research-article

Tensor maps for synchronizing heterogeneous shape collections

Authors:

Zhenxiao Liang,

Chandrajit BajajAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 38, Issue 4

Article No.: 106, Pages 1 - 18

https://doi.org/10.1145/3306346.3322944

Published: 12 July 2019 Publication History

Abstract

Establishing high-quality correspondence maps between geometric shapes has been shown to be the fundamental problem in managing geometric shape collections. Prior work has focused on computing efficient maps between pairs of shapes, and has shown a quantifiable benefit of joint map synchronization, where a collection of shapes are used to improve (denoise) the pairwise maps for consistency and correctness. However, these existing map synchronization techniques place very strong assumptions on the input shapes collection such as all the input shapes fall into the same category and/or the majority of the input pairwise maps are correct. In this paper, we present a multiple map synchronization approach that takes a heterogeneous shape collection as input and simultaneously outputs consistent dense pairwise shape maps. We achieve our goal by using a novel tensor-based representation for map synchronization, which is efficient and robust than all prior matrix-based representations. We demonstrate the usefulness of this approach across a wide range of geometric shape datasets and the applications in shape clustering and shape co-segmentation.

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References

[1]

Animashree Anandkumar, Rong Ge, Daniel Hsu, Sham M. Kakade, and Matus Telgarsky. 2014. Tensor Decompositions for Learning Latent Variable Models. J. Mach. Learn. Res. 15, 1 (Jan. 2014), 2773--2832. http://dl.acm.org/citation.cfm?id=2627435.2697055

Digital Library

[2]

Dragomir Anguelov, Praveen Srinivasan, Daphne Koller, Sebastian Thrun, Jim Rodgers, and James Davis. 2005. SCAPE: Shape Completion and Animation of People. ACM Trans. Graph. 24, 3 (July 2005), 408--416.

Digital Library

[3]

Federica Arrigoni, Beatrice Rossi, Pasqualina Fragneto, and Andrea Fusiello. 2018. Robust synchronization in SO(3) and SE(3) via low-rank and sparse matrix decomposition. Computer Vision and Image Understanding 174 (2018), 95 -- 113.

[4]

Morteza Ashraphijuo and Xiaodong Wang. 2017. Fundamental conditions for low-CP-rank tensor completion. The Journal of Machine Learning Research 18, 1 (2017), 2116--2145.

Digital Library

[5]

Chandrajit Bajaj, Tingran Gao, Zihang He, Qixing Huang, and Zhenxiao Liang. 2018. SMAC: Simultaneous Mapping and Clustering Using Spectral Decompositions. In Proceedings of the 35th International Conference on Machine Learning (Proceedings of Machine Learning Research), Jennifer Dy and Andreas Krause (Eds.), Vol. 80. PMLR, Stockholmsmassan, Stockholm Sweden, 324--333. http://proceedings.mlr.press/v80/bajaj18a.html

[6]

Mikhail Belkin and Partha Niyogi. 2001. Laplacian Eigenmaps and Spectral Techniques for Embedding and Clustering. In Proceedings of the 14th International Conference on Neural Information Processing Systems: Natural and Synthetic (NIPS'01). MIT Press, Cambridge, MA, USA, 585--591. http://dl.acm.org/citation.cfm?id=2980539.2980616

Digital Library

[7]

P. Berkhin. 2006. A Survey of Clustering Data Mining Techniques. In Grouping Multidimensional Data: Recent Advances in Clustering, Jacob Kogan, Charles Nicholas, and Marc Teboulle (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg, 25--71.

[8]

James C. Bezdek and Richard J. Hathaway. 2003. Convergence of alternating optimization. Neural, Parallel Sci. Comput. 11 (December 2003), 351--368. Issue 4.

Digital Library

[9]

Federica Bogo, Javier Romero, Matthew Loper, and Michael J. Black. 2014. FAUST: Dataset and Evaluation for 3D Mesh Registration. In 2014 IEEE Conference on Computer Vision and Pattern Recognition. IEEE Computer Society, Columbus, OH, USA, 3794--3801.

