Perspective 3D Reconstruction of Rigid Objects

  • Guanghui Wang
  • Q. M. Jonathan Wu
Part of the Advances in Pattern Recognition book series (ACVPR)


It is well known that projective depth recovery and camera calibration are two essential and difficult steps in the problem of 3D Euclidean structure and motion recovery from video sequences. This chapter presents two new algorithms to improve the performance of perspective factorization. The first one is a hybrid method for projective depths estimation. It initializes the depth scales via a projective structure reconstructed from two views with large camera movement, which are then optimized iteratively by minimizing reprojection residues. The algorithm is more accurate than previous methods and converges quickly. The second one is on camera self-calibration based on Kruppa constraints which can deal with a more general camera model. Then the Euclidean structure is recovered from factorization of the normalized tracking matrix. Extensive experiments on synthetic data and real sequences are performed for validation and comparison.


Camera Calibration Camera Parameter Camera Model Perspective Projection 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.


  1. 1.
    Christy, S., Horaud, R.: Euclidean shape and motion from multiple perspective views by affine iterations. IEEE Trans. Pattern Anal. Mach. Intell.18(11), 1098–1104 (1996) CrossRefGoogle Scholar
  2. 2.
    Faugeras, O.D., Luong, Q.T., Maybank, S.J.: Camera self-calibration: Theory and experiments. In: Proc. of European Conference on Computer Vision, pp. 321–334 (1992) Google Scholar
  3. 3.
    Han, M., Kanade, T.: Creating 3D models with uncalibrated cameras. In: Proc. of IEEE Computer Society Workshop on the Application of Computer Vision (2000) Google Scholar
  4. 4.
    Hartley, R.: Kruppa’s equations derived from the fundamental matrix. IEEE Trans. Pattern Anal. Mach. Intell.19(2), 133–135 (1997) CrossRefMathSciNetGoogle Scholar
  5. 5.
    Hartley, R.I., Zisserman, A.: Multiple View Geometry in Computer Vision, 2nd edn. Cambridge University Press, Cambridge (2004). ISBN: 0521540518 MATHCrossRefGoogle Scholar
  6. 6.
    Heyden, A., Åström, K.: Euclidean reconstruction from image sequences with varying and unknown focal length and principal point. In: Proc. of IEEE Conference on Computer Vision and Pattern Recognition, pp. 438–443 (1997) Google Scholar
  7. 7.
    Heyden, A., Åström, K.: Minimal conditions on intrinsic parameters for Euclidean reconstruction. In: Proc. of Asian Conference on Computer Vision, pp. 169–176 (1998) Google Scholar
  8. 8.
    Hu, Z., Wu, Y., Wu, F., Ma, S.D.: The number of independent Kruppa constraints fromN images. J. Comput. Sci. Technol.21(2), 209–217 (2006) MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Hung, Y., Tang, W.: Projective reconstruction from multiple views with minimization of 2D reprojection error. Int. J. Comput. Vis.66(3), 305–317 (2006) CrossRefGoogle Scholar
  10. 10.
    Luong, Q., Faugeras, O.: Self-calibration of a moving camera from point correspondences and fundamental matrices. Int. J. Comput. Vis.22(3), 261–289 (1997) CrossRefGoogle Scholar
  11. 11.
    Mahamud, S., Hebert, M.: Iterative projective reconstruction from multiple views. In: Proc. of IEEE Conference on Computer Vision and Pattern Recognition, vol. 2, pp. 430–437 (2000) Google Scholar
  12. 12.
    Maybank, S.: The projective geometry of ambiguous surfaces. Philos. Trans. Phys. Sci. Eng.332, 1–47 (1990) CrossRefMathSciNetGoogle Scholar
  13. 13.
    Maybank, S., Faugeras, O.: A theory of self-calibration of a moving camera. Int. J. Comput. Vis.8(2), 123–151 (1992) CrossRefGoogle Scholar
  14. 14.
    Oliensis, J., Hartley, R.: Iterative extensions of the Sturm/Triggs algorithm: Convergence and nonconvergence. IEEE Trans. Pattern Anal. Mach. Intell.29(12), 2217–2233 (2007) CrossRefGoogle Scholar
  15. 15.
    Torr, P.H.S., Zisserman, A., Maybank, S.J.: Robust detection of degenerate configurations while estimating the fundamental matrix. Comput. Vis. Image Underst.71(3), 312–333 (1998) CrossRefGoogle Scholar
  16. 16.
    Poelman, C., Kanade, T.: A paraperspective factorization method for shape and motion recovery. IEEE Trans. Pattern Anal. Mach. Intell.19(3), 206–218 (1997) CrossRefGoogle Scholar
  17. 17.
    Pollefeys, M., Koch, R., Van Gool, L.: Self-calibration and metric reconstruction in spite of varying and unknown intrinsic camera parameters. Int. J. Comput. Vis.32(1), 7–25 (1999) CrossRefGoogle Scholar
  18. 18.
    Pollefeys, M., Van Gool, L., Oosterlinck, A.: The modulus constraint: A new constraint for self-calibration. In: Proc. of International Conference on Pattern Recognition, vol. 1, pp. 349–353 (1996) Google Scholar
  19. 19.
    Quan, L.: Self-calibration of an affine camera from multiple views. Int. J. Comput. Vis.19(1), 93–105 (1996) CrossRefGoogle Scholar
  20. 20.
    Sturm, P.F., Triggs, B.: A factorization based algorithm for multi-image projective structure and motion. In: Proc. of European Conference on Computer Vision, vol. 2, pp. 709–720 (1996) Google Scholar
  21. 21.
    Triggs, B.: Factorization methods for projective structure and motion. In: Proc. of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 845–851 (1996) Google Scholar
  22. 22.
    Ueshiba, T., Tomita, F.: A factorization method for projective and Euclidean reconstruction from multiple perspective views via iterative depth estimation. In: Proc. of European Conference on Computer Vision, vol. 1, pp. 296–310 (1998) Google Scholar
  23. 23.
    Wang, G.: A hybrid system for feature matching based on SIFT and epipolar constraints. Tech. Rep. Department of ECE, University of Windsor (2006) Google Scholar
  24. 24.
    Wang, G., Wu, J.: Quasi-perspective projection with applications to 3D factorization from uncalibrated image sequences. In: Proc. of IEEE Conference on Computer Vision and Pattern Recognition, pp. 1–8 (2008) Google Scholar
  25. 25.
    Wang, G., Wu, J.: Perspective 3D Euclidean reconstruction with varying camera parameters. IEEE Trans. Circuits Syst. Video Technol.19(12), 1793–1803 (2009) CrossRefGoogle Scholar
  26. 26.
    Wang, G., Wu, J.: Stratification approach for 3-D Euclidean reconstruction of nonrigid objects from uncalibrated image sequences. IEEE Trans. Syst. Man Cybern., Part B38(1), 90–101 (2008) CrossRefGoogle Scholar
  27. 27.
    Xu, G., Sugimoto, N.: Algebraic derivation of the Kruppa equations and a new algorithm for self-calibration of cameras. J. Opt. Soc. Am. A16(10), 2419–2424 (1999) CrossRefMathSciNetGoogle Scholar
  28. 28.
    Zaharescu, A., Horaud, R.P., Ronfard, R., Lefort, L.: Multiple camera calibration using robust perspective factorization. In: Proc. of International Symposium on 3D Data Processing, Visualization and Transmission, pp. 504–511 (2006) Google Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Department of Systems Design EngineeringUniversity of WaterlooWaterlooCanada
  2. 2.Dept. Electrical & Computer EngineeringUniversity of WindsorWindsorCanada

Personalised recommendations