CvxNets: Learnable Convex Decomposition

CVPR, pp. 31-41, 2019.

Cited by: 18|Views236
EI
Weibo:
We introduce a network architecture to represent a low dimensional family of convexes

Abstract:

Any solid object can be decomposed into a collection of convex polytopes (in short, convexes). When a small number of convexes are used, such a decomposition can be thought of as a piece-wise approximation of the geometry. This decomposition is fundamental to real-time physics simulation in computer graphics, where it creates a unifying...More

Code:

Data:

0
Introduction
  • While images admit a standard representation in the form of a scalar function uniformly discretized on a grid, the curse of dimensionality has prevented the effective usage of analogous representations for learning 3D geometry.
  • In computer vision and robotics, analogous trade-offs exist: surface models are essential for the construction of low-dimensional parametric templates essential for tracking [6, 8], volumetric representations are key to capturing 3D data whose topology is unknown [48, 47], while part-based models provide a natural decomposition of an object into its semantic components.
  • Part-based models create a representation useful to reason about extent, mass, contact, ... quantities that are key to describing the scene, and planning motions [29, 28]
Highlights
  • While images admit a standard representation in the form of a scalar function uniformly discretized on a grid, the curse of dimensionality has prevented the effective usage of analogous representations for learning 3D geometry
  • One might follow Cezanne’s advice and “treat nature by means of the cylinder, the sphere, the cone, everything brought into proper perspective”, and think to approximate 3D geometry as geons [4] – collections of simple to interpret geometric primitives [68, 77], and their composition [60, 21]
  • One might rightfully start wondering “why so many representations of 3D data exist, and why would one be more advantageous than the other?” One observation is that multiple equivalent representations of 3D geometry exist because real-world applications need to perform different operations and queries on this data ( [9, Ch.1])
  • In computer graphics, points and polygons allow for very efficient rendering on GPUs, while volumes allow artists to sculpt geometry without having to worry about tessellation [51] or assembling geometry by smooth composition [2], while primitives enable highly efficient collision detection [66] and resolution [67]
  • We propose a novel representation for geometry based on primitive decomposition
  • We only find early attempts to approach convex hull computation via neural networks [34]
Methods
  • The authors quantitatively compare the method to a number of self-supervised algorithms with different characteristics.
  • The authors compare to the Structured Implicit Function SIF [21] method that represents solid geometry as an iso-level of a sum of weighted Gaussians; like VP [68], and in contrast to OccNet [44], this methods provides an interpretable encoding of geometry.
  • From the class of techniques that directly learn noninterpretable representations of implicit functions, the authors select OccNet [44], P2M [71], and AtlasNet [26]; in contrast to the previous methods, these solutions do not provide any form of shape decomposition.
  • The authors follow the same data pre-processing used by SIF [21]
Conclusion
  • The authors propose a differentiable representation of convex primitives that is amenable to learning.
  • The inferred representations are directly usable in graphics/physics pipelines; see Figure 1.
  • The authors' self-supervised technique provides more detailed reconstructions than very recently proposed partbased techniques (SIF [21] in Figure 9), and even consistently outperforms the leading reconstruction technique on multi-view input (OccNet [44] in Table 1).
  • Leveraging the invariance of hyperplane ordering, it would be interesting to investigate the effect of permutation-invariant encoders [63], or remove encoders altogether in favor of auto-decoder architectures [49]
Summary
  • Introduction:

    While images admit a standard representation in the form of a scalar function uniformly discretized on a grid, the curse of dimensionality has prevented the effective usage of analogous representations for learning 3D geometry.
  • In computer vision and robotics, analogous trade-offs exist: surface models are essential for the construction of low-dimensional parametric templates essential for tracking [6, 8], volumetric representations are key to capturing 3D data whose topology is unknown [48, 47], while part-based models provide a natural decomposition of an object into its semantic components.
  • Part-based models create a representation useful to reason about extent, mass, contact, ... quantities that are key to describing the scene, and planning motions [29, 28]
  • Methods:

