New methods for detecting concentric objects with high accuracy

Abstract

In fitting concentric geometric objects to digitized data, two approaches are commonly used in practice, the geometric approach and the algebraic approach. The former is iterative, and it requires a good initial guess. This paper focuses on the latter that is based on minimizing the algebraic distances when a constraint is imposed on parametric space yielding non-iterative methods. Each method depends on the constraint imposed on the parametric space and can be solved using the generalized eigenvalue problem. In this paper, we review the two existing methods developed. After establishing a general mathematical framework to solve this problem, the statistical properties of the methods have been established. Our analysis allows us to develop three estimators that outperform the existing ones. Moreover, the superiority of our methods and their practical performances are assessed by a series of numerical experiments on both synthetic and real data.