Advertisement

Journal of Mathematical Imaging and Vision

, Volume 10, Issue 3, pp 221–235 | Cite as

Shape Representation Using Fourier Coefficients of the Sinusoidal Transform

  • Ian Pratt
Article

Abstract

This paper investigates the use of the sinusoidal transform to represent convex regions of the plane. Formulae are derived for the determination of various geometrical features and relations in terms of sinusoidal transforms and their Fourier descriptors. Necessary and sufficient conditions for a periodic function to be the sinusoidal transform of a convex region are derived. Sinusoidal Fourier descriptors are shown to compare favourably with other shape-representation schemes based on Fourier descriptors.

shape representation Fourier descriptors convex plane Hough transform 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    H.G. Eggleston, Convexity, Cambridge University Press: Cambridge 1969.Google Scholar
  2. 2.
    G.H. Granlund, “Fourier processing for hand print character recognition,” IEEE Trans. Computers, Vol. C-21, pp. 195–201.Google Scholar
  3. 3.
    N. Kiryati and D. Maydan, “Calculating geometric properties from Fourier representation,” Pattern Recognition, Vol. 22, No. 5, pp. 469–475, 1988.Google Scholar
  4. 4.
    Chun-Shin Lin and Chia-Lin Hwang “New forms of shape invariants from elliptic Fourier descriptors,” in Pattern Recognition, Vol. 20, No. 5, pp. 535–545, 1987.Google Scholar
  5. 5.
    Violet Leavers, The Radon Transform, Springer: Berlin, 1994.Google Scholar
  6. 6.
    Eric Persoon and King-Sun Fu, “Shape discrimination using Fourier descriptors,” IEEE Transactions on Systems, Man and Cybernetics, Vol. SMC-7, No. 3, pp. 170–179, 1977.Google Scholar
  7. 7.
    I. Pratt, “Spatial Reasoning using Sinusoidal Oscillations,” in Proceedings, Tenth Annual Conference of the Cognitive Science Society, Montréal, Canada, 1988, pp. 219–225.Google Scholar
  8. 8.
    I. Pratt, “Path finding in free space using sinusoidal transforms III,” in Cognitive and Linguistic Aspects of Geographic Space, D.M. Mark (Ed.), Kluwer, 1991.Google Scholar
  9. 9.
    G.T. Toussaint, “Solving geometric problems with the ‘rotating callipers’ method,” in Proceedings, IEEE MELECON, Athens, 1983.Google Scholar
  10. 10.
    David, S. Touretzky, A. David Redish, and Hank S. Wan, “Neural representation of space using sinusoidal arrays,” Neural Computation, Vol. 5, No. 6, pp. 869–884, 1993.Google Scholar
  11. 11.
    Charles T. Zahn and Ralph Z. Roskies, “Fourier descriptors for plane closed curves,” IEEE Trans. on Computers, Vol. 21, pp. 269–281, 1972.Google Scholar

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Ian Pratt
    • 1
  1. 1.Department of Computer ScienceUniversity of ManchesterManchesterUK. ipratt@cs.man.ac.uk

Personalised recommendations