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Single-View Matching Constraints

  • Klas Nordberg
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4842)

Abstract

A single-view matching constraint is described which represents a necessary condition which 6 points in an image must satisfy if they are the images of 6 known 3D points under an arbitrary projective transformation. Similar to the well-known matching constrains for two or more view, represented by fundamental matrices or trifocal tensors, single-view matching constrains are represented by tensors and when multiplied with the homogeneous image coordinates the result vanishes when the condition is satisfied. More precisely, they are represented by 6-th order tensors on ℝ3 which can be computed in a simple manner from the camera projection matrix and the 6 3D points. The single-view matching constraints can be used for finding correspondences between detected 2D feature points and known 3D points, e.g., on an object, which are observed from arbitrary views. Consequently, this type of constraint can be said to be a representation of 3D shape (in the form of a point set) which is invariant to projective transformations when projected onto a 2D image.

Keywords

Image Point Projective Transformation Order Tensor Trifocal Tensor Homogeneous 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.

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References

  1. 1.
    Faugeras, O., Luong, Q., Maybank, S.: Camera self-calibration: theory and experiments. In: Sandini, G. (ed.) ECCV 1992. LNCS, vol. 588, pp. 321–334. Springer, Heidelberg (1992)Google Scholar
  2. 2.
    Faugeras, O.: What can be seen in three dimensions with an uncalibrated stereo rig? In: Sandini, G. (ed.) ECCV 1992. LNCS, vol. 588, pp. 563–578. Springer, Heidelberg (1992)Google Scholar
  3. 3.
    Hartley, R.: Estimation of relative camera positions for uncalibrated cameras. In: Sandini, G. (ed.) ECCV 1992. LNCS, vol. 588, pp. 579–587. Springer, Heidelberg (1992)Google Scholar
  4. 4.
    Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision, 2nd edn. Cambridge University Press, Cambridge (2003)Google Scholar
  5. 5.
    Shashua, A.: Triliearlity in visual recognition by alignment. In: Eklundh, J.-O. (ed.) ECCV 1994. LNCS, vol. 800, pp. 479–484. Springer, Heidelberg (1994)Google Scholar
  6. 6.
    Shashua, A.: Algebraic funtions for recoginition. IEEE Trans. on Pattern Recognition and Machine Intelligence 17 (1995)Google Scholar
  7. 7.
    Shashua, A., Werman, M.: On the trilinear tensor of three perspective views and its underlying geometry. In: Proceedings of International Conference on Computer Vision (1995)Google Scholar
  8. 8.
    Triggs, B.: Matching constraints and the joint image. In: Proceedings of International Conference on Computer Vision, Cambridge, MA, pp. 338–343 (1995)Google Scholar
  9. 9.
    Faugeras, O., Mourrain, B.: On the geometry and algebra of the point and line correspondences between N images. In: Proceedings of International Conference on Computer Vision, Cambridge, MA, pp. 951–956 (1995)Google Scholar
  10. 10.
    Hartley, R.I.: In defence of the 8-point algorithm. IEEE Trans. on Pattern Recognition and Machine Intelligence 19, 580–593 (1997)CrossRefGoogle Scholar
  11. 11.
    Nordberg, K.: Point matching constraints in two and three views. In: Hamprecht, F.A., Schnörr, C., Jähne, B. (eds.) Pattern Recognition. LNCS, vol. 4713, pp. 52–61. Springer, Heidelberg (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Klas Nordberg
    • 1
  1. 1.Computer Vision Laboratory, Department of Electrical Engineering, Linköping University 

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