Skip to main content

Non-rigid Self-calibration of a Projective Camera

  • Conference paper
Computer Vision – ACCV 2012 (ACCV 2012)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 7727))

Included in the following conference series:

  • 4745 Accesses

Abstract

Rigid structure-from-motion (SfM) usually consists of two steps: First, a projective reconstruction is computed which is then upgraded to Euclidean structure and motion in a subsequent step. Reliable algorithms exist for both problems. In the case of non-rigid SfM, on the other hand, especially the Euclidean upgrading has turned out to be difficult. A few algorithms have been proposed for upgrading an affine reconstruction, and are able to obtain successful 3D-reconstructions. For upgrading a non-rigid projective reconstruction, however, either simple sequences are used, or no 3D-reconstructions are shown at all.

In this article, an algorithm is proposed for estimating the self-calibration of a projectively reconstructed non-rigid scene. In contrast to other algorithms, neither prior knowledge of the non-rigid deformations is required, nor a subsequent step to align different motion bases. An evaluation with synthetic data reveals that the proposed algorithm is robust to noise and it is able to accurately estimate the 3D-reconstructions and the intrinsic calibration. Finally, reconstructions of a challenging real image with strong non-rigid deformation are presented.

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. Hartley, R.I., Zisserman, A.: Multiple View Geometry in Computer Vision, 2nd edn. Cambridge University Press (2004) ISBN: 0521540518

    Google Scholar 

  2. Bregler, C., Hertzmann, A., Biermann, H.: Recovering non-rigid 3d shape from image streams. In: IEEE Computer Vision and Pattern Recognition (CVPR), Hilton Head, SC, USA, pp. 690–696 (2000)

    Google Scholar 

  3. Triggs, B.: Autocalibration and the absolute quadric. In: Conf. Comp. Vis. and Pat. Recog. (CVPR) (1997)

    Google Scholar 

  4. Pollefeys, M., Koch, R., van Gool, L.: Self-calibration and metric reconstruction inspite of varying and unknown intrinsic camera parameters. Int. J. Comp. Vis. (IJCV) 32, 7–25 (1999)

    Article  Google Scholar 

  5. Seo, Y., Heyden, A.: Auto-calibration by linear iteration using the DAC equation. Img. Vis. Comp. 22, 919–926 (2004)

    Article  Google Scholar 

  6. Chandraker, M., Agarwal, S., Kahl, F., Nistér, D., Kriegman, D.: Autocalibration via rank-constrained estimation of the absolute quadric. In: Conf. Comp. Vis. and Pat. Recog. (CVPR) (2007)

    Google Scholar 

  7. Xiao, J., Chai, J., Kanade, T.: A closed-form solution to non-rigid shape and motion recovery. International Journal of Computer Vision 67, 233–246 (2006)

    Article  Google Scholar 

  8. Brand, M.: A direct method for 3D factorization of nonrigid motion observed in 2d. In: IEEE Computer Vision and Pattern Recognition (CVPR), Washington, DC, USA, pp. 122–128 (2005)

    Google Scholar 

  9. Olsen, S., Bartoli, A.: Implicit non-rigid structure-from-motion with priors. Journal of Mathematical Imaging and Vision 31, 233–244 (2008)

    Article  MathSciNet  Google Scholar 

  10. Torresani, L., Hertzmann, A., Bregler, C.: Nonrigid structure-from-motion: Estimating shape and motion with hierarchical priors. IEEE Pattern Analysis and Machine Intelligence (PAMI) 30, 878–892 (2008)

    Article  Google Scholar 

  11. Paladini, M., Del Bue, A., Stosic, M., Dodig, M., Xavier, J., Agapito, L.: Factorization for non-rigid and articulated structure using metric projections. In: IEEE Computer Vision and Pattern Recognition (CVPR), Miami, FL, USA, pp. 2898–2905 (2009)

    Google Scholar 

  12. Xiao, J., Kanade, T.: Uncalibrated perspective reconstruction of deformable structures. In: Proceedings of the 10th International Conference on Computer Vision (ICCV), vol. 2, pp. 1075–1082 (2005)

    Google Scholar 

  13. Hartley, R.I., Vidal, R.: Perspective Nonrigid Shape and Motion Recovery. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008, Part I. LNCS, vol. 5302, pp. 276–289. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  14. Brand, M.: Morphable 3D models from video. In: IEEE Computer Vision and Pattern Recognition (CVPR), pp. 456–463 (2001)

    Google Scholar 

  15. Heyden, A., Berthilsson, R., Sparr, G.: An iterative factorization method for projective structure and motion from image sequences. International Journal on Computer Vision 17, 981–991 (1999)

    Article  Google Scholar 

  16. Mahamud, S., Hebert, M.: Iterative projective reconstruction from multiple views. In: The Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, vol. 2, pp. 430–437 (2000)

    Google Scholar 

  17. Akhter, I., Sheikh, Y., Khan, S.: In defense of orthonormality constraints for nonrigid structure from motion. In: IEEE Computer Vision and Pattern Recognition (CVPR), Miami, FL, USA, pp. 1534–1541 (2009)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ackermann, H., Rosenhahn, B. (2013). Non-rigid Self-calibration of a Projective Camera. In: Lee, K.M., Matsushita, Y., Rehg, J.M., Hu, Z. (eds) Computer Vision – ACCV 2012. ACCV 2012. Lecture Notes in Computer Science, vol 7727. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37447-0_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-37447-0_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-37446-3

  • Online ISBN: 978-3-642-37447-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics