Fitting Concentric Elliptical Shapes Under General Model

TL;DR

This paper introduces a general approach for fitting concentric elliptical shapes in images, proposing new estimators, analyzing their statistical properties, and validating the methods through experiments on real and synthetic data.

Contribution

It extends existing methods to a more general setting, develops iterative estimators, and derives the constrained Cramér-Rao bound for this problem.

Findings

Proposed two new iterative estimators for concentric ellipse fitting.

Analyzed the estimators' variance and compared with the Cramér-Rao bound.

Validated the methods through numerical experiments on real and synthetic data.

Abstract

The problem of fitting concentric ellipses is a vital problem in image processing, pattern recognition, and astronomy. Several methods have been developed but all address very special cases. In this paper, this problem has been investigated under a more general setting, and two estimators for estimating the parameters have been proposed. Since both estimators are obtained iterative fashion, several numerical schemes are investigated and the best initial guess is determined. Furthermore, the constraint Cram\'{e} Rao lower bound for this problem is derived and it is compared with the variance of each estimator. Finally, our theory is assessed and validated by a series of numerical experiments on both real and synthetic data.