Advertisement

International Journal of Computer Vision

, Volume 14, Issue 1, pp 49–65 | Cite as

Recognition of planar shapes under affine distortion

  • E. J. Pauwels
  • T. Moons
  • L. J. Van Gool
  • P. Kempenaers
  • A. Oosterlinck
Article

Abstract

Methods for the recognition ofplanar shapes from arbitrary viewpoints are described. The adopted model of projection is orthographic. The invariant descriptions derived for this group are one-dimensional shape signatures comparable to the well-known curvature as a function of arc length description of Euclidean geometry. Since the use of such differential invariants in the affine case would lead to unacceptably high orders of derivatives, affine invariant descriptions based onsemi-differential invariants are proposed as an alternative. A systematic discussion of different types of these invariants is given. The usefulness and viability of this methodology is demonstrated on a database containing more than 40 objects.

Keywords

Image Processing Artificial Intelligence Computer Vision Computer Image Euclidean Geometry 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bartels, H., Beatty, C., and Barsky, A. 1987.An introduction to splines for use in computer graphics and geometric modeling, Morgan Kaufmann: Los Altos, CA.Google Scholar
  2. Bruckstein, A., and Netravali, A. 1990. On differential invariants of planar curves and recognizing partially occluded planar shapes, AT&T Technical Report.Google Scholar
  3. Costa, M., Haralick, R., Phillips, T., and Shapiro, L. 1989. Optimal affine-invariant point matching, SPIE Vol. 1095,Applications of Artificial Intelligence VII, pp. 515–530.Google Scholar
  4. Cyganski, D., Orr, J., Cott, T., and Dodson, R. 1987. Development, implementation, testing and application of an affine transform invariant curvature function. InProc. 1st Int. Conf. on Computer Vision, pp. 496–500.Google Scholar
  5. Huttenlocher, D.P., and Ullman, S. 1987.Object recognition using Allignment. In:Proc. 1st Int. Conf. on Computer Vision, pp. 102–111.Google Scholar
  6. Kempenaers, P., Van Gool, L., and Oosterlinck, A. 1991. Shape recognition under affine distortion. In: C. Arcelli, L. Cordelia, G. Sanniti di Baja, (eds.) Visual Form. Plenum: New York, pp. 323–332.Google Scholar
  7. Lamdan, Y., Schwartz, J., and Wolfson, H. 1988. On recognition of 3-D ojects from 2-D images, InProc. IEEE Int. Conf. on Robotics and Automation, pp. 1407–1413.Google Scholar
  8. Mannaert, H., and Oosterlinck, A. 1990. A Recursive Self-Organizing Network for Object Recognition. InProc. Int. Joint Conf. on Neural Networks, pp. II 405–408.Google Scholar
  9. Moons, T., Pauwels, E.J., Van Gool, L.J., and Oosterlinck, A. 1995. “Foundations of Semi-differential Invariants,”Int. J. of Computer Vision, vol. 14, no. 1, pp. 49–65.Google Scholar
  10. Olver, P.J. 1986.Applications of Lie groups to Differential Equations, Graduate Texts in Mathematics, Vol. 107, Springer-Verlag: Berlin/Heidelberg/New York/Tokyo.Google Scholar
  11. Pauwels, E.J., Moons, T., Van Gool, L.J., Kempenaers, P., and Oosterlinck, A. Jan 1994. Recognition of Planar Shapes under Affine Distortion. Technical Report: KUL/ESAT/MI2/9405, ESAT, Kath. Univ. Leuven.Google Scholar
  12. Rothwell, C.A., Zisserman, A., Forsyth, D.A., and Mundy, J.L. 1991. Using projective invariants for constant time library indexing in model based vision.Proc. BMVC91, pp. 62–70.Google Scholar
  13. Sagle, A.A., and Walde, R.E. 1973. Introduction to Lie Groups and Lie Algebras. Pure and Applied Mathematics, Vol. 51. Academic Press: New York.Google Scholar
  14. Van Gool, L., Kempenaers, P., and Oosterlinck, A. 1991. Recognition and semi-differential invariants. In IEEE Conf. on Computer Vision and Pattern Recognition, pp. 454–460.Google Scholar
  15. Van Gool, L., Brill, M., Barrett, E., Moons, T., and Pauwels, E.J. 1992. Semi-differential invariants for nonplanar curves. In: J. Mundy and A. Zisserman, (eds.) Geometric Invariance in Computer Vision. MIT Press: Cambridge, Massachusetts/London, England Chapter 15: pp. 293–309.Google Scholar

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • E. J. Pauwels
    • 1
  • T. Moons
    • 1
  • L. J. Van Gool
    • 1
  • P. Kempenaers
    • 1
  • A. Oosterlinck
    • 1
  1. 1.Katholieke Universiteit Leuven, ESAT-MI2LeuvenBelgium

Personalised recommendations