Pattern Analysis and Applications

, Volume 8, Issue 1–2, pp 72–83 | Cite as

Affine invariant fitting of algebraic curves using Fourier descriptors

  • Sait SenerEmail author
  • Mustafa Unel
Theoretical Advances


Both parametric and implicit representations are used in a variety of computer vision applications such as object modeling, recognition and pose estimation. In this paper, we present a new algebraic curve fitting technique based on the implicitization of affine invariant Fourier descriptors that can be used to model free-form objects captured from different viewpoints. Implicitization can be carried out quite efficiently using a numerical procedure rather than computing determinants of eliminant matrices, symbolically. Affine invariance of the proposed fitting technique is experimentally shown on a database of 2D free-form objects. Experimental results are provided to assess the robustness of our fitting method under data perturbations. Some invariant recognition examples are also presented.


Algebraic curves Implicit polynomials Fourier descriptors Affine invariance Fitting Matrix annihilation Object recognition Robustness Implicitization 


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Copyright information

© Springer-Verlag London Limited 2005

Authors and Affiliations

  1. 1.Department of Computer Science, Institute of InformaticsIstanbul Technical UniversityIstanbulTurkey
  2. 2.Faculty of Engineering and Natural SciencesSabanci UniversityIstanbulTurkey

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