    The authors quantitatively compare the method to a number of self-supervised algorithms with different characteristics.
  • The authors compare to the Structured Implicit Function SIF [21] method that represents solid geometry as an iso-level of a sum of weighted Gaussians; like VP [68], and in contrast to OccNet [44], this methods provides an interpretable encoding of geometry.
  • From the class of techniques that directly learn noninterpretable representations of implicit functions, the authors select OccNet [44], P2M [71], and AtlasNet [26]; in contrast to the previous methods, these solutions do not provide any form of shape decomposition.
  • The authors follow the same data pre-processing used by SIF [21]
  • Conclusion:

    The authors propose a differentiable representation of convex primitives that is amenable to learning.
  • The inferred representations are directly usable in graphics/physics pipelines; see Figure 1.
  • The authors' self-supervised technique provides more detailed reconstructions than very recently proposed partbased techniques (SIF [21] in Figure 9), and even consistently outperforms the leading reconstruction technique on multi-view input (OccNet [44] in Table 1).
  • Leveraging the invariance of hyperplane ordering, it would be interesting to investigate the effect of permutation-invariant encoders [63], or remove encoders altogether in favor of auto-decoder architectures [49]
Tables
  • Table1: Reconstruction performance on ShapeNet/Multi – We evaluate our method against P2M [<a class="ref-link" id="c71" href="#r71">71</a>], AtlasNet [<a class="ref-link" id="c26" href="#r26">26</a>], OccNet [<a class="ref-link" id="c44" href="#r44">44</a>] and SIF [<a class="ref-link" id="c21" href="#r21">21</a>]. We provide in input either (left) a collection of depth maps or (right) a single color image. For AtlasNet [<a class="ref-link" id="c26" href="#r26">26</a>], note that IoU cannot be measured as the meshes are not watertight. We omit VP [<a class="ref-link" id="c68" href="#r68">68</a>], as it only produces a very rough shape decomposition
Download tables as Excel
Related work
  • One of the simplest high-dimensional representations is voxels, and they are the most commonly used representation for discriminative [43, 54, 61] models, due to their similarity to image based convolutions. Voxels have also been used successfully for generative models [75, 16, 24, 57, 62, 74]. However, the memory requirements of voxels makes them unsuitable for resolutions larger than 643. One can reduce the memory consumption significantly by using octrees that take advantage of the sparsity of voxels [58, 72, 73, 64]. This can extend the resolution to 5123, for instance, but comes at the cost of more complicated implementation.

