Concentric Ellipse Fitting with Bias Correction and Specialized Geometric-Based Clustering Approach

Abstract

This paper addresses the problem of fitting concentric ellipses under general assumptions. We study two methods of obtaining an estimator of the concentric ellipse parameters under this model, namely the least squares and the gradient weighted algebraic fits. We address some practical issues in obtaining these estimators. In this paper, we study the statistical properties of those estimators and we developed a refinement with the highest accuracy for each estimator. We also address a practical issue in concentric ellipse fitting, namely, that each observation in the data set should be recognized as belonging to only one of the concentric ellipses. Most well-known clustering methods, such as spectral clustering, fail for this problem. We propose a clustering approach that can effectively be used for the implementation of our model. Our theory has been validated through intensive numerical experiments on synthetic and real data.