Concentric Ellipse Fitting Problem: Theory and Numerical Implementations

The problem of fitting ellipses has been popular since the 1970s, and remains a prominent area of research in statistics, computer vision, and engineering. This paper aims to address the problem of fitting concentric ellipses under general assumptions which started paying more attention recently due to its applications in engineering. We study two methods of obtaining an estimator of the concentric ellipse parameters under this model, namely, the least squares (LS) and the gradient weighted algebraic fits (GRAF). We address some practical issues in obtaining these estimators. Since our model is nonlinear, obtaining an estimate for the concentric ellipse parameters requires the implementation of numerical minimization schemes. We propose and compare several minimization schemes, and provide several initial guesses which yield the best convergence rates.