    Surfaces. In computer graphics, polygonal meshes are the standard representation of 3D objects. Meshes have also been considered for discriminative classification by applying graph convolutions to the mesh [42, 11, 27, 46]. Recently, meshes have also been considered as the output of a network [26, 32, 71]. A key weakness of these models is the fact that they may produce self-intersecting meshes. Another natural high-dimensional representation that has garnered some traction in vision is the point cloud representation. Point clouds are the natural representation of objects if one is using sensors such as depth cameras or LiDAR, and they require far less memory than voxels. Qi et al [53, 55] used point clouds as a representation for discriminative deep learning tasks. Hoppe et al [30] used point clouds for surface mesh reconstruction (see also [3] for a survey of other techniques). Fan et. al. [19] and Lin et. al. [37] used point clouds for 3D reconstruction using deep learning. However, these approaches require additional non-trivial postprocessing steps to generate the final 3D mesh.
Funding
  • Introduces a network architecture to represent a low dimensional family of convexes
  • Investigates the applications of this architecture including automatic convex decomposition, image to 3D reconstruction, and part-based shape retrieval
  • Proposes a novel representation for geometry based on primitive decomposition
  • Finds early attempts to approach convex hull computation via neural networks
  • Evaluates the template at random sample points x, and our training loss ensures O(x) ≈ O(x)
Reference
  • Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas Guibas. Learning representations and generative models for 3d point clouds. In International Conference on Machine Learning, pages 40–49, 2018. 1
    Google ScholarLocate open access versionFindings
  • Baptiste Angles, Marco Tarini, Loic Barthe, Brian Wyvill, and Andrea Tagliasacchi. Sketch-based implicit blending. ACM Transaction on Graphics (Proc. SIGGRAPH Asia), 2017. 2
    Google ScholarLocate open access versionFindings
  • Matthew Berger, Andrea Tagliasacchi, Lee M Seversky, Pierre Alliez, Gael Guennebaud, Joshua A Levine, Andrei Sharf, and Claudio T Silva. A survey of surface reconstruction from point clouds. In Computer Graphics Forum, volume 36, pages 301–329. Wiley Online Library, 2017. 2
    Google ScholarLocate open access versionFindings
  • Irving Biederman. Recognition-by-components: a theory of human image understanding. Psychological review, 1987. 1, 2
    Google ScholarLocate open access versionFindings
  • Thomas Binford. Visual perception by computer. In IEEE Conference of Systems and Control, 1971. 2
    Google ScholarLocate open access versionFindings
  • Volker Blanz and Thomas Vetter. A morphable model for the synthesis of 3D faces. In ACM Trans. on Graphics (Proceedings of SIGGRAPH), 1999. 2
    Google ScholarLocate open access versionFindings
  • James F Blinn. A generalization of algebraic surface drawing. ACM Trans. on Graphics (TOG), 1(3):235–256, 1982. 6
    Google ScholarLocate open access versionFindings
  • Federica Bogo, Angjoo Kanazawa, Christoph Lassner, Peter Gehler, Javier Romero, and Michael J Black. Keep it smpl: Automatic estimation of 3d human pose and shape from a single image. In Proceedings of the European Conference on Computer Vision, 2016. 2
    Google ScholarLocate open access versionFindings
  • Mario Botsch, Leif Kobbelt, Mark Pauly, Pierre Alliez, and Bruno Lévy. Polygon mesh processing. AK Peters/CRC Press, 2010. 1
    Google ScholarFindings
  • Andrew Brock, Theodore Lim, James M Ritchie, and Nick Weston. Generative and discriminative voxel modeling with convolutional neural networks. arXiv preprint arXiv:1608.04236, 2016. 1
    Findings
  • Michael M Bronstein, Joan Bruna, Yann LeCun, Arthur Szlam, and Pierre Vandergheynst. Geometric deep learning: going beyond euclidean data. IEEE Signal Processing Magazine, 34(4):18–42, 2017. 2
    Google ScholarLocate open access versionFindings
