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http://dx.doi.org/10.4134/CKMS.c180328

AN ALGORITHM FOR CIRCLE FITTING IN ℝ3  

Kim, Ik Sung (Department of Data Information Korea Maritime and Ocean University)
Publication Information
Communications of the Korean Mathematical Society / v.34, no.3, 2019 , pp. 1029-1047 More about this Journal
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;
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