Digital Library

[10]

Doug M. Boyer, Yaron Lipman, Elizabeth St. Clair, Jesus Puente, Biren A. Patel, Thomas Funkhouser, Jukka Jernvall, and Ingrid Daubechies. 2011. Algorithms to automatically quantify the geometric similarity of anatomical surfaces. Proceedings of the National Academy of Sciences 108, 45 (2011), 18221--18226. arXiv:https://www.pnas.org/content/108/45/18221.full.pdf

[11]

Alexander Bronstein, Michael Bronstein, and Ron Kimmel. 2008. Numerical Geometry of Non-Rigid Shapes (1 ed.). Springer Publishing Company, Incorporated, New York City.

Digital Library

[12]

E. J. Candes, X. Li, Y. Ma, and J. Wright. 2011. Robust principal component analysis? Journal of the ACM (JACM) 58, 3 (2011), 11.

Digital Library

[13]

E. J. Candes, T. Strohmer, and V. Voroninski. 2012. PhaseLift: Exact and stable signal recovery from magnitude measurements via convex programming. Communications on Pure and Applied Mathematics 66 (august 2012), 1241--1274. Issue 8.

[14]

Angel X. Chang, Thomas A. Funkhouser, Leonidas J. Guibas, Pat Hanrahan, Qi-Xing 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. CoRR abs/1512.03012 (2015).

[15]

Avishek Chatterjee and Venu Madhav Govindu. 2013. Efficient and Robust Large-Scale Rotation Averaging. In ICCV. IEEE Computer Society, Sydney, Australia, 521--528.

Digital Library

[16]

Yuxin Chen, Leonidas J. Guibas, and Qi-Xing Huang. 2014. Near-Optimal Joint Object Matching via Convex Relaxation. In Proceedings of the 31th International Conference on Machine Learning, ICML 2014, Beijing, China, 21--26 June 2014. JMLR, Inc., Beijing, China, 100--108.

Digital Library

[17]

Andrzej Cichocki, Danilo Mandic, Lieven De Lathauwer, Guoxu Zhou, Qibin Zhao, Cesar Caiafa, and Huy Anh Phan. 2015. Tensor decompositions for signal processing applications: From two-way to multiway component analysis. IEEE Signal Processing Magazine 32, 2 (2015), 145--163.

[18]

Luca Cosmo, Emanuele Rodolà, Andrea Albarelli, Facundo Mémoli, and Daniel Cremers. 2017. Consistent Partial Matching of Shape Collections via Sparse Modeling. Comput. Graph. Forum 36, 1 (2017), 209--221.

Digital Library

[19]

Lieven De Lathauwer, Josphine Castaing, and Jean-Franois Cardoso. 2007. Fourth-order cumulant-based blind identification of underdetermined mixtures. IEEE Transactions on Signal Processing 55, 6 (2007), 2965--2973.

Digital Library

[20]

Yuval Eldar, Michael Lindenbaum, Moshe Porat, and Yehoshua Y. Zeevi. 1997. The farthest point strategy for progressive image sampling. IEEE Trans. Image Processing 6, 9 (1997), 1305--1315.

Digital Library

[21]

Noa Fish, Oliver van Kaick, Amit Bermano, and Daniel Cohen-Or. 2016. Structure-oriented Networks of Shape Collections. ACM Trans. Graph. 35, 6, Article 171 (Nov. 2016), 14 pages.

Digital Library

[22]

Thomas Funkhouser, Michael Kazhdan, Philip Shilane, Patrick Min, William Kiefer, Ayellet Tal, Szymon Rusinkiewicz, and David Dobkin. 2004. Modeling by Example. ACM Trans. Graph. 23, 3 (Aug. 2004), 652--663.

Digital Library

[23]

Guojun Gan, Chaoqun Ma, and Jianhong Wu. 2007. Data Clustering: Theory, Algorithms, and Applications (ASA-SIAM Series on Statistics and Applied Probability). Society for Industrial and Applied Mathematics, Philadelphia, PA, USA.

