The Robust Algorithms for Finding the Center of an Arc

Two new algorithms for estimating centers of circular arcs under noisy conditions have been investigated. These algorithms, which are based on new least-squares estimators of a circular arc center, were shown to perform with very high accuracy and robutness. As compared with the previous iteration algorithms, both of our algorithms are computationally efficient because of the closed form solutions of linear equation systems. Therefore for most applications software implementation may be sufficient. In addition, there is no initial estimate required to ensure the convergence. Our experimental results show that our methods have been successfully used in some industrial applications, e.g., microscope metrology.