A Local-Global Commutative Preserving Functional Map for Shape Correspondence
Article No.: 13, Pages 1 - 7
Abstract
Existing non-rigid shape matching methods mainly involve two disadvantages. (a) Local details and global features of shapes can not be carefully explored. (b) A satisfactory trade-off between the matching accuracy and computational efficiency can be hardly achieved. To address these issues, we propose a local-global commutative preserving functional map (LGCP) for shape correspondence. The core of LGCP involves an intra-segment geometric submodel and a local-global commutative preserving submodel, which accomplishes the segment-to-segment matching and the point-to-point matching tasks, respectively. The first submodel consists of an ICP similarity term and two geometric similarity terms which guarantee the correct correspondence of segments of two shapes, while the second submodel guarantees the bijectivity of the correspondence on both the shape level and the segment level. Experimental results on both segment-to-segment matching and point-to-point matching show that, LGCP not only generate quite accurate matching results, but also exhibit a satisfactory portability and a high efficiency.
References
[1]
Dragomir Anguelov, Praveen Srinivasan, Daphne Koller, Sebastian Thrun, Jim Rodgers, and James Davis. 2005. SCAPE: Shape Completion and Animation of People. ACM Transactionhsh on Graphics 24, 3 (2005), 408–416.
[2]
M. Aubry, U. Schlickewei, and D. Cremers. 2011. The wave kernel signature: A quantum mechanical approach to shape analysis. In 2011 IEEE International Conference on Computer Vision Workshops, Vol. 1. 1626–1633.
[3]
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, Vol. 1. 3794–3801.
[4]
Alexander Bronstein, Ron Kimmel, and Michael Bronstein. 2009. Numerical Geometry of Non-Rigid Shapes, Monographs in Computer Science. Monographs in Computer Science.
[5]
A. M. Bronstein, M. M. Bronstein, and R. Kimmel. 2006. Generalized Multidimensional Scaling: A Framework for Isometry-Invariant Partial Surface Matching. Proceedings of the National Academy of Sciences 103, 5 (2006), 1168–1172.
[6]
Benedict J. Brown and Szymon Rusinkiewicz. 2007. Global Non-Rigid Alignment of 3-D Scans. ACM Transactions on Graphics 26, 3 (2007), 21:1–21:9.
[7]
Will Chang and Matthias Zwicker. 2008. Automatic Registration for Articulated Shapes. Computer Graphics Forum 27, 5 (2008), 1459–1468.
[8]
Q. Chen and V. Koltun. 2015. Robust Nonrigid Registration by Convex Optimization. In 2015 IEEE International Conference on Computer Vision. 2039–2047.
[9]
Marvin Eisenberger, Zorah Lähner, and Daniel Cremers. 2020. Smooth Shells: Multi-Scale Shape Registration With Functional Maps. In 2020 IEEE Conference on Computer Vision and Pattern Recognition, Vol. 1. 12262–12271.
[10]
V. Ganapathi-Subramanian, B. Thibert, M. Ovsjanikov, and L. Guibas. 2016. Stable Region Correspondences between Non-Isometric Shapes. 35, 5 (2016), 121–133.
[11]
Itay Kezurer, Shahar Z. Kovalsky, Ronen Basri, and Yaron Lipman. 2015. Tight Relaxation of Quadratic Matching. 34, 5 (2015), 115–128.
[12]
Vladimir G. Kim, Yaron Lipman, and Thomas Funkhouser. 2011. Blended Intrinsic Maps. 30, 4 (2011), 79:1–79:12.
[13]
Yanir Kleiman and Maks Ovsjanikov. 2019. Robust Structure-Based Shape Correspondence. Computer Graphics Forum 38, 1 (2019), 7–20.
[14]
Hao Li, Robert Sumner, and Mark Pauly. 2008. Global Correspondence Optimization for Non-Rigid Registration of Depth Scans. Computer Graphics Forum 27, 5 (2008), 1421–1430.
[15]
Yaron Lipman and Thomas Funkhouser. 2009. MöBius Voting for Surface Correspondence. ACM Transactions on Graphics 28, 3 (2009), 72:1–72:12.
[16]
Simone Melzi, Jing Ren, Emanuele Rodolà, Abhishek Sharma, Peter Wonka, and Maks Ovsjanikov. 2019. ZoomOut: Spectral Upsampling for Efficient Shape Correspondence. ACM Transactions on Graphics 38, 6 (11 2019), 1–14.
[17]
S. Melzi, E. Rodola, U. Castellani, and M. M. Bronstein. 2016. Shape Analysis with Anisotropic Windowed Fourier Transform. In 2016 International Conference on 3D Vision, Vol. 1. 470–478.
