Robust Homography Estimation from Planar Contours Based on Convexity

  • Alberto Ruiz
  • Pedro E. López de Teruel
  • Lorenzo Fernández
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3951)


We propose a homography estimation method from the contours of planar regions. Standard projective invariants such as cross ratios or canonical frames based on hot points obtained from local differential properties are extremely unstable in real images suffering from pixelization, thresholding artifacts, and other noise sources. We explore alternative constructions based on global convexity properties of the contour such as discrete tangents and concavities. We show that a projective frame can be robustly extracted from arbitrary shapes with at least one appreciable concavity. Algorithmic complexity and stability are theoretically discussed and experimentally evaluated in a number of real applications including projective shape matching, alignment and pose estimation. We conclude that the procedure is computationally efficient and notably robust given the ill-conditioned nature of the problem.


Convex Hull Cross Ratio Visual Servoing Symbol Recognition Canonical Frame 
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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  1. 1.
    Pizlo, Z., Rosenfeld, A.: Recognition of planar shapes from perspective images using contour-based invariants. Computer Vision, Graphics, and Image Processing 56(3), 330–350 (1992)MATHGoogle Scholar
  2. 2.
    Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision, 2nd edn. Cambridge University Press, Cambridge (2004)CrossRefMATHGoogle Scholar
  3. 3.
    Faugeras, O., Luong, Q.T., Papadopoulo, T.: The Geometry of Multiple Images. MIT Press, Cambridge (2001)Google Scholar
  4. 4.
    Mundy, J., Zisserman, A.: Appendix – Projective geometry for machine vision. In: Geometric Invariances in Computer Vision, MIT Press, Cambridge (1992)Google Scholar
  5. 5.
    Rothwell, C.A., Zisserman, A., Forsyth, D.A., Mundy, J.L.: Canonical frames for planar object recognition. In: Sandini, G. (ed.) ECCV 1992. LNCS, vol. 588, pp. 757–772. Springer, Heidelberg (1992)CrossRefGoogle Scholar
  6. 6.
    Carlsson, S., Mohr, R., Moons, T., Morin, L., Rothwell, C., Diest, M.V., Gool, L.V., Veillon, F., Zissermann, A.: Semi-local projective invariants for the recognition of smooth plane curve. IJCV 19(3), 211–236 (1996)CrossRefGoogle Scholar
  7. 7.
    Salden, A., Haar, B., Viergever, R.: Affine and projective differential geometric invariants of space curves. In: Vemuri, B. (ed.) Geometric Methods in Computer Vision II, SPIE (1993)Google Scholar
  8. 8.
    Zisserman, A., Blake, A., Rothwell, C., Van Gool, L., Van Diest, M.: Eliciting qualitative structure from image curve deformations. In: Proc. 4th IEEE ICCV, pp. 340–345 (1993)Google Scholar
  9. 9.
    Weiss, I.: Noise resistant invariants of curves. IEEE PAMI 15(9), 943–948 (1993)CrossRefGoogle Scholar
  10. 10.
    Lei, Z., Blane, M.M., Cooper, D.B.: 3L fitting of higher degree implicit polynomials. In: Proc. 3rd IEEE WACV, Sarasota, USA (1996)Google Scholar
  11. 11.
    Tarel, J., Civi, H., Cooper, D.B.: Pose estimation of free-form 3D objects without point matching using algebraic surface models. In: Proc. 1st IEEE Workshop on Model-Based 3D Image Analysis, Mumbai, India, pp. 13–21 (1998)Google Scholar
  12. 12.
    Schmid, C., Zisserman, A.: The geometry and matching of curves in multiple views. In: Burkhardt, H.-J., Neumann, B. (eds.) ECCV 1998. LNCS, vol. 1406, pp. 394–409. Springer, Heidelberg (1998)Google Scholar
  13. 13.
    Startchik, S., Milanese, R., Pun, T.: Projective and photometric invariant representation of planar disjoint shapes. Image and Vision Comp 16(9-10), 713–723 (1998)CrossRefGoogle Scholar
  14. 14.
    Chesi, G., Malis, E., Cipolla, R.: Collineation estimation from two unmatched views of an unknown planar contour for visual servoing. In: Proc. 10th BMVC, Nottingham, UK (1999)Google Scholar
  15. 15.
    Sato, J., Cipolla, R.: Extracting group transformations from image moments. Computer Vision and Image Understanding 73(1), 29–42 (1999)CrossRefMATHGoogle Scholar
  16. 16.
    Basri, R., Jacobs, D.: Projective alignment with regions. PAMI 23(5), 519–527 (2001)CrossRefGoogle Scholar
  17. 17.
    Mendonça, P.R.S., Wong, K.-Y.K., Cipolla, R.: Camera pose estimation and reconstruction from image profiles under circular motion. In: Vernon, D. (ed.) ECCV 2000. LNCS, vol. 1843, pp. 864–877. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  18. 18.
    Wong, K., Cipolla, R.: Structure and motion from silhouettes. In: Proc. 8th IEEE ICCV, Vancouver, Canada, pp. 217–222 (2001)Google Scholar
  19. 19.
    Cipolla, R., Giblin, P.: Visual Motion of Curves and Surfaces. Cambridge University Press, Cambridge (2000)MATHGoogle Scholar
  20. 20.
    Arbter, K., Snyder, W., Burkhardt, H., Hirzinger, G.: Application of affine-invariant fourier descriptors to recognition of 3D objects. PAMI 12(7), 640–647 (1990)CrossRefGoogle Scholar
  21. 21.
    Startchik, S., Milanese, R., Rauber, C., Pun, T.: Planar shape databases with affine invariant search. In: Proc. 1st Int. Workshop on Image Databases and Multimedia Search, Amsterdam, Netherlands (1996)Google Scholar
  22. 22.
    Vinther, S., Cipolla, R.: Object model acquisition and recognition using 3D affine invariants. In: Proc. 4th BMVC, Guilford, UK, pp. 369–378 (1993)Google Scholar
  23. 23.
    Stolfi, J.: Oriented Projective Geometry. Academic Press, Boston (1991)MATHGoogle Scholar
  24. 24.
    Melkman, A.: On-line construction of the convex hull of a simple polygon. Information Processing Letters 25, 11–12 (1987)MathSciNetCrossRefMATHGoogle Scholar
  25. 25.
    López-de-Teruel, P.E., Ruiz, A., Fernández, L.: Geobot: A high level visual perception architecture for autonomous robots. In: Proc. 4th IEEE ICVS, New York, USA (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Alberto Ruiz
    • 1
  • Pedro E. López de Teruel
    • 2
  • Lorenzo Fernández
    • 2
  1. 1.Dept. Informática y SistemasUniversity of MurciaSpain
  2. 2.Dept. Tecnología e Ingeniería de ComputadoresUniversity of MurciaSpain

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