Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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AN ALGORITHM FOR CIRCLE FITTING IN ℝ3

  • Kim, Ik Sung (Department of Data Information Korea Maritime and Ocean University)
  • Received : 2018.08.01
  • Accepted : 2018.12.13
  • Published : 2019.07.31
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Abstract

We are interested in the problem of determining the best fitted circle to a set of data points in space. This can be usually obtained by minimizing the geometric distances or various approximate algebraic distances from the fitted circle to the given data points. In this paper, we propose an algorithm in such a way that the sum of the squares of the geometric distances is minimized in ${\mathbb{R}}^3$. Our algorithm is mainly based on the steepest descent method with a view of ensuring the convergence of the corresponding objective function Q(u) to a local minimum. Numerical examples are given.

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References

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