Skip to main content

3D Shape Restoration via Matrix Recovery

  • Conference paper
Computer Vision – ACCV 2010 Workshops (ACCV 2010)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 6469))

Included in the following conference series:

Abstract

Cultural relics are often damaged and incomplete due to various reasons. For the purpose of helping archaeological studies, we present a novel method for simultaneously restoring the original shapes of a group of similar objects. Based on the assumption that similar shapes are approximately linearly correlated, we use a matrix recovery technique to achieve the restoration. In order to represent input shapes in a matrix form, vectorization of each aligned sample is carried out by stacking coordinates of dense corresponding points that are generated by a surface matching scheme using non-rigid deformation. An experiment using 3D scans of facial sculptures from Bayon is conducted, and the result verifies the feasibility and effectiveness of our method.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Kamakura, M., Oishi, T., Takamatsu, J., Ikeuchi, K.: Classification of Bayon faces using 3D models. In: The 11th International Conference on Virtual Systems and Multimedia, VSMM 2005 (2005)

    Google Scholar 

  2. Chalmovianský, P., Jüttler, B.: Filling holes in point clouds. In: Wilson, M.J., Martin, R.R. (eds.) Mathematics of Surfaces. LNCS, vol. 2768, pp. 196–212. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  3. Ju, T.: Robust repair of polygonal models. ACM Trans. Graph. 23, 888–895 (2004)

    Article  Google Scholar 

  4. Nooruddin, F.S., Turk, G.: Simplification and repair of polygonal models using volumetric techniques. IEEE Transactions on Visualization and Computer Graphics 9, 191–205 (2003)

    Article  Google Scholar 

  5. Sharf, A., Alexa, M., Cohen-Or, D.: Context-based surface completion. In: ACM SIGGRAPH 2004 (2004)

    Google Scholar 

  6. Breckon, T.P., Fisher, R.B.: Three-dimensional surface relief completion via nonparametric techniques. IEEE Transactions on Pattern Analysis and Machine Intelligence 30, 2249–2255 (2008)

    Article  Google Scholar 

  7. Pauly, M., Mitra, N.J., Giesen, J., Gross, M., Guibas, L.J.: Example-based 3D scan completion. In: SGP 2005: Proceedings of the Third Eurographics Symposium on Geometry Processing (2005)

    Google Scholar 

  8. Kraevoy, V., Sheffer, A.: Template-based mesh completion. In: SGP 2005: Proceedings of the Third Eurographics Symposium on Geometry Processing (2005)

    Google Scholar 

  9. Wright, J., Ganesh, A., Rao, S., Peng, Y., Ma, Y.: Robust principal component analysis: Exact recovery of corrupted low-rank matrices via convex optimization. In: Advances in Neural Information Processing Systems 22. MIT Press, Cambridge (2009)

    Google Scholar 

  10. Candès, E.J., Li, X., Ma, Y., Wright, J.: Robust principal component analysis? Submitted to Journal of the ACM (2009)

    Google Scholar 

  11. Peng, Y., Ganesh, A., Wright, J., Xu, W., Ma, Y.: RASL: Robust alignment by sparse and low-rank decomposition for linearly correlated images. In: Proc. IEEE Conf. on Computer Vision and Pattern Recognition, CVPR (2010)

    Google Scholar 

  12. Lin, Z., Chen, M., Wu, L., Ma, Y.: The augmented lagrange multiplier method for exact recovery of corrupted low-rank matrices. Submitted to Mathematical Programming (2009)

    Google Scholar 

  13. Zhang, H., Sheffer, A., Cohen-Or, D., Zhou, Q., van Kaick, O., Tagliasacchi, A.: Deformation-driven shape correspondence. In: Computer Graphics Forum (Special Issue of Symposium on Geometry Processing 2008), vol. 27, pp. 1431–1439 (2008)

    Google Scholar 

  14. Lipman, Y., Funkhouser, T.: Möbius voting for surface correspondence. In: ACM SIGGRAPH 2009 (2009)

    Google Scholar 

  15. Zeng, W., Zeng, Y., Wang, Y., Yin, X., Gu, X., Samaras, D.: 3D non-rigid surface matching and registration based on holomorphic differentials. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008, Part III. LNCS, vol. 5304, pp. 1–14. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  16. Zeng, Y., Gu, X., Samaras, D., Wang, C., Wang, Y., Paragios, N.: Dense non-rigid surface registration using high-order graph matching. In: Proc. IEEE Conf. on Computer Vision and Pattern Recognition, CVPR (2010)

    Google Scholar 

  17. Besl, P.J., McKay, N.D.: A method for registration of 3-D shapes. IEEE Transactions on Pattern Analysis and Machine Intelligence 14, 239–256 (1992)

    Article  Google Scholar 

  18. Li, X., Jia, T., Zhang, H.: Expression-insensitive 3D face recognition using sparse representation. In: Proc. IEEE Conf. on Computer Vision and Pattern Recognition, CVPR (2009)

    Google Scholar 

  19. Alvaro, C., Claudio, E., Antonio, O., Paulo, R.C.: 3D as-rigid-as-possible deformations using MLS. In: The 25th Computer Graphics International Conference, CGI 2007 (2007)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Lu, M., Zheng, B., Takamatsu, J., Nishino, K., Ikeuchi, K. (2011). 3D Shape Restoration via Matrix Recovery. In: Koch, R., Huang, F. (eds) Computer Vision – ACCV 2010 Workshops. ACCV 2010. Lecture Notes in Computer Science, vol 6469. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22819-3_31

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-22819-3_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22818-6

  • Online ISBN: 978-3-642-22819-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics