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Cyclic Functional Mapping: Self-supervised Correspondence Between Non-isometric Deformable Shapes

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Computer Vision – ECCV 2020 (ECCV 2020)

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Abstract

We present the first spatial-spectral joint consistency network for self-supervised dense correspondence mapping between non-isometric shapes. The task of alignment in non-Euclidean domains is one of the most fundamental and crucial problems in computer vision. As 3D scanners can generate highly complex and dense models, the mission of finding dense mappings between those models is vital. The novelty of our solution is based on a cyclic mapping between metric spaces, where the distance between a pair of points should remain invariant after the full cycle. As the same learnable rules that generate the point-wise descriptors apply in both directions, the network learns invariant structures without any labels while coping with non-isometric deformations. We show here state-of-the-art-results by a large margin for a variety of tasks compared to known self-supervised and supervised methods .

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Notes

  1. 1.

    An illustration of the distortion process is shown in Fig. 2.

References

  1. Abadi, M., et al.: TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems (2015). Software available from http://tensorflow.org/

  2. Aflalo, Y., Bronstein, A., Kimmel, R.: On convex relaxation of graph isomorphism. Proc. Natl. Acad. Sci. 112(10), 2942–2947 (2015)

    Article  MathSciNet  Google Scholar 

  3. Aflalo, Y., Dubrovina, A., Kimmel, R.: Spectral generalized multi-dimensional scaling. Int. J. Comput. Vision 118(3), 380–392 (2016)

    Article  MathSciNet  Google Scholar 

  4. Aflalo, Y., Kimmel, R., Raviv, D.: Scale invariant geometry for nonrigid shapes. SIAM J. Imaging Sci. 6(3), 1579–1597 (2013)

    Article  MathSciNet  Google Scholar 

  5. Aubry, M., Schlickewei, U., Cremers, D.: The wave kernel signature: a quantum mechanical approach to shape analysis. In: 2011 IEEE International Conference on Computer Vision Workshops (ICCV Workshops), pp. 1626–1633. IEEE (2011)

    Google Scholar 

  6. Ben-Chen, M., Gotsman, C., Bunin, G.: Conformal flattening by curvature prescription and metric scaling. Comput. Graph. Forum 27, 449–458 (2008). Wiley Online Library

    Article  Google Scholar 

  7. Bogo, F., Romero, J., Loper, M., Black, M.J.: FAUST: dataset and evaluation for 3D mesh registration. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, Piscataway, June 2014

    Google Scholar 

  8. Boscaini, D., Masci, J., Rodolà, E., Bronstein, M.M., Cremers, D.: Anisotropic diffusion descriptors. Comput. Graph. Forum 35, 431–441 (2016)

    Article  Google Scholar 

  9. Bronstein, A.M., Bronstein, M.M., Kimmel, R.: Generalized multidimensional scaling: a framework for isometry-invariant partial surface matching. Proc. Natl. Acad. Sci. 103(5), 1168–1172 (2006)

    Article  MathSciNet  Google Scholar 

  10. Bronstein, A.M., Bronstein, M.M., Kimmel, R.: Numerical Geometry of Non-Rigid Shapes. Springer, New York (2008)

    Google Scholar 

  11. Bronstein, M.M., Bronstein, A.M., Kimmel, R., Yavneh, I.: Multigrid multidimensional scaling. Numer. Linear Algebra Appl. 13(2–3), 149–171 (2006)

    Article  MathSciNet  Google Scholar 

  12. Bronstein, M.M., Kokkinos, I.: Scale-invariant heat kernel signatures for non-rigid shape recognition. In: 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp. 1704–1711. IEEE (2010)

    Google Scholar 

  13. Chen, Q., Koltun, V.: Robust nonrigid registration by convex optimization. In: Proceedings of the IEEE International Conference on Computer Vision, pp. 2039–2047 (2015)

    Google Scholar 

  14. Cosmo, L., Rodolà, E., Bronstein, M.M., Torsello, A., Cremers, D., Sahillioglu, Y.: SHREC’16: Partial matching of deformable shapes

    Google Scholar 

  15. Elad, A., Kimmel, R.: On bending invariant signatures for surfaces. IEEE Trans. Pattern Anal. Mach. Intell. 25(10), 1285–1295 (2003)

    Article  Google Scholar 

  16. Garland, M., Heckbert, P.S.: Surface simplification using quadric error metrics. In: Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques, pp. 209–216. ACM Press/Addison-Wesley Publishing Co. (1997)

    Google Scholar 

  17. Groueix, T., Fisher, M., Kim, V.G., Russell, B.C., Aubry, M.: 3D-CODED : 3D Correspondences by Deep Deformation. CoRR abs/1806.05228 (2018), http://arxiv.org/abs/1806.05228

  18. Halimi, O., Litany, O., Rodola, E., Bronstein, A.M., Kimmel, R.: Unsupervised learning of dense shape correspondence. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 4370–4379 (2019)

