Advertisement

International Journal of Computer Vision

, Volume 23, Issue 3, pp 235–259 | Cite as

Sequential Updating of Projective and Affine Structure from Motion

  • P.A. Beardsley
  • A. Zisserman
  • D.W. Murray
Article

Abstract

A structure from motion algorithm is described which recovers structure and camera position, modulo a projective ambiguity. Camera calibration is not required, and camera parameters such as focal length can be altered freely during motion. The structure is updated sequentially over an image sequence, in contrast to schemes which employ a batch process. A specialisation of the algorithm to recover structure and camera position modulo an affine transformation is described, together with a method to periodically update the affine coordinate frame to prevent drift over time. We describe the constraint used to obtain this specialisation.

Structure is recovered from image corners detected and matched automatically and reliably in real image sequences. Results are shown for reference objects and indoor environments, and accuracy of recovered structure is fully evaluated and compared for a number of reconstruction schemes. A specific application of the work is demonstrated—affine structure is used to compute free space maps enabling navigation through unstructured environments and avoidance of obstacles. The path planning involves only affine constructions.

Keywords

Image Sequence Path Planning Indoor Environment Coordinate Frame Real Image 
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. Armstrong, M., Zisserman, A., and Beardsley, P. A. 1994. Euclidean reconstruction from uncalibrated images. Proc. British Machine Vision Conference.Google Scholar
  2. Ayache, N. 1991. Artificial Vision for Mobile Robots. MIT Press: Cambridge.Google Scholar
  3. Bar-Shalom, Y. and Fortmann, T. E. 1988. Tracking and Data Association. Academic Press.Google Scholar
  4. Beardsley, P. A., Zisserman, A. P., and Murray, D. W. 1994. Navigation using affine structure and motion. In Proc. 3rd European Conference on Computer Vision, Springer-Verlag, pp. 85-96.Google Scholar
  5. Blake, A., Brady, M., Cipolla, R., Xie, Z., and Zisserman, A. P. 1991. Visual navigation around curved objects. In Proc. IEEE Int. Conf. Robotics and Automation, pp. 2490-2495.Google Scholar
  6. Blake, A., Zisserman, A., and Cipolla, R. 1992. Visual exploration of free-space. In Active Vision, Blake and Yuille (Eds.), MIT Press.Google Scholar
  7. Deriche, R., Zhang, Z., Luong, Q. T., and Faugeras, O. 1994. Robust recovery of the epipolar geometry for an uncalibrated stereo rig. In Proc. 3rd European Conference on Computer Vision, Springer-Verlag, pp. 567-576.Google Scholar
  8. Faugeras, O. D. 1992. What can be seen in three dimensions with an uncalibrated stereo rig? In Proc. 2nd European Conference on Computer Vision, Springer-Verlag, pp. 563-578.Google Scholar
  9. Faugeras, O. D., Luong, Q. T., and Maybank, S. J. 1992. Camera self-calibration: Theory and experiments. In Proc. 2nd European Conference on Computer Vision, Springer-Verlag, pp. 321-334.Google Scholar
  10. Faugeras, O. D. 1993. Three-Dimensional Computer Vision: A Geometric Viewpoint. MIT Press.Google Scholar
  11. Harris, C. G. 1987. Determination of ego-motion from matched points. In Third Alvey Vision Conference, pp. 189-192.Google Scholar
  12. Harris, C. G. and Pike, J. M. 1987. 3D positional integration from image sequences. In Third Alvey Vision Conference, pp. 233- 236.Google Scholar
  13. Harris, C. G. and Stephens, M. 1988. A combined corner and edge detector. In Fourth Alvey Vision Conference, pp. 147-151.Google Scholar
  14. Hartley, R. I. 1994. Projective reconstruction and invariants from multiple images. PAMI 16:1036-1041.Google Scholar
  15. Hartley, R. I. 1994. Euclidean reconstruction from uncalibrated views. In Applications of Invariance in Computer Vision, J. L. Mundy, A. Zisserman, and D. Forsyth (Eds.), Springer-Verlag, pp. 237-256.Google Scholar
  16. Hartley, R. I. 1995. In defence of the 8-point algorithm. In E. Grimson (Ed.), Proc. 5th International Conference on Computer Vision, Cambridge, MA.Google Scholar
  17. Hartley, R. I., Gupta, R., and Chang, T. 1992. Stereo from uncalibrated cameras. Proc. Conference Computer Vision and Pattern Recognition.Google Scholar
