Camera Motion Estimation Through Planar Deformation Determination

  • C. JoncheryEmail author
  • F. Dibos
  • G. Koepfler


In this paper, we propose a global method for estimating the motion of a camera which films a static scene. Our approach is direct, fast and robust, and deals with adjacent frames of a sequence. It is based on a quadratic approximation of the deformation between two images, in the case of a scene with constant depth in the camera coordinate system. This condition is very restrictive but we show that, provided translation and depth inverse variations are small enough, the error on optical flow involved by the approximation of depths by a constant is small. In this context, we propose a new model of camera motion which allows to separate the image deformation in a similarity and a “purely” projective application, due to change of optical axis direction. This model leads to a quadratic approximation of image deformation that we estimate with an M-estimator; we can immediately deduce camera motion parameters.


Camera motion estimation Planar application Optical flow quadratic approximation Parameter estimation 

Supplementary material

Video file


  1. 1.
    Azarbayejani, A., Pentland, A.P.: Recursive estimation of motion, structure and focal length. IEEE Trans. Pattern Anal. Mach. Intell. 17(6), 562–575 (1995) CrossRefGoogle Scholar
  2. 2.
    Yao, A., Calway, A.: Robust estimation of 3-d camera motion for uncalibrated augmented reality. Dept. of Computer Science, University of Bristol, CSTR-02-001 (2002) Google Scholar
  3. 3.
    Longuet-Higgins, H.C.: A computer algorithm for reconstructing a scene from two projections. Nature 293(10), 133–135 (1981) CrossRefGoogle Scholar
  4. 4.
    Faugeras, O.: Three-Dimensional Computer Vision, a Geometric Viewpoint. MIT Press, Cumberland (1993) Google Scholar
  5. 5.
    Faugeras, O., Maybank, S.: Motion from point matches: multiplicity of solutions. Int. J. Comput. Vis. 4(3), 225–246 (1990) CrossRefGoogle Scholar
  6. 6.
    Huang, T., Faugeras, O.: Some properties of the Ematrix in two-view motion estimation. IEEE Trans. Pattern Anal. Mach. Intell. 11(12), 1310–1312 (1989) CrossRefGoogle Scholar
  7. 7.
    Faugeras, O., Luong, Q.T., Papadopoulo, T.: The Geometry of Multiple Images. MIT Press, Cumberland (2000) Google Scholar
  8. 8.
    Bruss, A.R., Horn, B.K.: Passive navigation. Comput. Graph. Image Process. 21, 3–20 (1983) CrossRefGoogle Scholar
  9. 9.
    Heeger, D., Jepson, A.: Subspace methods for recovering rigid motion I: algorithm and implementation. Int. J. Comput. Vis. 7(2), 95–117 (1992) CrossRefGoogle Scholar
  10. 10.
    Ma, Y., Koseckà, J., Sastry, S.: Linear differential algorithm for motion recovery: a geometric approach. Int. J. Comput. Vis. 36(1), 71–89 (2000) CrossRefGoogle Scholar
  11. 11.
    Brooks, M.J., Chojnacki, W., Baumela, L.: Determining the ego-motion of an uncalibrated camera from instantaneous optical flow. J. Opt. Soc. Am. A 14(10), 2670–2677 (1997) CrossRefGoogle Scholar
  12. 12.
    Tomasi, C., Shi, J.: Direction of heading from image deformations. In: IEEE Conf. on Computer Vision and Pattern Recognition, pp. 422–427 (1993) Google Scholar
  13. 13.
    Lawn, J., Cipolla, R.: Robust egomotion estimation from affine motion parallax. In: Proc. 3rd European Conf on Computer Vision, pp. 205–210. Stockholm, Sweden (1994) Google Scholar
  14. 14.
    Tian, T.Y., Tomasi, C., Heeger, D.J.: Comparison of approaches to egomotion computation. In: Proc. of Conf. on Computer Vision and Pattern Recognition, pp. 315–320 (1996) Google Scholar
  15. 15.
    Irani, M., Rousso, B., Peleg, S.: Recovery of ego-motion using region alignement. IEEE Trans. Pattern Anal. Mach. Intell. 19(3), 268–272 (1997) CrossRefGoogle Scholar
  16. 16.
    Horn, B.K., Weldon, E.J.: Direct methods for recovering motion. Int. J. Comput. Vis. 2, 51–76 (1988) CrossRefGoogle Scholar
  17. 17.
    Bergen, J.R., Anandan, P., Hanna, K.J., Hingorani, R.: Hierarchical model-based motion estimation. In: Proc. of European Conf. on Computer Vision and Pattern Recognition, vol. 2, pp. 237–252 (1992) Google Scholar
  18. 18.
    Negahdaripour, S., Horn, B.K.P.: Direct passive navigation. IEEE Trans. Pattern Anal. Mach. Intell. 9(1), 168–176 (1987) zbMATHCrossRefGoogle Scholar
  19. 19.
    Dibos, F., Koepfler, G., Monasse, P.: Image Alignment. Geometric Level Set Methods in Imaging, Vision and Graphics. Springer, Berlin (2003) Google Scholar
  20. 20.
    Odobez, J.M., Bouthemy, P.: Robust Multiresolution Estimation of Parametric Motion Models. J. Vis. Commun. Image Represent. 6(4), 348–365 (1995) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.MAP5Université Paris DescartesParis Cedex 06France
  2. 2.LAGAL2TI Université Paris 13VilletaneuseFrance

Personalised recommendations