Semi-doubly optimal concentric circles fitting with presence of heteroscedasticity

Previous studies focus on homogeneous and isotropic assumptions about the noisy data. Many methods have been developed recently for fitting concentric circles to data. In this paper, these statistical assumptions have been relaxed. To the best of our knowledge, only one iterative method has been recently developed. Due to its complexity, no such algorithm is available to compute the reliable maximum likelihood estimator (MLE). Accordingly, we have developed four new methods that outperform the existing methods including the orthogonal distance regression (ODR). We also discuss which of these methods is superior according to the four principles: statistical efficiency, accuracy, robustness, and computational efficiency. Numerical experiments on synthetic and real images have been conducted to validate our findings.