Affine Epipolar Direction from Two Views of a Planar Contour

  • Maria Alberich-Carramiñana
  • Guillem Alenyà
  • Juan Andrade-Cetto
  • Elisa Martínez
  • Carme Torras
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4179)


Most approaches to camera motion estimation from image sequences require matching the projections of at least 4 non-coplanar points in the scene. The case of points lying on a plane has only recently been addressed, using mainly projective cameras. We here study what can be recovered from two uncalibrated views of a planar contour under affine viewing conditions. We prove that the affine epipolar direction can be recovered provided camera motion is free of cyclorotation. The proposed method consists of two steps: 1) computing the affinity between two views by tracking a planar contour, and 2) recovering the epipolar direction by solving a second-order equation on the affinity parameters. Two sets of experiments were performed to evaluate the accuracy of the method. First, synthetic image streams were used to assess the sensitivity of the method to controlled changes in viewing conditions and to image noise. Then, the method was tested under more realistic conditions by using a robot arm to obtain calibrated image streams, which permit comparing our results to ground truth.


Active Contour Camera Motion Synthetic Image Camera Model Epipolar Line 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Beardsley, P.A., Zisserman, A., Murray, D.W.: Sequential updating of projective and affine structure from motion. Intl. J. of Computer Vision 23, 235–259 (1997)CrossRefGoogle Scholar
  2. 2.
    McLauchlan, P.F., Murray, D.W.: A unifying framework for structure and motion recovery from image sequences. In: Proc. Intl. Conf. on Computer Vision, pp. 314–320 (1995)Google Scholar
  3. 3.
    Koenderink, J., van Doorn, A.J.: Affine structure from motion. J. Opt. Soc. Am. A 8, 377–385 (1991)CrossRefGoogle Scholar
  4. 4.
    Shapiro, L., Zisserman, A., Brady, M.: 3d motion recovery via affine epipolar geometry. Intl. J. of Computer Vision 16, 147–182 (1995)CrossRefGoogle Scholar
  5. 5.
    Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision, 2nd edn. Cambridge University Press, Cambridge (2004)MATHGoogle Scholar
  6. 6.
    Sturm, P., Maybank, S.J.: On plane-based camera calibration: a general algorithm, singularities, applications. In: Proc. IEEE Conf. on Computer Vision and Pattern Recognition, vol. 1, pp. 432–437 (1999)Google Scholar
  7. 7.
    Demirdjian, D., Zisserman, A., Horaud, R.: Stereo autocalibration from one plane. In: Proc. 6th European Conf. on Computer Vision, pp. 625–639 (2000)Google Scholar
  8. 8.
    Malis, E., Cipolla, R.: Camera self-calibration from unknown planar structures enforcing the multiview constraints between collineations. IEEE Trans. on Pattern Analysis and Machine Intelligence 24, 1268–1272 (2002)CrossRefGoogle Scholar
  9. 9.
    Bartoli, A., Sturm, P., Horaud, R.: Structure and motion from two uncalibrated views using points on planes. In: Proc. 3rd. Intl. Conf. on 3D Digital Imaging and Modeling, Canada, pp. 83–90 (2001)Google Scholar
  10. 10.
    Kaminski, J.Y., Shashua, A.: On calibration and reconstruction from planar curves. In: Proc. European Conf. on Computer Vision, pp. 678–694 (2000)Google Scholar
  11. 11.
    Alberich-Carramiñana, M., Alenyá, G., Andrade-Cetto, J., Martínez, E., Torras, C.: Affine epipolar direction from two views of a planar contour. Technical Report IRI-DT-2005/03, Institute of Robotics (IRI) (2005)Google Scholar
  12. 12.
    Blake, A., Isard, M.: Active Contours. Springer, Heidelberg (1998)Google Scholar
  13. 13.
    Foley, J., van Dam, A., Feiner, S., Hughes, F.: Computer Graphics. Principles and Practice. Addison-Wesley Publishing Company, Reading (1996)MATHGoogle Scholar
  14. 14.
    Alenyà, G., Martínez, E., Torras, C.: Fusing visual and inertial sensing to recover robot egomotion. Journal of Robotics Systems 21, 23–32 (2004)CrossRefGoogle Scholar
  15. 15.
    Martínez, E., Torras, C.: Qualitative vision for the guidance of legged robots in unstructured environments. Pattern Recognition 34, 1585–1599 (2001)MATHCrossRefGoogle Scholar
  16. 16.
    Martínez, E., Torras, C.: Contour-based 3d motion recovery while zooming. Robotics and Autonomous Systems 44, 219–227 (2003)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Maria Alberich-Carramiñana
    • 1
  • Guillem Alenyà
    • 2
  • Juan Andrade-Cetto
    • 3
  • Elisa Martínez
    • 4
  • Carme Torras
    • 2
  1. 1.Departament de Matemàtica Aplicada IBarcelona
  2. 2.Institut de Robòtica i Informàtica IndustrialBarcelona
  3. 3.Centre de Visió per Computador, UAB Edifici OBellaterraSpain
  4. 4.CiTS La Salle, Universitat Ramon Llull Pge.Barcelona

Personalised recommendations