Planar Symmetry Detection by Random Sampling and Voting Process

  • Atsushi Imiya
  • Tomoki Ueno
  • Iris Fermin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1876)


We propose a randomized method for the detection of symmetry in planar polygons without assuming the predetermination of the centroids of the objects. Using a voting process, which is the main concept of the Hough transform in image processing, we transform the geometric computation for symmetry detection which is usually based on graph theory and combinatorial optimization, to the peak detection problem in a voting space in the context of the Hough transform.


  1. 1.
    Imiya, A., Fermin, I., Motion analysis by random sampling and voting process, Computer Vision and Image Understanding, 73, 309–328, 1999.zbMATHCrossRefGoogle Scholar
  2. 2.
    Imiya, A., Fermin, I., Voting method for planarity and motion detection, Image and Vision Computing, 17, 867–879, 1999.CrossRefGoogle Scholar
  3. 3.
    Tsai, W., Chou, S., Detection of generalized principal axes in rotationally symmetric shapes, Pattern Recognition, 24, 95–104, 1991.CrossRefMathSciNetGoogle Scholar
  4. 4.
    Atallah, M., On symmetry detection, IEEE Transactions on Computers, 34, 663–673, 1985.CrossRefMathSciNetGoogle Scholar
  5. 5.
    Lin, J., Universal principal axes: An easy-to-contruct tool useful in defining shape orientations for almost every kind of shape, Pattern Recognition, 26, 485–493, 1993.CrossRefGoogle Scholar
  6. 6.
    Lin, J., Detection of rotationally symmetric shape orientations by fold-invariant shape-specific points, Pattern Recognition, 25, 473–482, 1992.CrossRefGoogle Scholar
  7. 7.
    Leou, J.J, Tsai, W.H, Automatic rotational symmetry shape determination for shape analysis, Pattern Recognition, 20, 571–582, 1987.CrossRefGoogle Scholar
  8. 8.
    Lin, J.-C., Tsai, W.-H., Chen, J.-A., Detecting number of folds by a simple mathematical property, Pattern Recognition Letters, 15, 1081–1088, 1994.CrossRefGoogle Scholar
  9. 9.
    Lin, J., A simplified fold number detector for shapes with monotonic radii, Pattern Recognition, 29, 997–1005, 1996.CrossRefGoogle Scholar
  10. 10.
    Yip, R., Lam, W., Tam, P., Leung, D., A Hough transform technique for the detection of rotational symmetry, Pattern Recognition Letters, 15, 919–928, 1994.CrossRefGoogle Scholar
  11. 11.
    Imiya, A., Ueno, T., Fermin, I, Symmetry detection by random sampling and voting process, Proceedings of 10th ICIAP, 400–405, 1999.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Atsushi Imiya
    • 1
  • Tomoki Ueno
    • 1
  • Iris Fermin
    • 1
  1. 1.Dept. of IISChiba UniversityChibaJapan

Personalised recommendations