Skip to main content
SpringerLink
Log in

Weak-perspective structure from motion by fast alternation

  • Original Article
  • Published:
The Visual Computer Aims and scope Submit manuscript

Abstract

This paper addresses the problem of moving object reconstruction. Several methods have been published in the past 20 years including stereo reconstruction as well as multi-view factorization methods. In general, reconstruction algorithms compute the 3D structure of the object and the camera parameters in a non-optimal way, and then a nonlinear and numerical optimization algorithm refines the reconstructed camera parameters and 3D coordinates. In this paper, we propose an adjustment method which is the improved version of the well-known Tomasi–Kanade factorization method. The novelty, which yields the high speed of the algorithm, is that the core of the proposed method is an alternation and we give optimal solutions to the subproblems in the alternation. The improved method is discussed here and it is compared to the widely used bundle adjustment algorithm.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Arun, K.S., Huang, T.S., Blostein, S.D.: Least-squares fitting of two 3-D point sets. IEEE Trans. Pattern Anal. Mach. Intell. 9(5), 698–700 (1987)

    Article  Google Scholar 

  2. Delaunay, B.: Sur la sphere vide. Izv. Akad. Nauk SSSR, Otd. Mat. Estestv. Nauk 7, 793–800 (1934)

    Google Scholar 

  3. Berthilsson, R., Heyden, A., Sparr, G.: Recursive structure and motion from image sequences using shape and depth spaces. In: CVPR’97: Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition, p. 444 (1997)

    Chapter  Google Scholar 

  4. Triggs, B., McLauchlan, P., Hartley, R., Fitzgibbon, A.: Bundle adjustment—a modern synthesis. In: Triggs, W., Zisserman, A., Szeliski, R. (eds.) Vision Algorithms: Theory and Practice. LNCS, pp. 298–375. Springer, Berlin (2000)

    Chapter  Google Scholar 

  5. Björck, Å: Numerical Methods for Least Squares Problems. SIAM, Philadelphia (1996)

    MATH  Google Scholar 

  6. Bregler, C., Hertzmann, A., Biermann, H.: Recovering non-rigid 3d shape from image streams. In: CVPR 2000: Proceedings of the 2000 Conference on Computer Vision and Pattern Recognition, pp. 690–696 (2000)

    Google Scholar 

  7. Buchanan, A.M.: Investigation into matrix factorization when elements are unknown. Technical report, University of Oxford (2004). http://www.robots.ox.ac.uk/~amb

  8. Buchanan, A.M., Fitzgibbon, A.W.: Damped newton algorithms for matrix factorization with missing data. In: CVPR05, vol. 2, pp. 316–322 (2005)

    Google Scholar 

  9. Hajder, L.: An iterative improvement of the Tomasi Kanade factorization. In: Third Hungarian Conference on Computer Graphics and Geometry, pp. 30–36 (2005)

    Google Scholar 

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

    MATH  Google Scholar 

  11. Horn, B.K.P., Hilden, H.M., Negahdaripourt, S.: Closed-form solution of absolute orientation using orthonormal matrices. J. Opt. Soc. Am. 5(7), 1127–1135 (1988)

    Article  Google Scholar 

  12. Hajder, L., Chetverikov, D.: Weak-perspective structure from motion for strongly contaminated data. Pattern Recognit. Lett. 27, 1581–1589 (2006)

    Article  Google Scholar 

  13. Mahamud, S., Hebert, M.: Iterative projective reconstruction from multiple views. In: CVPR, pp. 2430–2437 (2000)

    Google Scholar 

  14. Martinec, D., Pajdla, T.: 3d reconstruction by fitting low-rank matrices with missing data. In: CVPR’05: Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’05), vol. 1, pp. 198–205, Washington, DC, USA. IEEE Comput. Soc., Los Alamitos (2005)

    Google Scholar 

  15. Oliensis, J., Hartley, R.: Iterative extensions of the sturm/triggs algorithm: convergence and nonconvergence. IEEE Trans. Pattern Anal. Mach. Intell. 29(12), 2217–2233 (2007)

    Article  Google Scholar 

  16. Poelman, C.J., Kanade, T.: A paraperspective factorization method for shape and motion recovery. IEEE Trans. Pattern Anal. Mach. Intell. 19(3), 206–218 (1997)

    Article  Google Scholar 

  17. Rousseeuw, P.J., Leroy, A.M.: Robust Regression and Outlier Detection. Wiley, New York (1987)

    Book  MATH  Google Scholar 

  18. Sturm, P., Triggs, B.: A factorization based algorithm for multi-image projective structure and motion. In: ECCV, vol. 2, pp. 709–720 (1996)

    Google Scholar 

  19. Tomasi, C., Kanade, T.: Shape and motion from image streams under orthography: a factorization approach. Int. J. Comput. Vis. 9, 137–154 (1992)

    Article  Google Scholar 

  20. Torresani, L., Hertzmann, A., Bregler, C.: Nonrigid structure-from-motion: estimating shape and motion with hierarchical priors. IEEE Trans. Pattern Anal. Mach. Intell. 30(5), 878–892 (2008)

    Article  Google Scholar 

  21. Torresani, L., Yang, D.B., Alexander, E.J., Bregler, C.: Tracking and modeling non-rigid objects with rank constraints. In: CVPR 2001: Proceedings of the 2001 Conference on Computer Vision and Pattern Recognition, pp. 493–500 (2001)

    Google Scholar 

  22. Trajković, M., Hedley, M.: Robust recursive structure and motion recovery under affine projection. In: Proc. British Machine Vision Conference (1997)

    Google Scholar 

  23. Vidal, R., Hartley, R.: Motion segmentation with missing data using PowerFactorization and GPCA. In: Proc. Computer Vision and Pattern Recognition, pp. 310–316 (2004)

    Google Scholar 

  24. Wang, G., Wu, Q.M.J., Sun, G.: Quasi-perspective projection with applications to 3d factorization from uncalibrated image sequences. In: CVPR (2008)

    Google Scholar 

  25. Weinshall, D., Tomasi, C.: Linear and incremental acquisition of invariant shape models from image sequences. IEEE Trans. Pattern Anal. Mach. Intell. 17(5), 512–517 (1995)

    Article  Google Scholar 

  26. Xiao, J., Chai, J., Kanade, T.: A closed-form solution to non-rigid shape and motion recovery. Int. J. Comput. Vis. 67(2), 233–246 (2006)

    Article  Google Scholar 

  27. Zinßer, T., Schmidt, J., Niemann, H.: Point set registration with integrated scale estimation. In: Sadykhov, R., Ablameiko, S., Doudkin, A., Podenok, L. (eds.) Proceedings of the Eighth International Conference on Pattern Recognition and Image Processing (PRIP), Minsk, Republic of Belarus, pp. 116–119 (2005)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer and Automation Research Institute, Hungarian Academy of Sciences, Kende u. 13–17, 1111, Budapest, Hungary

    Levente Hajder & Csaba Kazó

  2. Department of Automation and Applied Informatics, Budapest University of Technology and Economics, Goldmann Gy. tér 3, 1111, Budapest, Hungary

    Ákos Pernek & Csaba Kazó

Authors
  1. Levente Hajder
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ákos Pernek
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Csaba Kazó
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Levente Hajder.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hajder, L., Pernek, Á. & Kazó, C. Weak-perspective structure from motion by fast alternation. Vis Comput 27, 387–399 (2011). https://doi.org/10.1007/s00371-011-0553-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00371-011-0553-3

Keywords

Search

Navigation