  • Angel X Chang, Thomas Funkhouser, Leonidas Guibas, Pat Hanrahan, Qixing Huang, Zimo Li, Silvio Savarese, Manolis Savva, Shuran Song, Hao Su, et al. Shapenet: An information-rich 3d model repository. arXiv preprint arXiv:1512.03012, 2015. 6
    Findings
  • Bernard M Chazelle. Convex decompositions of polyhedra. In Proceedings of the thirteenth annual ACM symposium on Theory of computing, pages 70–79. ACM, 1981. 3
    Google ScholarLocate open access versionFindings
  • Zhiqin Chen, Kangxue Yin, Matthew Fisher, Siddhartha Chaudhuri, and Hao Zhang. Bae-net: Branched autoencoder for shape co-segmentation. Proceedings of International Conference on Computer Vision (ICCV), 2019. 7
    Google ScholarLocate open access versionFindings
  • Zhiqin Chen and Hao Zhang. Learning implicit fields for generative shape modeling. Proceedings of Computer Vision and Pattern Recognition (CVPR), 2019. 2, 4
    Google ScholarLocate open access versionFindings
  • Christopher B Choy, Danfei Xu, JunYoung Gwak, Kevin Chen, and Silvio Savarese. 3d-r2n2: A unified approach for single and multi-view 3d object reconstruction. In Proceedings of the European Conference on Computer Vision. Springer, 202, 6, 7
    Google ScholarLocate open access versionFindings
  • Erwin Coumans and Yunfei Bai. PyBullet, a python module for physics simulation for games, robotics and machine learning. pybullet.org, 2016–2019. 1
    Google ScholarFindings
  • Siyan Dong, Matthias Niessner, Andrea Tagliasacchi, and Kevin Kai Xu. Multi-robot collaborative dense scene reconstruction. ACM Trans. on Graphics (Proceedings of SIGGRAPH), 2019. 7
    Google ScholarLocate open access versionFindings
  • Haoqiang Fan, Hao Su, and Leonidas J Guibas. A point set generation network for 3d object reconstruction from a single image. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 605–613, 2017. 1, 2
    Google ScholarLocate open access versionFindings
  • Matheus Gadelha, Subhransu Maji, and Rui Wang. 3d shape induction from 2d views of multiple objects. In International Conference on 3D Vision (3DV), 2017. 1
    Google ScholarLocate open access versionFindings
  • Kyle Genova, Forrester Cole, Daniel Vlasic, Aaron Sarna, William T Freeman, and Thomas Funkhouser. Learning shape templates with structured implicit functions. arXiv preprint arXiv:1904.06447, 2019. 1, 2, 3, 4, 6, 7, 8
    Findings
  • Mukulika Ghosh, Nancy M Amato, Yanyan Lu, and JyhMing Lien. Fast approximate convex decomposition using relative concavity. Computer-Aided Design, 45(2):494–504, 2013. 3
    Google ScholarLocate open access versionFindings
  • Elmer G Gilbert, Daniel W Johnson, and S Sathiya Keerthi. A fast procedure for computing the distance between complex objects in three-dimensional space. IEEE Journal on Robotics and Automation, 1988. 2
    Google ScholarLocate open access versionFindings
  • Rohit Girdhar, David F Fouhey, Mikel Rodriguez, and Abhinav Gupta. Learning a predictable and generative vector representation for objects. In Proceedings of the European Conference on Computer Vision, pages 484–499. Springer, 2016. 2
    Google ScholarLocate open access versionFindings
  • Ronald L. Graham. An efficient algorithm for determining the convex hull of a finite planar set. Info. Pro. Lett., 1:132– 133, 1972. 3
    Google ScholarLocate open access versionFindings
  • Thibault Groueix, Matthew Fisher, Vladimir G Kim, Bryan C Russell, and Mathieu Aubry. A papier-mache approach to learning 3d surface generation. In Proceedings of Computer Vision and Pattern Recognition (CVPR), 2018. 1, 2, 6, 8
    Google ScholarLocate open access versionFindings
  • Kan Guo, Dongqing Zou, and Xiaowu Chen. 3d mesh labeling via deep convolutional neural networks. ACM Transactions on Graphics (TOG), 35(1):3, 2015. 2
    Google ScholarLocate open access versionFindings
  • Eric Heiden, David Millard, and Gaurav Sukhatme. Real2sim transfer using differentiable physics. Workshop on Closing the Reality Gap in Sim2real Transfer for Robotic Manipulation, 2019. 2
    Google ScholarFindings
  • Eric Heiden, David Millard, Hejia Zhang, and Gaurav S Sukhatme. Interactive differentiable simulation. arXiv preprint arXiv:1905.10706, 2019. 2
    Findings