Digital Library

[24]

Lin Gao, Yan-Pei Cao, Yu-Kun Lai, Hao-Zhi Huang, Leif Kobbelt, and Shi-Min Hu. 2015. Active Exploration of Large 3D Model Repositories. IEEE Trans. Vis. Comput. Graph. 21, 12 (2015), 1390--1402.

Digital Library

[25]

Daniela Giorgi, Silvia Biasotti, and Laura Paraboschi. 2007. Shape retrieval contest 2007: Watertight models track. SHREC competition 8, 7 (2007).

[26]

Aleksey Golovinskiy and Thomas Funkhouser. 2008. Randomized Cuts for 3D Mesh Analysis. ACM Trans. Graph. 27, 5, Article 145 (Dec. 2008), 12 pages.

Digital Library

[27]

G.H. Golub and C.F. Van Loan. 1996. Matrix computations. Johns Hopkins University Press, Baltimore, MD.

[28]

Kan Guo, Dongqing Zou, and Xiaowu Chen. 2015. 3D Mesh Labeling via Deep Convolutional Neural Networks. ACM Trans. Graph. 35, 1, Article 3 (Dec. 2015), 12 pages.

Digital Library

[29]

Ruizhen Hu, Lubin Fan, and Ligang Liu. 2012. Co-Segmentation of 3D Shapes via Subspace Clustering. Comput. Graph. Forum 31, 5 (Aug. 2012), 1703--1713.

Digital Library

[30]

Qixing Huang, Vladlen Koltun, and Leonidas Guibas. 2011. Joint Shape Segmentation with Linear Programming. ACM Trans. Graph. 30, 6, Article 125 (Dec. 2011), 12 pages.

Digital Library

[31]

Qixing Huang, Fan Wang, and Leonidas Guibas. 2014. Functional Map Networks for Analyzing and Exploring Large Shape Collections. ACM Transactions on Graphics 33, 4, Article 36 (July 2014), 11 pages.

Digital Library

[32]

Qi-Xing Huang, Simon Flöry, Natasha Gelfand, Michael Hofer, and Helmut Pottmann. 2006. Reassembling Fractured Objects by Geometric Matching. ACM Trans. Graph. 25, 3 (July 2006), 569--578.

Digital Library

[33]

Qi-Xing Huang and Leonidas Guibas. 2013. Consistent Shape Maps via Semidefinite Programming. In Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing (SGP '13). Eurographics Association, Aire-la-Ville, Switzerland, Switzerland, 177--186.

Digital Library

[34]

Qi-Xing Huang, Guo-Xin Zhang, Lin Gao, Shi-Min Hu, Adrian Butscher, and Leonidas Guibas. 2012. An Optimization Approach for Extracting and Encoding Consistent Maps in a Shape Collection. ACM Trans. Graph. 31, 6, Article 167 (Nov. 2012), 11 pages.

Digital Library

[35]

Xiangru Huang, Zhenxiao Liang, Chandrajit Bajaj, and Qixing Huang. 2017. Translation Synchronization via Truncated Least Squares. In Advances in Neural Information Processing Systems 30, I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett (Eds.). Curran Associates, Inc., Long Beach, CA, USA, 1459--1468. http://papers.nips.cc/paper/6744-translation-synchronization-via-truncated-least-squares.pdf

Digital Library

[36]

Xiangru Huang, Zhenxiao Liang, Xiaowei Zhou, Yao Xie, Leonidas J. Guibas, and Qixing Huang. 2019. Learning Transformation Synchronization. In Proceedings IEEE Conf. on Computer Vision and Pattern Recognition (CVPR). IEEE, Piscataway, NJ, USA.

[37]

Daniel Huber. 2002. Automatic Three-dimensional Modeling from Reality. Ph.D. Dissertation. Robotics Institute, Carnegie Mellon University, Pittsburgh, PA.

Digital Library

[38]

Evangelos Kalogerakis, Melinos Averkiou, Subhransu Maji, and Siddhartha Chaudhuri. 2017. 3D Shape Segmentation with Projective Convolutional Networks. In CVPR. IEEE Computer Society, 6630--6639.

