR.Google Scholar
- Ben Mildenhall, Pratul P Srinivasan, Matthew Tancik, Jonathan T Barron, Ravi Ramamoorthi, and Ren Ng. 2020. NeRF: Representing scenes as neural radiance fields for view synthesis. In ECCV.Google Scholar
- Thomas Müller, Alex Evans, Christoph Schied, and Alexander Keller. 2022. Instant Neural Graphics Primitives with a Multiresolution Hash Encoding. arXiv preprint arXiv:2201.05989 (2022).Google Scholar
- Michael Oechsle, Lars Mescheder, Michael Niemeyer, Thilo Strauss, and Andreas Geiger. 2019. Texture fields: Learning texture representations in function space. In ICCV. Yutaka Ohtake, Alexander Belyaev, Marc Alexa, Greg Turk, and Hans-Peter Seidel. 2003. Multi-level partition of unity implicits. ACM Trans. Graph. (SIGGRAPH) 22, 3 (2003).Google Scholar
- A Cengiz Öztireli, Gael Guennebaud, and Markus Gross. 2009. Feature preserving point set surfaces based on non-linear kernel regression. Comput. Graph. Forum (EG) 28, 2 (2009).Google Scholar
- Jeong Joon Park, Peter Florence, Julian Straub, Richard Newcombe, and Steven Lovegrove. 2019. DeepSDF: Learning continuous signed distance functions for shape representation. In CVPR.Google Scholar
- Songyou Peng, Michael Niemeyer, Lars Mescheder, Marc Pollefeys, and Andreas Geiger. 2020. Convolutional occupancy networks. In ECCV.Google Scholar
- Charles R. Qi, Hao Su, Kaichun Mo, and Leonidas J. Guibas. 2017a. PointNet: Deep learning on point sets for 3D classification and segmentation. In CVPR.Google Scholar
- Charles R. Qi, Hao Su, Matthias Nießner, Angela Dai, Mengyuan Yan, and Leonidas J.Google Scholar
- Guibas. 2016. Volumetric and multi-view CNNs for object classification on 3D data. In CVPR.Google Scholar
- 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 NeurIPS.Google Scholar
- 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.Google Scholar
Cross Ref
- Scott Schaefer and Joe Warren. 2004. Dual marching cubes: Primal contouring of dual grids. In Pacific Graphics.Google Scholar
- Tianjia Shao, Yin Yang, Yanlin Weng, Qiming Hou, and Kun Zhou. 2018. H-CNN: spatial hashing based CNN for 3D shape analysis. IEEE. T. Vis. Comput. Gr. (2018).Google Scholar
- Andrei Sharf, Thomas Lewiner, Gil Shklarski, Sivan Toledo, and Daniel Cohen-Or. 2007. Interactive topology-aware surface reconstruction. ACM Trans. Graph. (SIGGRAPH) 26, 3 (2007).Google Scholar
Digital Library
- Martin Simonovsky and Nikos Komodakis. 2017. Dynamic edge-conditioned filters in convolutional neural networks on graphs. In CVPR.Google Scholar
- Vincent Sitzmann, Julien NP Martel, Alexander W Bergman, David B Lindell, and Gordon Wetzstein. 2020. Implicit Neural Representations with Periodic Activation Functions. In NeurIPS.Google Scholar
- Towaki Takikawa, Joey Litalien, Kangxue Yin, Karsten Kreis, Charles Loop, Derek Nowrouzezahrai, Alec Jacobson, Morgan McGuire, and Sanja Fidler. 2021. Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes. In CVPR.Google Scholar
- Matthew Tancik, Pratul P. Srinivasan, Ben Mildenhall, Sara Fridovich-Keil, Nithin Raghavan, Utkarsh Singhal, Ravi Ramamoorthi, Jonathan T. Barron, and Ren Ng. 2020. Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains. In NeurIPS.Google Scholar
- Jia-Heng Tang, Weikai Chen, Jie Yang, Bo Wang, Songrun Liu, Bo Yang, and Lin Gao. 2021. OctField: Hierarchical Implicit Functions for 3D Modeling. In NeurIPS.Google Scholar
- Maxim Tatarchenko, Alexey Dosovitskiy, and Thomas Brox. 2017. Octree generating networks: efficient convolutional architectures for high-resolution 3D outputs. In ICCV.Google Scholar
