Advertisement

Iterative Extensions of the Sturm/Triggs Algorithm: Convergence and Nonconvergence

  • John Oliensis
  • Richard Hartley
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3954)

Abstract

We show that SIESTA, the simplest iterative extension of the Sturm/Triggs algorithm, descends an error function. However, we prove that SIESTA does not converge to usable results. The iterative extension of Mahamud et al. has similar problems, and experiments with “balanced” iterations show that they can fail to converge. We present CIESTA, an algorithm which avoids these problems. It is identical to SIESTA except for one extra, simple stage of computation. We prove that CIESTA descends an error and approaches fixed points. Under weak assumptions, it converges. The CIESTA error can be minimized using a standard descent method such as Gauss–Newton, combining quadratic convergence with the advantage of minimizing in the projective depths.

Keywords

Stationary Point Quadratic Convergence Bundle Adjustment Projective Depth Real Image Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Berthilsson, R., Heyden, A., Sparr, G.: Recursive Structure and Motion from Image Sequences Using Shape and Depth Spaces. In: CVPR, pp. 444–449 (1997)Google Scholar
  2. 2.
    Buchanan, A., Fitzgibbon, A.: Damped Newton Algorithms for Matrix Factorization with Missing Data. In: CVPR (2005)Google Scholar
  3. 3.
    Dutta, R., Manmatha, R., Williams, L.R., Riseman, E.M.: A data set for quantitative motion analysis. In: CVPR, pp. 159–164 (1989)Google Scholar
  4. 4.
    Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision, Cambridge (2000)Google Scholar
  5. 5.
    Heyden, A., Berthilsson, R., Sparr, G.: An iterative factorization method for projective structure and motion from image sequences. IVC 17, 981–991 (1999)CrossRefGoogle Scholar
  6. 6.
    Kumar, R., Hanson, A.R.: Sensitivity of the Pose Refinement Problem to Accurate Estimation of Camera Parameters. In: ICCV, pp. 365–369 (1990)Google Scholar
  7. 7.
    Mahamud, S., Hebert, M., Omori, Y., Ponce, J.: Provably-Convergent Iterative Methods for Projective Structure from Motion. In: CVPR, vol. I, pp. 1018–1025 (2001)Google Scholar
  8. 8.
    Mahamud, S., Hebert, M.: Iterative Projective Reconstruction from Multiple Views. In: CVPR, vol. II, pp. 430–437 (2000)Google Scholar
  9. 9.
    Sturm, P., Triggs, B.: A factorization based algorithm for multi–image projective structure and motion. In: Buxton, B.F., Cipolla, R. (eds.) ECCV 1996. LNCS, vol. 1065, pp. 709–720. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  10. 10.
    Tomasi, C., Kanade, T.: Shape and motion from image streams under orthography: A factorization method. IJCV 9, 137–154 (1992)CrossRefGoogle Scholar
  11. 11.
    Triggs, B.: Factorization methods for projective structure and motion. In: CVPR, pp. 845–851 (1996)Google Scholar
  12. 12.
    Zhang, Z.: A Flexible New Technique for Camera Calibration. PAMI 22(11), 1330–1334 (2000); Microsoft Technical Report MSR-TR-98-71 (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • John Oliensis
    • 1
  • Richard Hartley
    • 2
  1. 1.Department of Computer ScienceStevens Institute of TechnologyHobokenUSA
  2. 2.Australian National University and National ICTAustralia

Personalised recommendations