An algorithm for circle fitting in $\mathbb{R}^3$
Commun. Korean Math. Soc. 2019 Vol. 34, No. 3, 1029-1047
Published online July 31, 2019
Ik Sung Kim
Korea Maritime and Ocean University
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.
Keywords : circle fitting, geometric distance, steepest descent
MSC numbers : Primary 65D18, 68U05
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