[18]
Facundo Mémoli. 2011. Gromov-Wasserstein Distances and the Metric Approach to Object Matching. Foundations of Computational Mathematics 11, 4 (2011), 417–487.
[19]
Maks Ovsjanikov, Mirela Ben-Chen, Justin Solomon, Adrian Butscher, and Leonidas Guibas. 2012. Functional Maps: A Flexible Representation of Maps between Shapes. ACM Transactions on Graphics 31, 4 (2012), 30:1–30:11.
[20]
Maks Ovsjanikov, Quentin Mérigot, Facundo Mémoli, and Leonidas Guibas. 2010. One Point Isometric Matching with the Heat Kernel. Computer Graphics Forum 29, 5 (2010), 1555–1564.
[21]
Gautam Pai, Jing Ren, Simone Melzi, Peter Wonka, and Maks Ovsjanikov. 2021. Fast Sinkhorn Filters: Using Matrix Scaling for Non-Rigid Shape Correspondence with Functional Maps. In 2021 IEEE Conference on Computer Vision and Pattern Recognition, Vol. 1. 384–393.
[22]
J. Pokrass, A. Bronstein, Michael Bronstein, P. Sprechmann, and G. Sapiro. 2013. Sparse Modeling of Intrinsic Correspondences. Computer Graphics Forum 32, 2 (2013), 459–468.
[23]
Jing Ren, Simone Melzi, Maks Ovsjanikov, and Peter Wonka. 2020. MapTree: recovering multiple solutions in the space of maps. ACM Transactions on Graphics 39, 6 (11 2020), 1–17.
[24]
Jing Ren, Adrien Poulenard, Peter Wonka, and Maks Ovsjanikov. 2018. Continuous and Orientation-Preserving Correspondences via Functional Maps. ACM Transactions on Graphics 37, 248 (11 2018), 1–16.
[25]
E. Rodolí, L. Cosmo, M. M. Bronstein, A. Torsello, and D. Cremers. 2017. Partial Functional Correspondence. Computer Graphics Forum 36, 1 (2017), 222–236.
[26]
Raif Rustamov. 2007. Laplace-Beltrami eigenfunctions for deformation invariant shape representation. In Proceedings of the Fifth Eurographics Symposium on Geometry Processing, Vol. 1. 225–233.
[27]
Yusuf Sahillioglu and Yücel Yemez. 2011. Coarse-to-Fine Combinatorial Matching for Dense Isometric Shape Correspondence. 30, 5 (2011), 1461–1470.
[28]
Justin Solomon, Gabriel Peyré, Vladimir G. Kim, and Suvrit Sra. 2016. Entropic Metric Alignment for Correspondence Problems. ACM Transactions on Graphics 35, 4 (2016), 72:1–72:13.
[29]
J. Sun, M. Ovsjanikov, and L. Guibas. 2009. A Concise and Provably Informative Multi-Scale Signature-Based on Heat Diffusion. Computer Graphics Forum 28, 5 (7 2009), 1383–1392.
[30]
Art Tevs, Alexander Berner, M. Wand, Ivo Ihrke, and H.-P Seidel. 2011. Intrinsic Shape Matching by Planned Landmark Sampling. Computer Graphics Forum 30, 2 (2011), 543–552.
[31]
Oliver van Kaick, Ghassan Hamarneh, and Daniel Cohen-Or. 2011. A Survey on Shape Correspondence. Computer Graphics Forum 30, 6 (2011), 1681–1707.
[32]
M. Vestner, Z. Lähner, A. Boyarski, O. Litany, R. Slossberg, T. Remez, E. Rodola, A. Bronstein, M. Bronstein, R. Kimmel, and D. Cremers. 2017. Efficient Deformable Shape Correspondence via Kernel Matching. In 2017 International Conference on 3D Vision, Vol. 1. 517–526.
[33]
Chaohui Wang, Michael Bronstein, Alexander Bronstein, and Nikos Paragios. 2011. Discrete Minimum Distortion Correspondence Problems for Non-rigid Shape Matching. In 2011 International Conference on Scale Space and Variational Methods in Computer Vision, Vol. 1. 580–591.
[34]
Y. Yao, B. Deng, W. Xu, and J. Zhang. 2020. Quasi-Newton Solver for Robust Non-Rigid Registration. In 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition, Vol. 1. 7597–7606.
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Published In
December 2021
508 pages
ISBN:9781450386074
DOI:10.1145/3469877
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Published: 10 January 2022
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