    Google Scholar 

  19. He, K., Zhang, X., Ren, S., Sun, J.: Deep residual learning for image recognition. CoRR abs/1512.03385 (2015). http://arxiv.org/abs/1512.03385

  20. Huang, Q.X., Guibas, L.: Consistent shape maps via semidefinite programming. Comput. Graph. Forum 32, 177–186 (2013). Wiley Online Library

    Article  Google Scholar 

  21. Huang, Q., Wang, F., Guibas, L.: Functional map networks for analyzing and exploring large shape collections. ACM Trans. Graph. (TOG) 33(4), 1–11 (2014)

    MATH  Google Scholar 

  22. Kim, V.G., Lipman, Y., Funkhouser, T.: Blended intrinsic maps. ACM Trans. Graphics (TOG) 30, 79 (2011). ACM

    Google Scholar 

  23. Li, C.L., Simon, T., Saragih, J., Póczos, B., Sheikh, Y.: LBS Autoencoder: self-supervised fitting of articulated meshes to point clouds. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 11967–11976 (2019)

    Google Scholar 

  24. Lipman, Y., Daubechies, I.: Conformal Wasserstein distances: comparing surfaces in polynomial time. Adv. Math. 227(3), 1047–1077 (2011)

    Article  MathSciNet  Google Scholar 

  25. Litany, O., Remez, T., Rodolà, E., Bronstein, A.M., Bronstein, M.M.: Deep functional maps: structured prediction for dense shape correspondence. CoRR abs/1704.08686 (2017). http://arxiv.org/abs/1704.08686

  26. Litany, O., Rodolà, E., Bronstein, A.M., Bronstein, M.M.: Fully spectral partial shape matching. Comput. Graph. Forum 36, 247–258 (2017). Wiley Online Library

    Article  Google Scholar 

  27. Litman, R., Bronstein, A.M.: Learning spectral descriptors for deformable shape correspondence. IEEE Trans. Pattern Anal. Mach. Intell. 36(1), 171–180 (2013)

    Article  Google Scholar 

  28. Liu, M.Y., Breuel, T., Kautz, J.: Unsupervised image-to-image translation networks. In: Advances in Neural Information Processing Systems, pp. 700–708 (2017)

    Google Scholar 

  29. Masci, J., Boscaini, D., Bronstein, M., Vandergheynst, P.: Geodesic convolutional neural networks on Riemannian manifolds. In: Proceedings of the IEEE International Conference on Computer Vision Workshops, pp. 37–45 (2015)

    Google Scholar 

  30. Ovsjanikov, M., Ben-Chen, M., Solomon, J., Butscher, A., Guibas, L.: Functional maps: a flexible representation of maps between shapes. ACM Trans. Graph. (TOG) 31(4), 30 (2012)

    Article  Google Scholar 

  31. Pottmann, H., Wallner, J., Huang, Q.X., Yang, Y.L.: Integral invariants for robust geometry processing. Comput. Aided Geometr. Des. 26(1), 37–60 (2009)

    Article  MathSciNet  Google Scholar 

  32. Raviv, D., Bronstein, A.M., Bronstein, M.M., Waisman, D., Sochen, N., Kimmel, R.: Equi-affine invariant geometry for shape analysis. J. Math. Imaging Vis. 50(1–2), 144–163 (2014)

    Article  MathSciNet  Google Scholar 

  33. Raviv, D., Bronstein, M.M., Bronstein, A.M., Kimmel, R., Sochen, N.: Affine-invariant diffusion geometry for the analysis of deformable 3D shapes. In: CVPR 2011, pp. 2361–2367. IEEE (2011)

    Google Scholar 

  34. Raviv, D., Dubrovina, A., Kimmel, R.: Hierarchical matching of non-rigid shapes. In: Bruckstein, A.M., ter Haar Romeny, B.M., Bronstein, A.M., Bronstein, M.M. (eds.) SSVM 2011. LNCS, vol. 6667, pp. 604–615. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-24785-9_51

    Chapter  Google Scholar 

  35. Raviv, D., Dubrovina, A., Kimmel, R.: Hierarchical framework for shape correspondence. Numer. Math. Theory Methods Appl. 6(1), 245–261 (2013)

    Article  MathSciNet  Google Scholar 

  36. Raviv, D., Kimmel, R.: Affine invariant geometry for non-rigid shapes. Int. J. Comput. Vision 111(1), 1–11 (2015)

    Article  MathSciNet  Google Scholar 

  37. Raviv, D., Raskar, R.: Scale invariant metrics of volumetric datasets. SIAM J. Imaging Sci. 8(1), 403–425 (2015)

    Article  MathSciNet  Google Scholar 

  38. Rodolà, E., Cosmo, L., Bronstein, M.M., Torsello, A., Cremers, D.: Partial functional correspondence. Comput. Graph. Forum 36, 222–236 (2017). Wiley Online Library

    Article  Google Scholar 

  39. Rodolà, E., Rota Bulo, S., Windheuser, T., Vestner, M., Cremers, D.: Dense non-rigid shape correspondence using random forests. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 4177–4184 (2014)