  18. Hartley, R. I. and Sturm, P. 1995. Triangulation. In Proc. Conf. Computer Analysis of Images and Patterns, Prague, Czech Republic.Google Scholar
  19. Hollinghurst, N. and Cipolla, R. 1993. Uncalibrated stereo hand-eye coordination. In Proc. British Machine Vision Conference 93, pp. 389-398.Google Scholar
  20. Koenderink, J. J. and VanDoorn, A. J. 1991. Affine structure from motion. J. Opt. Soc. Am. A, 8(2):377-385.Google Scholar
  21. Langer, D., Rosenblatt, J. K., and Hebert, M. 1994. An integrated system for autonomous off-road navigation. In Proc. IEEE Conf. Robotics and Automation, IEEE, pp. 414-419.Google Scholar
  22. Latombe, J. C. 1991. Robot Motion Planning. Kluwer Academic Publishers.Google Scholar
  23. Luong, Q. T., Deriche, R., Faugeras, O., and Papadopoulo, T. 1993. On determining the fundamental matrix. Technical report 1894, INRIA, Sophia-Antipolis, France.Google Scholar
  24. Luong, Q. T. and Vieville, T. 1994. Canonic representations for the geometries of multiple projective views. In Proc. 3rd European Conference on Computer Vision, Springer-Verlag, pp. 589-597.Google Scholar
  25. Maybank, S. J. 1993. Theory of Reconstruction from Image Motion. Springer-Verlag, Berlin.Google Scholar
  26. McLauchlan, P. F., Reid, I. D., and Murray, D. W. 1994. Recursive affine structure and motion from image sequences. In Proc. 3rd European Conference on Computer Vision, Springer-Verlag, pp. 217-224.Google Scholar
  27. Mohr, R., Veillon, R., and Quan, L. 1993. Relative 3D reconstruction using multiple uncalibrated images. Proc. Conference Computer Vision and Pattern Recognition, pp. 543-548.Google Scholar
  28. Mohr, R., Boufama, B., and Brand, P. 1994. Accurate projective reconstruction. In Applications of Invariance in Computer Vision, J. L. Mundy, A. Zisserman, and D. Forsyth (Eds.), Springer-Verlag, pp. 257-276.Google Scholar
  29. Moons, T., van Gool, T., van Diest, M., and Oosterlinck, A. 1994. Affine structure from perspective image pairs obtained by a translating camera. In Applications of Invariance in Computer Vision, J. L. Mundy, A. Zisserman, and D. Forsyth (Eds.), Springer-Verlag, pp. 297-316Google Scholar
  30. Mundy, J. L. and Zisserman, A. P. 1992. Geometric Invariance in Computer Vision. MIT Press.Google Scholar
  31. Mundy, J. L. and Zisserman, A. 1994. Repeated structures: Image correspondence constraints and ambiguity of 3D reconstruction. In Applications of Invariance in Computer Vision, J. L. Mundy, A. Zisserman, and D. Forsyth (Eds.), Springer-Verlag, pp. 89- 106.Google Scholar
  32. Press, W., Flannery, B., Teukolsky, S., and Vetterling, W. 1988. Numerical Recipes in C, Cambridge University Press.Google Scholar
  33. Reid, I. D. and Murray, D. W. 1993. Tracking foveated corner clusters using affine structure. In Proc. 4th International Conference on Computer Vision, IEEE Computer Society Press: Los Alamitos, CA, pp. 76-83.Google Scholar
  34. Rothwell, C. A., Csurka, G., and Faugeras, O. 1995. A comparison of projective reconstruction methods for pairs of views. In Proc. 5th International Conference on Computer Vision, E. Grimson (Ed.), Cambridge, MA.Google Scholar
  35. Semple, J. G. and Kneebone, G. T. 1952. Algebraic Projective Geometry. Oxford University Press.Google Scholar
  36. Szeliski, R. and Kang, S. B. 1993. Recovering 3D shape and motion from image streams using non-linear least squares. DEC technical report 93/3.Google Scholar
  37. Torr, P. H. S. 1995. Motion segmentation and outlier detection. Ph. D. thesis, Dept. of Engineering Science, University of Oxford.Google Scholar
  38. Torr, P. H. S., Beardsley, P. A., and Murray, D. W. 1994. Robust vision. In Proc. British Machine Vision Conference 94.Google Scholar
  39. Zhang, Z. and Faugeras, O. 1992. 3D Dynamic Scene Analysis. Springer-Verlag, 1992.Google Scholar
  40. Zhang, Z., Deriche, R., Faugeras, O., and Luong, Q. 1995. A robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry. Artificial Intelligence, 78:87-119.Google Scholar

Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • P.A. Beardsley
    • 1
  • A. Zisserman
    • 1
  • D.W. Murray
    • 1
  1. 1.Department of Engineering ScienceUniversity of OxfordOxfordUK

Personalised recommendations