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Finding Structure in Point Cloud Data with the Robust Isoperimetric Loss

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Scale Space and Variational Methods in Computer Vision (SSVM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 11603))

Abstract

We present a new regularization method to find structure in point clouds corrupted by outliers. The method organizes points into a graph structure, and uses isoperimetric inequalities to craft a loss function that is minimized alternatingly to identify outliers, and annihilate their effect. It can operate in the presence of large amounts of outliers, and inlier noise. The approach is applicable to both low-dimensional point clouds, such as those obtained from stereo or structured light, as well as high-dimensional ones.

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References

  1. Candès, E.J., Li, X., Ma, Y., Wright, J.: Robust principal component analysis? J. ACM (JACM) 58(3), 11:1–11:37 (2011). Article No. 11

    Article  MathSciNet  Google Scholar 

  2. Chung, F., Grigor’yan, A., tung Yau, S.: Higher eigenvalues and isoperimetric inequalities on Riemannian manifolds and graphs (1999)

    Google Scholar 

  3. Deutsch, S., Bertozzi, A., Soatto, S.: Zero shot learning with the isoperimetric loss. Technical report, University of California, Los Angeles (UCLA) (2018)

    Google Scholar 

  4. Deutsch, S., Medioni, G.: Intersecting manifolds: detection, segmentation, and labeling. In: Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence (2015)

    Google Scholar 

  5. Deutsch, S., Medioni, G.: Unsupervised learning using the tensor voting graph. In: Scale Space and Variational Methods in Computer Vision (SSVM) (2015)

    Google Scholar 

  6. Deutsch, S., Medioni, G.G.: Learning the geometric structure of manifolds with singularities using the tensor voting graph. J. Math. Imaging Vis. 57(3), 402–422 (2017)

    Article  MathSciNet  Google Scholar 

  7. Deutsch, S., Ortega, A., Medioni, G.: Manifold denoising based on spectral graph wavelets. In: International Conference on Acoustics, Speech and Signal Processing (ICASSP) (2016)

    Google Scholar 

  8. Deutsch, S., Ortega, A., Medioni, G.G.: Robust denoising of piece-wise smooth manifolds. In: 2018 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2018, Calgary, AB, Canada, 15–20 April 2018, pp. 2786–2790 (2018)

    Google Scholar 

  9. Elhamifar, E., Vidal, R.: Sparse subspace clustering. In: CVPR, pp. 2790–2797 (2009)

    Google Scholar 

  10. Fischler, M.A., Bolles, R.C.: Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Commun. ACM 24, 381–395 (1981)

    Article  MathSciNet  Google Scholar 

  11. Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore (1996)

    MATH  Google Scholar 

  12. Hammond, D.K., Vandergheynst, P., Gribonval, R.: Wavelets on graphs via spectral graph theory. Appl. Comput. Harmon. Anal. 30, 129–150 (2011)

    Article  MathSciNet  Google Scholar 

  13. Hein, M., Maier, M.: Manifold denoising, pp. 561–568 (2007)

    Google Scholar 

  14. Liu, G., Lin, Z., Yu, Y.: Robust subspace segmentation by low-rank representation (2010)

    Google Scholar 

  15. Mordohai, P., Medioni, G.: Dimensionality estimation, manifold learning and function approximation using tensor voting. J. Mach. Learn. Res. 11, 411–450 (2010)

    MathSciNet  MATH  Google Scholar 

  16. Rusu, R.B., Cousins, S.: 3D is here: point cloud library (PCL). In: IEEE International Conference on Robotics and Automation (ICRA), Shanghai, China, 9–13 May 2011

    Google Scholar 

  17. Scharstein, D., et al.: High-resolution stereo datasets with subpixel-accurate ground truth. In: Jiang, X., Hornegger, J., Koch, R. (eds.) GCPR 2014. LNCS, vol. 8753, pp. 31–42. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11752-2_3

    Chapter  Google Scholar 

  18. Suter, D., Chin, T., Wang, H.: Simultaneously fitting and segmenting multiple-structure data with outliers. IEEE Trans. Pattern Anal. Mach. Intell. 34, 1177–1192 (2011)

    Google Scholar 

  19. Zhang, Z., Zha, H.: Principal manifolds and nonlinear dimension reduction via local tangent space alignment. SIAM J. Sci. Comput. 26, 313–338 (2002)

    Article  Google Scholar 

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Acknowledgments

This work was supported in part by ONR grant #N00014-19-1-2229 and ARO grant #W911NF-17-1-0304.

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Authors and Affiliations

  1. University of California, Los Angeles, USA

    Shay Deutsch & Stefano Soatto

  2. Information Sciences Institute, University of Southern California, Marina Del Rey, CA, US

    Iacopo Masi

Authors
  1. Shay Deutsch
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  2. Iacopo Masi
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  3. Stefano Soatto
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Corresponding author

Correspondence to Shay Deutsch .

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Editors and Affiliations

  1. University of Lübeck, Lübeck, Germany

    Jan Lellmann

  2. University of Erlangen-Nuremberg (FAU), Erlangen, Germany

    Martin Burger

  3. University of Lübeck, Lübeck, Germany

    Jan Modersitzki

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Deutsch, S., Masi, I., Soatto, S. (2019). Finding Structure in Point Cloud Data with the Robust Isoperimetric Loss. In: Lellmann, J., Burger, M., Modersitzki, J. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2019. Lecture Notes in Computer Science(), vol 11603. Springer, Cham. https://doi.org/10.1007/978-3-030-22368-7_3

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  • DOI: https://doi.org/10.1007/978-3-030-22368-7_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-22367-0

  • Online ISBN: 978-3-030-22368-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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