Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ORTHOGONAL DISTANCE FITTING OF ELLIPSES

  • Kim, Ik-Sung (Department of Applied Mathematics, Korea Maritime University)
  • Published : 2002.01.01
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Abstract

We are interested in the curve fitting problems in such a way that the sum of the squares of the orthogonal distances to the given data points is minimized. Especially, the fitting an ellipse to the given data points is a problem that arises in many application areas, e.g. computer graphics, coordinate metrology, etc. In [1] the problem of fitting ellipses was considered and numerically solved with general purpose methods. In this paper we present another new ellipse fitting algorithm. Our algorithm if mainly based on the steepest descent procedure with the view of ensuring the convergence of the corresponding quadratic function Q(u) to a local minimum. Numerical examples are given.

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References

  1. BIT v.34 Least-squares fitting of circles and ellipses W. Gander;G. H. Golub;R. Strebel https://doi.org/10.1007/BF01934268
  2. Solving problems in scientific computing using maple and matlab Some least squares problems W. Gander;U. von Matt;W. Gander(ed.);J. Hrebicek(ed.)
  3. Proceedings of IMACS-GAMM Inter. Symposium on Numerical Methods and Error Bounds Orthogonal squared distance fitting with parabolas H. Spath
  4. Comp. J. v.14 Parametric curve fitting M. Grossmann https://doi.org/10.1093/comjnl/14.2.169

Cited by

  1. Guaranteed Ellipse Fitting with a Confidence Region and an Uncertainty Measure for Centre, Axes, and Orientation vol.52, pp.2, 2015, https://doi.org/10.1007/s10851-014-0536-x
  2. Determining ellipses from low-resolution images with a comprehensive image formation model vol.36, pp.2, 2019, https://doi.org/10.1364/JOSAA.36.000212