[39]

Evangelos Kalogerakis, Aaron Hertzmann, and Karan Singh. 2010. Learning 3D Mesh Segmentation and Labeling. In ACM SIGGRAPH 2010 Papers (SIGGRAPH '10). ACM, New York, NY, USA, Article 102, 12 pages.

Digital Library

[40]

Raghunandan H. Keshavan, Andrea Montanari, and Sewoong Oh. 2010. Matrix Completion from a Few Entries. IEEE Trans. Inf. Theor. 56, 6 (June 2010), 2980--2998.

Digital Library

[41]

Vladimir G. Kim, Wilmot Li, Niloy J. Mitra, Siddhartha Chaudhuri, Stephen DiVerdi, and Thomas Funkhouser. 2013. Learning Part-based Templates from Large Collections of 3D Shapes. ACM Trans. Graph. 32, 4, Article 70 (July 2013), 12 pages.

Digital Library

[42]

Vladimir G. Kim, Wilmot Li, Niloy J. Mitra, Stephen DiVerdi, and Thomas Funkhouser. 2012. Exploring Collections of 3D Models Using Fuzzy Correspondences. ACM Trans. Graph. 31, 4, Article 54 (July 2012), 11 pages.

Digital Library

[43]

Vladimir G. Kim, Yaron Lipman, and Thomas Funkhouser. 2011. Blended Intrinsic Maps. ACM Trans. Graph. 30, 4 (July 2011), 79:1--79:12.

Digital Library

[44]

Tamara G. Kolda and Brett W. Bader. 2009. Tensor Decompositions and Applications. SIAM Rev. 51, 3 (2009), 455--500.

Digital Library

[45]

Vladislav Kraevoy and Alla Sheffer. 2004. Cross-parameterization and Compatible Remeshing of 3D Models. ACM Trans. Graph. 23, 3 (Aug. 2004), 861--869.

Digital Library

[46]

Vladislav Kreavoy, Dan Julius, and Alla Sheffer. 2007. Model Composition from Interchangeable Components. In Proceedings of the 15th Pacific Conference on Computer Graphics and Applications. IEEE Computer Society, Washington, DC, USA, 129--138.

Digital Library

[47]

Dana Lahat, Tülay Adalı, and Christian Jutten. 2015. Multimodal Data Fusion: An Overview of Methods, Challenges and Prospects. Proceedings of the IEEE 103, 9 (Aug. 2015), 1449--1477.

[48]

Spyridon Leonardos, Xiaowei Zhou, and Kostas Daniilidis. 2017. Distributed consistent data association via permutation synchronization. In ICRA. IEEE, Singapore, 2645--2652.

[49]

Canyi Lu, Jiashi Feng, Yudong Chen, Wei Liu, Zhouchen Lin, and Shuicheng Yan. 2016. Tensor Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Tensors via Convex Optimization. In CVPR. IEEE Computer Society, Las Vegas, NV, USA, 5249--5257.

[50]

Damien Muti and Salah Bourennane. 2005. Multidimensional filtering based on a tensor approach. Signal Processing 85, 12 (2005), 2338--2353.

Digital Library

[51]

Andy Nguyen, Mirela Ben-Chen, Katarzyna Welnicka, Yinyu Ye, and Leonidas Guibas. 2011. An Optimization Approach to Improving Collections of Shape Maps. Computer Graphics Forum 30 (2011), 1481--1491. Issue 5.

[52]

Ryutarou Ohbuchi, Kunio Osada, Takahiko Furuya, and Tomohisa Banno. 2008. Salient local visual features for shape-based 3D model retrieval. In Shape Modeling and Applications, 2008. SMI 2008. IEEE International Conference on. IEEE Computer Society, Berkeley, CA, USA, 93--102.

[53]

Robert Osada, Thomas Funkhouser, Bernard Chazelle, and David Dobkin. 2002. Shape Distributions. ACM Trans. Graph. 21, 4 (Oct. 2002), 807--832.

