Circle fitting from the polarity transformation regression

• New non-linear least squares circle fitting algorithm with analytic estimators.
• Novel use of the polarity transformation for circle fitting.
• The algorithm is at the accuracy level of other well-known algebraic methods.
• We develop a geometrical link between the orthogonal and the algebraic fittings.

Geometrical fitting is useful in different fields of science and technology, in particular least squares minimum (LSM) methods are widespread in contact probing for coordinate measuring machines, as well as a reference shape for surface metrology. We present a new intuitive and simple LSM algorithm for circle fitting, the polarity transformation regression. It is a non-linear algebraic method from a generic geometric transformation. We derive the explicit expression of the model estimators from the data points. Then, the algorithm is compared with other methods based on simulation and some literature data sets. The proposed algorithm presents a comparable accuracy, low computational effort and good behavior with outliers based on the initial test, outperforming other well-known algebraic methods in some of the studied data sets. The basis of the algorithm is finally suggested for other potential uses.