  • Hugues Hoppe, Tony DeRose, Tom Duchamp, John McDonald, and Werner Stuetzle. Surface reconstruction from unorganized points. In ACM SIGGRAPH Computer Graphics, volume 26, pages 71–78. ACM, 1992. 2
    Google ScholarLocate open access versionFindings
  • Angjoo Kanazawa, Shubham Tulsiani, Alexei A Efros, and Jitendra Malik. Learning category-specific mesh reconstruction from image collections. In Proceedings of the European Conference on Computer Vision, 2018. 1
    Google ScholarLocate open access versionFindings
  • Chen Kong, Chen-Hsuan Lin, and Simon Lucey. Using locally corresponding cad models for dense 3d reconstructions from a single image. In Proceedings of Computer Vision and Pattern Recognition (CVPR), pages 4857–4865, 2017. 2
    Google ScholarLocate open access versionFindings
  • David H Laidlaw, W Benjamin Trumbore, and John F Hughes. Constructive solid geometry for polyhedral objects. In ACM Trans. on Graphics (Proceedings of SIGGRAPH), 1986. 2
    Google ScholarLocate open access versionFindings
  • Yee Leung, Jiang-She Zhang, and Zong-Ben Xu. Neural networks for convex hull computation. IEEE Transactions on Neural Networks, 8(3):601–611, 1997. 3
    Google ScholarLocate open access versionFindings
  • Yiyi Liao, Simon Donne, and Andreas Geiger. Deep marching cubes: Learning explicit surface representations. In Proceedings of Computer Vision and Pattern Recognition (CVPR), 2018. 1
    Google ScholarLocate open access versionFindings
  • Jyh-Ming Lien and Nancy M Amato. Approximate convex decomposition of polyhedra. In Computer Aided Geometric Design (Proc. of the Symposium on Solid and physical modeling), pages 121–131. ACM, 2007. 3
    Google ScholarLocate open access versionFindings
  • Chen-Hsuan Lin, Chen Kong, and Simon Lucey. Learning efficient point cloud generation for dense 3d object reconstruction. In Thirty-Second AAAI Conference on Artificial Intelligence, 2018. 2
    Google ScholarLocate open access versionFindings
  • Guilin Liu, Zhonghua Xi, and Jyh-Ming Lien. Nearly convex segmentation of polyhedra through convex ridge separation. Computer-Aided Design, 78:137–146, 2016. 3
    Google ScholarLocate open access versionFindings
  • William E Lorensen and Harvey E Cline. Marching cubes: A high resolution 3d surface construction algorithm. ACM siggraph computer graphics, 1987. 4
    Google ScholarLocate open access versionFindings
  • Khaled Mamou and Faouzi Ghorbel. A simple and efficient approach for 3d mesh approximate convex decomposition. In 2009 16th IEEE international conference on image processing (ICIP), pages 3501–3504. IEEE, 2009. 3
    Google ScholarLocate open access versionFindings
  • Khaled Mamou, E Lengyel, and Ed AK Peters. Volumetric hierarchical approximate convex decomposition. Game Engine Gems 3, pages 141–158, 2016. 3
    Google ScholarLocate open access versionFindings
  • Jonathan Masci, Davide Boscaini, Michael Bronstein, and Pierre Vandergheynst. Geodesic convolutional neural networks on riemannian manifolds. In Proceedings of the IEEE international conference on computer vision workshops, pages 37–45, 2015. 2
    Google ScholarLocate open access versionFindings
  • Daniel Maturana and Sebastian Scherer. Voxnet: A 3d convolutional neural network for real-time object recognition. In 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 922–928. IEEE, 2015. 2
    Google ScholarLocate open access versionFindings
  • Lars Mescheder, Michael Oechsle, Michael Niemeyer, Sebastian Nowozin, and Andreas Geiger. Occupancy networks: Learning 3d reconstruction in function space. arXiv preprint arXiv:1812.03828, 2018. 2, 4, 6, 8, 14
    Findings
  • Kaichun Mo, Shilin Zhu, Angel X Chang, Li Yi, Subarna Tripathi, Leonidas J Guibas, and Hao Su. Partnet: A largescale benchmark for fine-grained and hierarchical part-level 3d object understanding. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 909–918, 2019. 6, 7
    Google ScholarLocate open access versionFindings
  • Federico Monti, Davide Boscaini, Jonathan Masci, Emanuele Rodola, Jan Svoboda, and Michael M Bronstein. Geometric deep learning on graphs and manifolds using mixture model cnns. In Proceedings of Computer Vision and Pattern Recognition (CVPR), pages 5115–5124, 2017. 2