Digital Library

[54]

Maks Ovsjanikov, Mirela Ben-Chen, Justin Solomon, Adrian Butscher, and Leonidas J. Guibas. 2012. Functional maps: a flexible representation of maps between shapes. ACM Trans. Graph. 31, 4 (2012), 30:1--30:11.

Digital Library

[55]

Deepti Pachauri, Risi Kondor, and Vikas Singh. 2013. Solving the multi-way matching problem by permutation synchronization. In Advances in Neural Information Processing Systems 26, C. J. C. Burges, L. Bottou, M. Welling, Z. Ghahramani, and K. Q. Weinberger (Eds.). Curran Associates, Inc., Lake Tahoe, Nevada, US, 1860--1868. http://papers.nips.cc/paper/4987-solving-the-multi-way-matching-problem-by-permutation-synchronization.pdf

Digital Library

[56]

Dau Pelleg and Andrew Moore. 2000. X-means: Extending K-means with Efficient Estimation of the Number of Clusters. In In Proceedings of the 17th International Conf. on Machine Learning. Morgan Kaufmann, San Francisco, CA, USA, 727--734.

Digital Library

[57]

Charles Ruizhongtai Qi, Li Yi, Hao Su, and Leonidas J. Guibas. 2017. PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space. CoRR abs/1706.02413 (2017).

[58]

W.M. Rand. 1971. Objective criteria for the evaluation of clustering methods. J. Amer. Statist. Assoc. 66, 336 (1971), 846--850.

[59]

E. Rodolà, L. Cosmo, M. M. Bronstein, A. Torsello, and D. Cremers. 2017. Partial Functional Correspondence. Comput. Graph. Forum 36, 1 (Jan. 2017), 222--236.

Digital Library

[60]

Raif M. Rustamov. 2007. Laplace-Beltrami Eigenfunctions for Deformation Invariant Shape Representation. In Proceedings of the Fifth Eurographics Symposium on Geometry Processing (SGP '07). Eurographics Association, Aire-la-Ville, Switzerland, Switzerland, 225--233. http://dl.acm.org/citation.cfm?id=1281991.1282022

Digital Library

[61]

John Schreiner, Arul Asirvatham, Emil Praun, and Hugues Hoppe. 2004. Inter-surface Mapping. ACM Trans. Graph. 23, 3 (Aug. 2004), 870--877.

Digital Library

[62]

Vatsal Sharan and Gregory Valiant. 2017. Orthogonalized ALS: A Theoretically Principled Tensor Decomposition Algorithm for Practical Use. In Proceedings of the 34th International Conference on Machine Learning (Proceedings of Machine Learning Research), Doina Precup and Yee Whye Teh (Eds.), Vol. 70. PMLR, International Convention Centre, Sydney, Australia, 3095--3104.

Digital Library

[63]

Amnon Shashua and Tamir Hazan. 2005. Non-negative Tensor Factorization with Applications to Statistics and Computer Vision. In Proceedings of the 22Nd International Conference on Machine Learning (ICML '05). ACM, New York, NY, USA, 792--799.

Digital Library

[64]

Yanyao Shen, Qixing Huang, Nati Srebro, and Sujay Sanghavi. 2016. Normalized Spectral Map Synchronization. In Advances in Neural Information Processing Systems 29, D. D. Lee, M. Sugiyama, U. V. Luxburg, I. Guyon, and R. Garnett (Eds.). Curran Associates, Inc., Barcelona, Spain, 4925--4933. http://papers.nips.cc/paper/6128-normalized-spectral-map-synchronization.pdf

Digital Library

[65]

Oana Sidi, Oliver van Kaick, Yanir Kleiman, Hao Zhang, and Daniel Cohen-Or. 2011. Unsupervised Co-segmentation of a Set of Shapes via Descriptor-space Spectral Clustering. ACM Trans. Graph. 30, 6, Article 126 (Dec. 2011), 10 pages.

Digital Library

[66]

Nicholas D Sidiropoulos, Rasmus Bro, and Georgios B Giannakis. 2000. Parallel factor analysis in sensor array processing. IEEE transactions on Signal Processing 48, 8 (2000), 2377--2388.

