Advertisement

Structure and motion from points, lines and conics with affine cameras

  • Fredrik Kahl
  • Anders Heyden
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1406)

Abstract

In this paper we present an integrated approach that solves the structure and motion problem for affine cameras. Given images of corresponding points, lines and conics in any number of views, a reconstruction of the scene structure and the camera motion is calculated, up to an affine transformation. Starting with three views, two novel concepts are introduced. The first one is a quasi-tensor consisting of 20 components and the second one is another quasitensor consisting of 12 components. These tensors describe the viewing geometry for three views taken by an affine camera. It is shown how correspondences of points, lines and conics can be used to constrain the tensor components. A set of affine camera matrices compatible with the quasi-tensors can easily be calculated from the tensor components. The resulting camera matrices serve as an initial guess in a factorisation method, using points, lines and conics concurrently, generalizing the well-known factorisation method by Tomasi-Kanade. Finally, examples are given that illustrate the developed methods on both simulated and real data.

Keywords

Root Mean Square Tensor Component Camera Motion Point Correspondence Bundle Adjustment 
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.
    R. Berthilsson and K. åström. Reconstruction of 3d-curves from 2d-images using affine shape methods for curves. In Proc. Conf. Computer Vision and Pattern Recognition, 1997.Google Scholar
  2. 2.
    O. Faugeras and B. Mourrain. On the geometry and algebra of the point and line correspondences between n images. In Proc. 5th Int. Conf. on Computer Vision, MIT, Boston, MA, pages 951–956, 1995.Google Scholar
  3. 3.
    B. Gelbaum. Linear Algebra: Basic, Practice and Theory. North-Holand, 1989.Google Scholar
  4. 4.
    R. I. Hartley. A linear method for reconstruction from lines and points. In Proc. 5th Int. Conf. on Computer Vision, MIT, Boston, MA, pages 882–887, 1995.Google Scholar
  5. 5.
    R. I. Hartley. Lines and points in three views and the trifocal tensor. Int. Journal of Computer Vision, 22(2):125–140, 1997.CrossRefGoogle Scholar
  6. 6.
    A. Heyden. Projective structure and motion from image sequences using subspace methods. In Proc. 10th Scandinavian Conf. on Image Analysis, Lappeenranta, Finland, pages 963–968, 1997.Google Scholar
  7. 7.
    F. Kahl and K. åström. Motion estimation in image sequences using the deformation of apparent contours. In Proc. 6th Int. Conf. on Computer Vision, Mumbai, India, 1998.Google Scholar
  8. 8.
    F. Kahl and A. Heyden. Using conic correspondences in two images to estimate the epipolar geometry. In Proc. 6th Int. Conf. on Computer Vision, Mumbai, India, 1998.Google Scholar
  9. 9.
    J. L. Mundy and A. Zisserman, editors. Geometric invariance in Computer Vision. MIT Press, Cambridge Ma, USA, 1992.Google Scholar
  10. 10.
    T. Papadopoulo and O. Faugeras. Computing structure and motion of general 3d curves from monocular sequences of perspective images. In B Buxton and R. Cipolla, editors, Proc. 4th, European Conf. on Computer Vision, Cambridge, UK, pages 696–708. Springer-Verlag, 1996.Google Scholar
  11. 11.
    L. Quan. Conic reconstruction and correspondence from two views. IEEE Trans. Pattern Analysis and Machine Intelligence, 18(2):151–160, February 1996.CrossRefGoogle Scholar
  12. 12.
    L. Quan and T. Kanade. Affine structure from line correspondences with uncalibrated affine cameras. IEEE Trans. Pattern Analysis and Machine Intelligence, 19(8), August 1997.Google Scholar
  13. 13.
    J. G. Semple and G. T. Kneebone. Algebraic Projective Geometry. Clarendon Press, Oxford, 1952.Google Scholar
  14. 14.
    L. S. Shapiro. Affine Analysis of Image Sequences. Cambridge University Press, 1995.Google Scholar
  15. 15.
    G. Sparr. Simultaneous reconstruction of scene structure and camera locations from uncalibrated image sequences. In Proc. Int. Conf. on Pattern Recognition, Vienna, Austria, 1996.Google Scholar
  16. 16.
    P. Sturm and B. Triggs. A factorization based algorithm for multi-image projective structure and motion. In Proc. 4th European Conf. on Computer Vision, Cambridge, UK, pages 709–720, 1996.Google Scholar
  17. 17.
    C. Tomasi and T. Kanade. Shape and motion from image streams under orthography: a factorization method. Int. Journal of Computer Vision, 9(2):137–154, 1992.CrossRefGoogle Scholar
  18. 18.
    P. Torr. Motion Segmentation and Outlier Detection. PhD thesis, Department of Engineering Science, University of Oxford, 1995.Google Scholar
  19. 19.
    B. Triggs. Matching constraints and the joint image. In Proc. 5th Int. Conf. on Computer Vision, MIT, Boston, MA, pages 338–343, 1995.Google Scholar
  20. 20.
    J. Weng, T.S. Huang, and N. Ahuja. Motion and structure from line correspondances: Closed-form solution, uniqueness, and optimization. IEEE Trans. Pattern Analysis and Machine Intelligence, 14(3), 1992.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Fredrik Kahl
    • 1
  • Anders Heyden
    • 1
  1. 1.Dept of MathematicsLund UniversityLundSweden

Personalised recommendations