- Hugues Thomas, Charles R. Qi, Jean-Emmanuel Deschaud, Beatriz Marcotegui, François Goulette, and Leonidas J. Guibas. 2019. KPConv: Flexible and deformable convolution for point clouds. In ICCV.Google Scholar
- Benjamin Ummenhofer and Vladlen Koltun. 2021. Adaptive Surface Reconstruction With Multiscale Convolutional Kernels. In ICCV.Google Scholar
- Petar Veličković, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Liò, and Yoshua Bengio. 2018. Graph Attention Networks. In ICLR.Google Scholar
- Hao Wang, Nadav Schor, Ruizhen Hu, Haibin Huang, Daniel Cohen-Or, and Hui Huang. 2018a. Global-to-local generative model for 3D shapes. ACM Trans. Graph. (SIGGRAPH ASIA) 37, 6 (2018).Google Scholar
- Peng-Shuai Wang, Yang Liu, Yu-Xiao Guo, Chun-Yu Sun, and Xin Tong. 2017. O-CNN: Octree-based convolutional neural networks for 3D shape analysis. ACM Trans. Graph. (SIGGRAPH) 36, 4 (2017).Google Scholar
Digital Library
- Peng-Shuai Wang, Yang Liu, and Xin Tong. 2020. Deep Octree-based CNNs with Output-Guided Skip Connections for 3D Shape and Scene Completion. In CVPR Workshop.Google Scholar
Cross Ref
- Peng-Shuai Wang, Chun-Yu Sun, Yang Liu, and Xin Tong. 2018b. Adaptive O-CNN: A patch-based deep representation of 3D shapes. ACM Trans. Graph. (SIGGRAPH ASIA) 37, 6 (2018).Google Scholar
- Yue Wang, Yongbin Sun, Ziwei Liu, Sanjay E Sarma, Michael M Bronstein, and Justin M Solomon. 2019. Dynamic graph CNN for learning on point clouds. ACM Trans. Graph. 38, 5 (2019).Google Scholar
Digital Library
- Francis Williams, Zan Gojcic, Sameh Khamis, Denis Zorin, Joan Bruna, Sanja Fidler, and Or Litany. 2022. Neural Fields as Learnable Kernels for 3D Reconstruction. In CVPR.Google Scholar
- Francis Williams, Matthew Trager, Joan Bruna, and Denis Zorin. 2021. Neural splines: Fitting 3D surfaces with infinitely-wide neural networks. In CVPR.Google Scholar
- Jiajun Wu, Chengkai Zhang, Tianfan Xue, William T. Freeman, and Joshua B. Tenenbaum. 2016. Learning a probabilistic latent space of object shapes via 3D generative-adversarial modeling. In NeurIPS.Google Scholar
Digital Library
- Wenxuan Wu, Zhongang Qi, and Li Fuxin. 2019. PointConv: Deep Convolutional Networks on 3D Point Clouds. In CVPR.Google Scholar
- Zonghan Wu, Shirui Pan, Fengwen Chen, Guodong Long, Chengqi Zhang, and S Yu Philip. 2020. A comprehensive survey on graph neural networks. IEEE Transactions on Neural Networks and Learning Systems 32, 1 (2020).Google Scholar
- Zhirong Wu, Shuran Song, Aditya Khosla, Fisher Yu, Linguang Zhang, Xiaoou Tang, and Jianxiong Xiao. 2015. 3D ShapeNets: A deep representation for volumetric shape modeling. In CVPR.Google Scholar
- Hongyi Xu and Jernej Barbič. 2014. Signed Distance Fields for Polygon Soup Meshes. In Proceedings of Graphics Interface.Google Scholar
- Mutian Xu, Runyu Ding, Hengshuang Zhao, and Xiaojuan Qi. 2021. PAConv: Position Adaptive Convolution with Dynamic Kernel Assembling on Point Clouds. In CVPR.Google Scholar
- Yifan Xu, Tianqi Fan, Mingye Xu, Long Zeng, and Yu Qiao. 2018. SpiderCNN: Deep Learning on Point Sets with Parameterized Convolutional Filters. In ECCV.Google Scholar
- Hengshuang Zhao, Li Jiang, Jiaya Jia, Philip Torr, and Vladlen Koltun. 2021. Point transformer. In ICCV.Google Scholar
- Kun Zhou, Minmin Gong, Xin Huang, and Baining Guo. 2011. Data-parallel octrees for surface reconstruction. IEEE. T. Vis. Comput. Gr. 17, 5 (2011).Google Scholar
- Received January 2022; accepted March 2022; final version May 2022Google Scholar
Index Terms
Dual octree graph networks for learning adaptive volumetric shape representations
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