대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제34권3호
  • /
  • Pages.1029-1047
  • /
  • 2019
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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AN ALGORITHM FOR CIRCLE FITTING IN ℝ3

  • Kim, Ik Sung (Department of Data Information Korea Maritime and Ocean University)
  • 투고 : 2018.08.01
  • 심사 : 2018.12.13
  • 발행 : 2019.07.31
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초록

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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참고문헌

  1. I. D. Coope, Circle tting by linear and nonlinear least squares, J. Optim. Theory Appl. 76 (1993), no. 2, 381-388. https://doi.org/10.1007/BF00939613
  2. D. Eberly, Least squares tting of data, Geometric Tools, LCC, Report, 1999.
  3. W. Gander, G. H. Golub, and R. Strebel, Least-squares tting of circles and ellipses, BIT 34 (1994), no. 4, 558-578. https://doi.org/10.1007/BF01934268
  4. D. Gruntz, Finding the "best fit" circle, The MathWorks Newsletter 1 (1990), p. 5.
  5. I. S. Kim, Geometric tting of circles, Korean J. Com. Appl. Math. 7 (2000), no. 3, 983-994.
  6. R. J. Lopez, Classroom tips and techniques: fitting circles in space to 3-D data, Application Demonstration Maplesoft, 2005.
  7. L. Maisonobe, Finding the circle that bestts a set of points, Report, 2007.
  8. P. Rangarajan and K. Kanatani, Improved algebraic methods for circle fitting, Electron. J. Stat. 3 (2009), 1075-1082. https://doi.org/10.1214/09-EJS488
  9. C. Rusu, M. Tico, P. Kuosmanen, and E. J. Delp, Classical geometrical approach to circle fitting-review and new developments, J. Electronic Imaging 12, (2003), no. 1, 179-193. https://doi.org/10.1117/1.1525792
  10. D. Umbach and K. N. Jones, A few methods for fitting circles to data, IEEE transactions on instrumentation and measurement 20 (2000), 179-193.