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Circle fitting by linear and nonlinear least squares. (English) Zbl 0790.65012
Summary: The problem of determining the circle of the best fit to a set of points in the plane (or the obvious generalization to \(n\)-dimensions) is easily formulated as a nonlinear total least squares problem which may be solved using a Gauss-Newton minimization algorithm. This straightforward approach is shown to be inefficient and extremely sensitive to the presence of outliers. An alternative formulation allows the problem to be reduced to a linear least squares problem which is trivially solved. The recommended approach is shown to have the added advantage of being much less sensitive to outliers than the nonlinear least squares approach.

MSC:
65D10 Numerical smoothing, curve fitting
65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
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