Skip to main content
Log in

A Variational Framework for Structure from Motion in Omnidirectional Image Sequences

  • Published:
Journal of Mathematical Imaging and Vision Aims and scope Submit manuscript

Abstract

We address the problem of depth and ego-motion estimation from omnidirectional images. We propose a correspondence-free structure-from-motion problem for sequences of images mapped on the 2-sphere. A novel graph-based variational framework is first proposed for depth estimation between pairs of images. The estimation is cast as a TV-L1 optimization problem that is solved by a fast graph-based algorithm. The ego-motion is then estimated directly from the depth information without explicit computation of the optical flow. Both problems are finally addressed together in an iterative algorithm that alternates between depth and ego-motion estimation for fast computation of 3D information from motion in image sequences. Experimental results demonstrate the effective performance of the proposed algorithm for 3D reconstruction from synthetic and natural omnidirectional images.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Agrawal, A., Chellappa, R.: Robust ego-motion estimation and 3d model refinement using depth based parallax model. In: Proceedings of IEEE International Conference on Image Processing, vol. 4, pp. 2483–2486 (2004). doi:10.1109/ICIP.2004.1421606

    Google Scholar 

  2. Aujol, J., Gilboa, G., Chan, T., Osher, S.: Structure-texture image decomposition—modeling, algorithms, and parameter selection. Int. J. Comput. Vis. 67(1), 111–136 (2006). doi:10.1007/s11263-006-4331-z

    Article  Google Scholar 

  3. Bagnato, L., Frossard, P., Vandergheynst, P.: Optical flow and depth from motion for omnidirectional images using a tv-l1 variational framework on graphs. In: Proceedings of IEEE International Conference on Image Processing, pp. 1469–1472 (2009). doi:10.1109/ICIP.2009.5414552

    Google Scholar 

  4. Baker, S., Nayar, S.K.: A theory of single-viewpoint catadioptric image formation. Int. J. Comput. Vis. 35, 175–196 (1999). doi:10.1023/A:1008128724364

    Article  Google Scholar 

  5. Beauchemin, S., Barron, J.: The computation of optical flow. ACM Comput. Surv. 27(3), 433–466 (1995)

    Article  Google Scholar 

  6. Bruss, A., Horn, B.: Passive navigation. Comput. Vis. Graph. 21(1), 3–20 (1983)

    Article  Google Scholar 

  7. Chambolle, A.: An algorithm for total variation minimization and applications. J. Math. Imaging Vis. 20(1–2), 89–97 (2004)

    MathSciNet  Google Scholar 

  8. Daniilidis, K., Makadia, A., Bulow, T.: Image processing in catadioptric planes: spatiotemporal derivatives and optical flow computation. In: Proceedings of the Third Workshop on Omnidirectional Vision, pp. 3–10 (2002)

    Chapter  Google Scholar 

  9. Faugeras, O., Luong, Q.T., Papadopoulo, T.: The Geometry of Multiple Images. MIT Press, New York (2001)

    MATH  Google Scholar 

  10. Gilboa, G., Osher, S.: Nonlocal operators with applications to image processing. Multiscale Model. Simul. 7(3), 1005–1028 (2008). doi:10.1137/070698592

    Article  MathSciNet  MATH  Google Scholar 

  11. Gluckman, J., Nayar, S.: Ego-motion and omnidirectional cameras. In: Proceedings of Sixth International Conference on Computer Vision, pp. 999–1005 (1998)

    Google Scholar 

  12. Hanna, K.: Direct multi-resolution estimation of ego-motion and structure from motion. In: Proceedings of the IEEE Workshop on Visual Motion, pp. 156–162 (1991)

    Chapter  Google Scholar 

  13. Heeger, D., Jepson, A.: Subspace methods for recovering rigid motion. 1. algorithm and implementation. Int. J. Comput. Vis. 7(2), 95–117 (1992)

    Article  Google Scholar 

  14. Horn, B., Schunck, B.: Determining optical flow. Artif. Intell. 17(1–3), 185–203 (1981)

    Article  Google Scholar 

  15. Horn, B., Weldon, E.: Direct methods for recovering motion. Int. J. Comput. Vis. 2(1), 51–76 (1988)

    Article  Google Scholar 

  16. Jepson, A., Heeger, D.: A fast subspace algorithm for recovering rigid motion. In: Proceedings of the IEEE Workshop on Visual Motion, pp. 124–131 (1991). doi:10.1109/WVM.1991.212779

    Chapter  Google Scholar 

  17. Lucas, B., Kanade, T.: An iterative image registration technique with an application to stereo vision. Int. Joint Conf. Artif. Intell. 81, 674–679 (1981)

    Google Scholar 

  18. Makadia, A., Geyer, C., Daniilidis, K.: Correspondence-free structure from motion. Int. J. Comput. Vis. 75(3) (2007)

  19. Nikolova, M.: A variational approach to remove outliers and impulse noise. J. Math. Imaging Vis. 20, 99–120 (2004)

    Article  MathSciNet  Google Scholar 

  20. Peyré, G., Bougleux, S., Cohen, L.: Non-local regularization of inverse problems. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) Computer Vision, ECCV 2008. Lecture Notes in Computer Science, vol. 5304, pp. 57–68. Springer, Berlin/Heidelberg (2008)

    Google Scholar 

  21. Rudin, L., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal. Physica D 60, 259–268 (1992)

    Article  MATH  Google Scholar 

  22. Scharstein, D., Szeliski, R.: A taxonomy and evaluation of dense two-frame stereo correspondence algorithms. Int. J. Comput. Vis. 47, 7–42 (2002)

    Article  MATH  Google Scholar 

  23. Sinclair, D., Blake, A., Murray, D.: Robust estimation of egomotion from normal flow. Int. J. Comput. Vis. 13(1), 57–69 (1994)

    Article  Google Scholar 

  24. Tian, T., Tomasi, C., Heeger, D.: Comparison of approaches to egomotion computation. In: Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, pp. 315–320 (1996)

    Google Scholar 

  25. Tosic, I., Bogdanova, I., Frossard, P., Vandergheynst, P.: Multiresolution motion estimation for omnidirectional images. In: Proceedings of EUSIPCO (2005)

    Google Scholar 

  26. Zach, C., Pock, T., Bischof, H.: A duality based approach for realtime tv-l1 optical flow. In: Hamprecht, F., Schnörr, C., Jähne, B. (eds.) Pattern Recognition. Lecture Notes in Computer Science, vol. 4713, pp. 214–223. Springer, Berlin/Heidelberg (2007)

    Chapter  Google Scholar 

  27. Zhou, D., Scholkopf, B.: A regularization framework for learning from graph data. In: ICML Workshop on Statistical Relational Learning, pp. 132–137 (2004)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Luigi Bagnato.

Additional information

This work has been partially supported by the Swiss National Science Foundation under Grant 200021-125651.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bagnato, L., Frossard, P. & Vandergheynst, P. A Variational Framework for Structure from Motion in Omnidirectional Image Sequences. J Math Imaging Vis 41, 182–193 (2011). https://doi.org/10.1007/s10851-011-0267-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10851-011-0267-1

Keywords

Navigation