Digital Library

[67]

Nicholas D. Sidiropoulos, Lieven De Lathauwer, Xiao Fu, Kejun Huang, Evangelos E. Papalexakis, and Christos Faloutsos. 2017. Tensor Decomposition for Signal Processing and Machine Learning. Trans. Sig. Proc. 65, 13 (July 2017), 3551--3582.

Digital Library

[68]

Hang Su, Subhransu Maji, Evangelos Kalogerakis, and Erik Learned-Miller. 2015. Multi-view Convolutional Neural Networks for 3D Shape Recognition. In Proceedings of the 2015 IEEE International Conference on Computer Vision (ICCV) (ICCV '15). IEEE Computer Society, Washington, DC, USA, 945--953.

Digital Library

[69]

Robert W. Sumner and Jovan Popović. 2004. Deformation transfer for triangle meshes. ACM Trans. Graph. 23, 3 (Aug. 2004), 399--405.

Digital Library

[70]

Jimeng Sun, Dacheng Tao, and Christos Faloutsos. 2006. Beyond Streams and Graphs: Dynamic Tensor Analysis. In Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD '06). ACM, New York, NY, USA, 374--383.

Digital Library

[71]

Jian-Tao Sun, Hua-Jun Zeng, Huan Liu, Yuchang Lu, and Zheng Chen. 2005. CubeSVD: A Novel Approach to Personalized Web Search. In Proceedings of the 14th International Conference on World Wide Web (WWW '05). ACM, New York, NY, USA, 382--390.

Digital Library

[72]

Yifan Sun, Zhenxiao Liang, Xiangru Huang, and Qixing Huang. 2018. Joint Map and Symmetry Synchronization. In Computer Vision - ECCV 2018 - 15th European Conference, Munich, Germany, September 8--14, 2018, Proceedings, Part V. Springer, Munich, Germany, 257--275.

[73]

Oliver van Kaick, Kai Xu, Hao Zhang, Yanzhen Wang, Shuyang Sun, Ariel Shamir, and Daniel Cohen-Or. 2013. Co-hierarchical Analysis of Shape Structures. ACM Trans. Graph. 32, 4, Article 69 (July 2013), 10 pages.

Digital Library

[74]

Oliver van Kaick, Hao Zhang, Ghassan Hamarneh, and Daniel Cohen-Or. 2011. A Survey on Shape Correspondence. Comput. Graph. Forum 30, 6 (2011), 1681--1707.

[75]

M. A. O. Vasilescu and Demetri Terzopoulos. 2002. Multilinear Analysis of Image Ensembles: TensorFaces. In Proceedings of the 7th European Conference on Computer Vision-Part I (ECCV '02). Springer-Verlag, London, UK, UK, 447--460. http://dl.acm.org/citation.cfm?id=645315.649173

Digital Library

[76]

Daniel Vlasic, Matthew Brand, Hanspeter Pfister, and Jovan Popović. 2005. Face transfer with multilinear models. ACM transactions on graphics (TOG) 24, 3 (2005), 426--433.

Digital Library

[77]

Fan Wang, Qixing Huang, and Leonidas J. Guibas. 2013. Image Co-segmentation via Consistent Functional Maps. In Proceedings of the 2013 IEEE International Conference on Computer Vision (ICCV '13). IEEE Computer Society, Washington, DC, USA, 849--856.

Digital Library

[78]

Lanhui Wang and Amit Singer. 2013. Exact and Stable Recovery of Rotations for Robust Synchronization. Information and Inference: A Journal of the IMA 2 (2013), 145--193. Issue 2.

[79]

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 Trans. Graph. 31, 6, Article 165 (Nov. 2012), 10 pages.

Digital Library

[80]

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 CVPR. IEEE Computer Society, 1912--1920.

[81]

Kun Xu, Kang Chen, Hongbo Fu, Wei-Lun Sun, and Shi-Min Hu. 2013. Sketch2Scene: Sketch-based Co-retrieval and Co-placement of 3D Models. ACM Trans. Graph. 32, 4, Article 123 (July 2013), 15 pages.

Digital Library

[82]

Rui Xu and D. Wunsch, II. 2005. Survey of Clustering Algorithms. Trans. Neur. Netw. 16, 3 (May 2005), 645--678.

Digital Library

[83]

Li Yi, Leonidas Guibas, Aaron Hertzmann, Vladimir G. Kim, Hao Su, and Ersin Yumer. 2017a. Learning Hierarchical Shape Segmentation and Labeling from Online Repositories. ACM Trans. Graph. 36, 4, Article 70 (July 2017), 12 pages.

Digital Library

[84]

Li Yi, Vladimir G. Kim, Duygu Ceylan, I-Chao Shen, Mengyan Yan, Hao Su, Cewu Lu, Qixing Huang, Alla Sheffer, and Leonidas Guibas. 2016. A Scalable Active Framework for Region Annotation in 3D Shape Collections. ACM Trans. Graph. 35, 6, Article 210 (Nov. 2016), 210:1--210:12 pages.

Digital Library

[85]

Li Yi, Hao Su, Xingwen Guo, and Leonidas J. Guibas. 2017b. SyncSpecCNN: Synchronized Spectral CNN for 3D Shape Segmentation. In CVPR. IEEE Computer Society, 6584--6592.

[86]

Mehmet Ersin Yumer and Levent Burak Kara. 2012. Co-abstraction of Shape Collections. ACM Trans. Graph. 31, 6, Article 166 (Nov. 2012), 11 pages.

Digital Library

[87]

Christopher Zach, Manfred Klopschitz, and Marc Pollefeys. 2010. Disambiguating visual relations using loop constraints. In CVPR. IEEE Computer Society, San Francisco, CA, 1426--1433. http://dblp.uni-trier.de/db/conf/cvpr/cvpr2010.html#ZachKP10

[88]

Hongyang Zhang, Vatsal Sharan, Moses Charikar, and Yingyu Liang. 2018. Recovery Guarantees for Quadratic Tensors with Limited Observations. CoRR abs/1811.00148 (2018).

[89]

Zaiwei Zhang, Zhenxiao Liang, Lemeng Wu, Xiaowei Zhou, and Qixing Huang. 2019. Path-Invariant Map Networks. In Proceedings IEEE Conf. on Computer Vision and Pattern Recognition (CVPR). IEEE, Piscataway, NJ, USA.

[90]

Xiaowei Zhou, Menglong Zhu, and Kostas Daniilidis. 2015. Multi-image Matching via Fast Alternating Minimization. In ICCV. IEEE Computer Society, Santiago, Chile, 4032--4040.

Digital Library

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He JZhang TKobayashi HKawamoto AZhou YNomura TZhu B(2024)Multi-level Partition of Unity on Differentiable Moving ParticlesACM Transactions on Graphics10.1145/368798943:6(1-21)Online publication date: 19-Dec-2024
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Index Terms

Tensor maps for synchronizing heterogeneous shape collections
1. Computer systems organization
  1. Dependable and fault-tolerant systems and networks
    1. Redundancy
  2. Embedded and cyber-physical systems
    1. Embedded systems
    2. Robotics
2. Networks
  1. Network properties
    1. Network reliability

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cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 38, Issue 4

August 2019

1480 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/3306346

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Published: 12 July 2019

Published in TOG Volume 38, Issue 4

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Cited By

He JZhang TKobayashi HKawamoto AZhou YNomura TZhu B(2024)Multi-level Partition of Unity on Differentiable Moving ParticlesACM Transactions on Graphics10.1145/368798943:6(1-21)Online publication date: 19-Dec-2024
https://dl.acm.org/doi/10.1145/3687989
Huang GFang QZhang ZLiu LFu X(2024)Stochastic Normal Orientation for Point CloudsACM Transactions on Graphics10.1145/368794443:6(1-12)Online publication date: 19-Dec-2024
https://dl.acm.org/doi/10.1145/3687944
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