Abstract
Recently, several methods have been proposed for describing plane, non-algebraic curves in a projectively invariant fashion. These curve representations are invariant under changes in viewpoint and therefore ideally suited for recognition.
We report the results of a study where the strengths and weaknesses of a number of semi-local methods are compared on the basis of the same images and edge data. All the methods define a distinguished or canonical projective frame for the curve segment which is used for projective normalisation. In this canonical frame the curve has a viewpoint invariant signature. Measurements on the signature are invariants. All the methods presented are designed to work on real images where extracted data will not be ideal, and parts of curves will be missing because of poor contrast or occlusion.
We compare the stability and discrimination of the signatures and invariants over a number of example curves and viewpoints. The paper concludes with a discussion of how the various methods can be integrated within a recognition system.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Åström, K. 1994. Fundamental difficulties with projective normalization of planar curves. In Applications of Invariance in Computer Vision, J., Mundy, A., Zisserman, and D., Forsyth (Eds.). Lecture Notes in Computer Science 825, Springer-Verlag: Berlin, pp. 199–214.
Bruckstein, A. and Netravali, A. 1992. Differential invariants of planar curves and recognizing partially occluded shapes. In Visual Form, C., Arcelli, L., Cordella, and G., Sanniti di Baja (Eds.), Plenum: New York, pp. 89–99.
Carlsson, S. 1992. Projectively invariant decomposition of planar shapes. In Geometric Invariance in Computer Vision, J., Mundy, and A., Zisserman (Eds.), MIT-Press: Cambridge, MA, pp. 267–273.
Carlsson, S. 1993. Projectively invariant decomposition and recognition of planar shapes. In Proc. of 4th Int. Conf. on Computer Vision, Berlin, Germany, pp. 471–475. Also in Int. Journal of Computer Vision 17(2), 1996, pp. 193–209.
Duda, R. and Hart, P. 1973. Pattern Classification and Scene Analysis. John Wiley: Chichester.
Kempenaers, P., Van Gool, L., and Oosterlinck, A. 1992. Semidifferential invariants: Algebraic-differential hybrids. In SPIE Proceedings on Hybrid Image and Signal Processing III, Orlando, Vol. 1702, pp. 41–52.
Lamdan, Y., Schwartz, J., and Wolfson, H. 1988. Object recognition by affine invariant matching. In Proc. Comp. Vision and Pattern Recogn., pp. 335–344.
Rothwell, C. 1993. Recognition Using Perspective Invariance, Ph.D. Thesis. Univ. of Oxford: Oxford, UK.
Rothwell, C., Zisserman, A., Forsyth, D., and Mundy, J. 1995. Planar object recognition using projective shape representation. Intern. Journal of Comp. Vision 16(1), pp. 57–99.
Rothwell, C., Zisserman, A., Forsyth, D., and Mundy, J. 1992. Canonical frames for planar object recognition. In Proc. of the 2nd European Conf. on Comp. Vision, Santa Margherita Ligure, Italy, pp. 757–772.
Van, Diest, M., Van, Gool, L., and Moons, T. 1993. Semi-differential invariant descriptions of plane contour segments under perspective. Kath. Univ. Leuven, Leuven, Belgium. Techn. Rep. KUL/ESAT/MI2/9305.
Van Diest, M. Van Gool, L., Moons, T., and Pauwels, E. 1994. Projective invariants for planar contour recognition. In Proc. of the 3rd European Conf. on Computer Vision, Stockholm, Sweden, Vol. 1, pp. 527–534.
Van, Gool, L., Moons, T., Pauwels, E., and Oosterlinck, A., 1992. Semi-differential invariants. In Geometric Invariance in Computer Vision, J., Mundy and A., Zisserman (Eds.), MIT Press: Cambridge, MA, pp. 193–214.
Author information
Authors and Affiliations
Additional information
Postdoctoral Research Fellow of the Belgian National Fund for Scientific Research (N.F.W.O.).
Rights and permissions
About this article
Cite this article
Carlsson, S., Mohr, R., Moons, T. et al. Semi-local projective invariants for the recognition of smooth plane curves. Int J Comput Vision 19, 211–236 (1996). https://doi.org/10.1007/BF00055145
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00055145