    Google ScholarLocate open access versionFindings
  • Richard A Newcombe, Dieter Fox, and Steven M Seitz. Dynamicfusion: Reconstruction and tracking of non-rigid scenes in real-time. In Proceedings of the IEEE conference on computer vision and pattern recognition, 2015. 2
    Google ScholarLocate open access versionFindings
  • Richard A Newcombe, Shahram Izadi, Otmar Hilliges, David Molyneaux, David Kim, Andrew J Davison, Pushmeet Kohi, Jamie Shotton, Steve Hodges, and Andrew Fitzgibbon. Kinectfusion: Real-time dense surface mapping and tracking. In Proc. ISMAR. IEEE, 2011. 2
    Google ScholarLocate open access versionFindings
  • Jeong Joon Park, Peter Florence, Julian Straub, Richard Newcombe, and Steven Lovegrove. Deepsdf: Learning continuous signed distance functions for shape representation. arXiv preprint arXiv:1901.05103, 2019. 2, 4, 8
    Findings
  • Despoina Paschalidou, Ali Osman Ulusoy, and Andreas Geiger. Superquadrics revisited: Learning 3d shape parsing beyond cuboids. In Proceedings IEEE Conf. on Computer Vision and Pattern Recognition (CVPR), 2019. 2, 8
    Google ScholarLocate open access versionFindings
  • Jason Patnode. Character Modeling with Maya and ZBrush: Professional polygonal modeling techniques. Focal Press, 2012. 1
    Google ScholarFindings
  • Franco P Preparata and Se June Hong. Convex hulls of finite sets of points in two and three dimensions. Communications of the ACM, 20(2):87–93, 1977. 3
    Google ScholarLocate open access versionFindings
  • Charles R Qi, Hao Su, Kaichun Mo, and Leonidas J Guibas. Pointnet: Deep learning on point sets for 3d classification and segmentation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2017. 2
    Google ScholarLocate open access versionFindings
  • Charles R Qi, Hao Su, Matthias Nießner, Angela Dai, Mengyuan Yan, and Leonidas J Guibas. Volumetric and multi-view cnns for object classification on 3d data. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 5648–5656, 2016. 2
    Google ScholarLocate open access versionFindings
  • Charles Ruizhongtai Qi, Li Yi, Hao Su, and Leonidas J Guibas. Pointnet++: Deep hierarchical feature learning on point sets in a metric space. In Advances in Neural Information Processing Systems, pages 5099–5108, 2017. 2
    Google ScholarLocate open access versionFindings
  • Anurag Ranjan, Timo Bolkart, Soubhik Sanyal, and Michael J Black. Generating 3d faces using convolutional mesh autoencoders. In Proceedings of the European Conference on Computer Vision (ECCV), 2018. 1
    Google ScholarLocate open access versionFindings
  • Danilo Jimenez Rezende, SM Ali Eslami, Shakir Mohamed, Peter Battaglia, Max Jaderberg, and Nicolas Heess. Unsupervised learning of 3d structure from images. In Advances in Neural Information Processing Systems, 2016. 1, 2
    Google ScholarLocate open access versionFindings
  • Gernot Riegler, Ali Osman Ulusoy, and Andreas Geiger. Octnet: Learning deep 3d representations at high resolutions. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 3577–3586, 2017. 1, 2
    Google ScholarLocate open access versionFindings
  • Lawrence G Roberts. Machine perception of threedimensional solids. PhD thesis, Massachusetts Institute of Technology, 1963. 2
    Google ScholarFindings
  • Gopal Sharma, Rishabh Goyal, Difan Liu, Evangelos Kalogerakis, and Subhransu Maji. Csgnet: Neural shape parser for constructive solid geometry. In Proceedings of Computer Vision and Pattern Recognition (CVPR), 2018. 1, 2
    Google ScholarLocate open access versionFindings
  • Shuran Song and Jianxiong Xiao. Deep sliding shapes for amodal 3d object detection in rgb-d images. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 808–816, 2016. 2
    Google ScholarLocate open access versionFindings
  • David Stutz and Andreas Geiger. Learning 3d shape completion from laser scan data with weak supervision. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 1955–1964, 2018. 1, 2
    Google ScholarLocate open access versionFindings
  • Weiwei Sun, Wei Jiang, Eduard Trulls, Andrea Tagliasacchi, and Kwang Moo Yi. Attentive context normalization for robust permutation-equivariant learning. arXiv preprint arXiv:1907.02545, 2019. 8
