Robust Fitting of Circle Arcs

Geometric fitting is present in different fields of sciences, engineering and astronomy. In particular, circular arc primitives are some of the most commonly employed geometric features in digital image analysis and visual pattern recognition. In this paper, a robust geometric method based on mean absolute error to fit a set of points is proposed. Most geometric and algebraic methods are sensitive to noise and outlier points and so the results are not usually acceptable. It is well known that the least absolute error criterion leads to robust estimations. However, the objective function is non differentiable and thus algorithms based on gradient cannot be applied. We propose an algorithm based on left and right side partial derivatives that is computationally efficient as an alternative to conventional algorithms, and evaluate the sensitivity of circle fits for different types of data.