Advertisement

Local Spectral Graph Convolution for Point Set Feature Learning

  • Chu Wang
  • Babak Samari
  • Kaleem SiddiqiEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11208)

Abstract

Feature learning on point clouds has shown great promise, with the introduction of effective and generalizable deep learning frameworks such as pointnet++. Thus far, however, point features have been abstracted in an independent and isolated manner, ignoring the relative layout of neighboring points as well as their features. In the present article, we propose to overcome this limitation by using spectral graph convolution on a local graph, combined with a novel graph pooling strategy. In our approach, graph convolution is carried out on a nearest neighbor graph constructed from a point’s neighborhood, such that features are jointly learned. We replace the standard max pooling step with a recursive clustering and pooling strategy, devised to aggregate information from within clusters of nodes that are close to one another in their spectral coordinates, leading to richer overall feature descriptors. Through extensive experiments on diverse datasets, we show a consistent demonstrable advantage for the tasks of both point set classification and segmentation. Our implementations are available at https://github.com/fate3439/LocalSpecGCN.

Keywords

Point set features Graph convolution Spectral filtering Spectral coordinates Clustering Deep learning 

Notes

Acknowledgments

We thank Charles Ruizhongtai Qi who not only released the pointnet++ implementation upon which our own work is based, but was also kind enough to provide many helpful hints on how to use it. We are also grateful to the Natural Sciences and Engineering Research Council of Canada for research funding.

References

  1. 1.
    Qi, C.R., Yi, L., Su, H., Guibas, L.J.: Pointnet++: deep hierarchical feature learning on point sets in a metric space. In: NIPS (2017)Google Scholar
  2. 2.
    Qi, C.R., Su, H., Mo, K., Guibas, L.J.: PointNet: deep learning on point sets for 3D classification and segmentation. In: CVPR (2016)Google Scholar
  3. 3.
    Defferrard, M., Bresson, X., Vandergheynst, P.: Convolutional neural networks on graphs with fast localized spectral filtering. In: NIPS (2016)Google Scholar
  4. 4.
    Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. In: ICLR (2017)Google Scholar
  5. 5.
    Shuman, D.I., Narang, S.K., Frossard, P., Ortega, A., Vandergheynst, P.: The emerging field of signal processing on graphs: extending high-dimensional data analysis to networks and other irregular domains. IEEE Sig. Process. Mag. 30(3), 83–98 (2013)CrossRefGoogle Scholar
  6. 6.
    Wang, C., Pelillo, M., Siddiqi, K.: Dominant set clustering and pooling for multi-view 3D object recognition. In: BMVC (2017)Google Scholar
  7. 7.
    Lombaert, H., Grady, L., Cheriet, F.: FOCUSR: feature oriented correspondence using spectral regularization-a method for precise surface matching. IEEE Trans. Pattern Anal. Mach. Intell. (2013)Google Scholar
  8. 8.
    Bronstein, A.M., Bronstein, M.M., Kimmel, R.: Numerical Geometry of Non-rigid Shapes. Monographs in Computer Science. Springer, New York (2008).  https://doi.org/10.1007/978-0-387-73301-2CrossRefzbMATHGoogle Scholar
  9. 9.
    Chung, F.R.: Spectral Graph Theory. Number 92 in Regional Conference Series in Mathematics. Am. Mathe. Soc. (1997)Google Scholar
  10. 10.
    Shi, J., Malik, J.: Normalized cuts and image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 22(8), 888–905 (2000)CrossRefGoogle Scholar
  11. 11.
    Monti, F., Boscaini, D., Masci, J., Rodolà, E., Svoboda, J., Bronstein, M.M.: Geometric deep learning on graphs and manifolds using mixture model CNNs. In: CVPR (2017)Google Scholar
  12. 12.
    Wu, Z., et al.: 3D shapenets: a deep representation for volumetric shapes. In: CVPR (2015)Google Scholar
  13. 13.
    Siddiqi, K., Zhang, J., Macrini, D., Shokoufandeh, A., Bouix, S., Dickinson, S.: Retrieving articulated 3D models using medial surfaces. Mach. Vis. Appl. 19(4), 261–274 (2008)CrossRefGoogle Scholar
  14. 14.
    Yi, L., et al.: A scalable active framework for region annotation in 3D shape collections. ACM Trans. Graph. (TOG) (2016)Google Scholar
  15. 15.
    Yi, L., Su, H., Guo, X., Guibas, L.: SyncSpecCNN: synchronized spectral CNN for 3D shape segmentation. In: CVPR (2017)Google Scholar
  16. 16.
    Dai, A., Chang, A.X., Savva, M., Halber, M., Funkhouser, T., Nießner, M.: ScanNet: richly-annotated 3D reconstructions of indoor scenes. In: CVPR (2017)Google Scholar
  17. 17.
    Simard, P.Y., Steinkraus, D., Platt, J.C., et al.: Best practices for convolutional neural networks applied to visual document analysis. In: ICDAR (2003)Google Scholar
  18. 18.
    LeCun, Y., Bottou, L., Bengio, Y., Haffner, P.: Gradient-based learning applied to document recognition. Proc. IEEE 86(11), 2278–2324 (1998)CrossRefGoogle Scholar
  19. 19.
    Lin, M., Chen, Q., Yan, S.: Network in network. In: ICLR (2014)Google Scholar
  20. 20.
    Qi, C.R., Su, H., Niessner, M., Dai, A., Yan, M., Guibas, L.J.: Volumetric and multi-view CNNs for object classification on 3D data. In: CVPR (2016)Google Scholar
  21. 21.
    Su, H., Maji, S., Kalogerakis, E., Learned-Miller, E.: Multi-view convolutional neural networks for 3D shape recognition. In: ICCV (2015)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.School of Computer Science and Center for Intelligent MachinesMcGill UniversityMontrealCanada

Personalised recommendations