    Findings
  • Maxim Tatarchenko, Alexey Dosovitskiy, and Thomas Brox. Octree generating networks: Efficient convolutional architectures for high-resolution 3d outputs. In Proceedings of the IEEE International Conference on Computer Vision, pages 2088–2096, 2017. 1, 2
    Google ScholarLocate open access versionFindings
  • Maxim Tatarchenko, Stephan R Richter, René Ranftl, Zhuwen Li, Vladlen Koltun, and Thomas Brox. What do single-view 3d reconstruction networks learn? In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 3405–3414, 2019. 7
    Google ScholarLocate open access versionFindings
  • Daniel Thul, Sohyeon Jeong, Marc Pollefeys, et al. Approximate convex decomposition and transfer for animated meshes. In SIGGRAPH Asia 2018 Technical Papers, page 226. ACM, 2018. 2, 3, 5
    Google ScholarLocate open access versionFindings
  • Anastasia Tkach, Mark Pauly, and Andrea Tagliasacchi. Sphere-meshes for real-time hand modeling and tracking. ACM Transaction on Graphics (Proc. SIGGRAPH Asia), 2016. 2
    Google ScholarLocate open access versionFindings
  • Shubham Tulsiani, Hao Su, Leonidas J Guibas, Alexei A Efros, and Jitendra Malik. Learning shape abstractions by assembling volumetric primitives. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2017. 1, 2, 3, 4, 5, 6, 7, 8
    Google ScholarLocate open access versionFindings
  • Ali Osman Ulusoy, Andreas Geiger, and Michael J Black. Towards probabilistic volumetric reconstruction using ray potentials. In International Conference on 3D Vision (3DV), 2015. 1
    Google ScholarLocate open access versionFindings
  • Anton van den Hengel, Chris Russell, Anthony Dick, John Bastian, Daniel Pooley, Lachlan Fleming, and Lourdes Agapito. Part-based modelling of compound scenes from images. In Proceedings of Computer Vision and Pattern Recognition (CVPR), pages 878–886, 2015. 2
    Google ScholarLocate open access versionFindings
  • Nanyang Wang, Yinda Zhang, Zhuwen Li, Yanwei Fu, Wei Liu, and Yu-Gang Jiang. Pixel2mesh: Generating 3d mesh models from single rgb images. In Proceedings of the European Conference on Computer Vision, 2018. 1, 2, 6, 8
    Google ScholarLocate open access versionFindings
  • Peng-Shuai Wang, Yang Liu, Yu-Xiao Guo, Chun-Yu Sun, and Xin Tong. O-cnn: Octree-based convolutional neural networks for 3d shape analysis. ACM Transactions on Graphics (TOG), 36(4):72, 2017. 2
    Google ScholarLocate open access versionFindings
  • Peng-Shuai Wang, Chun-Yu Sun, Yang Liu, and Xin Tong. Adaptive o-cnn: a patch-based deep representation of 3d shapes. In SIGGRAPH Asia 2018 Technical Papers, page 217. ACM, 2018. 1, 2
    Google ScholarLocate open access versionFindings
  • Jiajun Wu, Chengkai Zhang, Tianfan Xue, Bill Freeman, and Josh Tenenbaum. Learning a probabilistic latent space of object shapes via 3d generative-adversarial modeling. In Advances in neural information processing systems, pages 82– 90, 2016. 1, 2
    Google ScholarLocate open access versionFindings
  • Zhirong Wu, Shuran Song, Aditya Khosla, Fisher Yu, Linguang Zhang, Xiaoou Tang, and Jianxiong Xiao. 3d shapenets: A deep representation for volumetric shapes. In Proceedings of Computer Vision and Pattern Recognition (CVPR), pages 1912–1920, 2015. 2
    Google ScholarLocate open access versionFindings
  • Fenggen Yu, Kun Liu, Yan Zhang, Chenyang Zhu, and Kai Xu. Partnet: A recursive part decomposition network for fine-grained and hierarchical shape segmentation. Proceedings of Computer Vision and Pattern Recognition (CVPR), 2019. 8
    Google ScholarLocate open access versionFindings
  • Chuhang Zou, Ersin Yumer, Jimei Yang, Duygu Ceylan, and Derek Hoiem. 3d-prnn: Generating shape primitives with recurrent neural networks. In Proceedings of the IEEE International Conference on Computer Vision, 2017. 1
    Google ScholarLocate open access versionFindings
  • 6. Union of smooth indicator functions
    Google ScholarFindings
  • 7. Merged guidance loss and localization loss
    Google ScholarFindings
  • 8. Proof of auxiliary null-space loss
    Google ScholarFindings
Your rating :
0

 

Tags
Comments