    Google Scholar 

  40. Roufosse, J.M., Sharma, A., Ovsjanikov, M.: Unsupervised deep learning for structured shape matching. In: Proceedings of the IEEE International Conference on Computer Vision, pp. 1617–1627 (2019)

    Google Scholar 

  41. Rustamov, R.M.: Laplace-Beltrami eigenfunctions for deformation invariant shape representation. In: Proceedings of the Fifth Eurographics Symposium on Geometry Processing, SGP 2007, pp. 225–233. Eurographics Association, Aire-la-Ville (2007). http://dl.acm.org/citation.cfm?id=1281991.1282022

  42. Rustamov, R.M., Ovsjanikov, M., Azencot, O., Ben-Chen, M., Chazal, F., Guibas, L.: Map-based exploration of intrinsic shape differences and variability. ACM Trans. Graph. (TOG) 32(4), 1–12 (2013)

    Article  Google Scholar 

  43. Sethian, J.A.: A fast marching level set method for monotonically advancing fronts. Proc. Natl. Acad. Sci. 93(4), 1591–1595 (1996)

    Article  MathSciNet  Google Scholar 

  44. Starck, J., Hilton, A.: Spherical matching for temporal correspondence of non-rigid surfaces. In: Tenth IEEE International Conference on Computer Vision (ICCV 2005), Volume 1, vol. 2, pp. 1387–1394. IEEE (2005)

    Google Scholar 

  45. Sun, J., Ovsjanikov, M., Guibas, L.: A concise and provably informative multi-scale signature based on heat diffusion. Comput. Graph. Forum 28, 1383–1392 (2009). Wiley Online Library

    Article  Google Scholar 

  46. Szeliski, R., et al.: SCAPE: shape completion and animation of people, vol. 24 (2005)

    Google Scholar 

  47. Tevs, A., Berner, A., Wand, M., Ihrke, I., Seidel, H.P.: Intrinsic shape matching by planned landmark sampling. Comput. Graph. Forum 30, 543–552 (2011). Wiley Online Library

    Article  Google Scholar 

  48. Tombari, F., Salti, S., Di Stefano, L.: Unique signatures of histograms for local surface description. In: Daniilidis, K., Maragos, P., Paragios, N. (eds.) ECCV 2010. LNCS, vol. 6313, pp. 356–369. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15558-1_26

    Chapter  Google Scholar 

  49. Vestner, M., et al.: Efficient deformable shape correspondence via kernel matching. In: 2017 International Conference on 3D Vision (3DV), pp. 517–526. IEEE (2017)

    Google Scholar 

  50. Vestner, M., Litman, R., Rodolà, E., Bronstein, A., Cremers, D.: Product manifold filter: non-rigid shape correspondence via kernel density estimation in the product space. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 3327–3336 (2017)

    Google Scholar 

  51. Yi, Z., Zhang, H., Tan, P., Gong, M.: Dualgan: unsupervised dual learning for image-to-image translation. In: Proceedings of the IEEE International Conference on Computer Vision, pp. 2849–2857 (2017)

    Google Scholar 

  52. Zaharescu, A., Boyer, E., Varanasi, K., Horaud, R.: Surface feature detection and description with applications to mesh matching. In: 2009 IEEE Conference on Computer Vision and Pattern Recognition, pp. 373–380. IEEE (2009)

    Google Scholar 

  53. Zhu, J.Y., Park, T., Isola, P., Efros, A.A.: Unpaired image-to-image translation using cycle-consistent adversarial networks. In: Proceedings of the IEEE International Conference on Computer Vision, pp. 2223–2232 (2017)

    Google Scholar 

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Acknowledgment

D.R. is partially funded by the Zimin Institute for Engineering Solutions Advancing BetterLives, the Israeli consortiums for soft robotics and autonomous driving, and the Shlomo Shmeltzer Institute for Smart Transportation.

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Authors and Affiliations

  1. Tel Aviv University, Tel Aviv, Israel

    Dvir Ginzburg & Dan Raviv

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  1. Dvir Ginzburg
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  2. Dan Raviv
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Correspondence to Dvir Ginzburg .

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  1. University of Oxford, Oxford, UK

    Andrea Vedaldi

  2. Graz University of Technology, Graz, Austria

    Horst Bischof

  3. University of Freiburg, Freiburg im Breisgau, Germany

    Thomas Brox

  4. University of North Carolina at Chapel Hill, Chapel Hill, NC, USA

    Jan-Michael Frahm

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Ginzburg, D., Raviv, D. (2020). Cyclic Functional Mapping: Self-supervised Correspondence Between Non-isometric Deformable Shapes. In: Vedaldi, A., Bischof, H., Brox, T., Frahm, JM. (eds) Computer Vision – ECCV 2020. ECCV 2020. Lecture Notes in Computer Science(), vol 12350. Springer, Cham. https://doi.org/10.1007/978-3-030-58558-7_3

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