Error analysis for circle fitting algorithms

TL;DR

This paper provides a comprehensive error analysis of various circle fitting algorithms, revealing their differences and leading to a new algebraic method that surpasses existing techniques in accuracy.

Contribution

The paper offers a detailed higher-order error analysis of popular circle fitting methods and introduces a novel algebraic algorithm that outperforms all existing approaches.

Findings

Higher order error terms explain differences between methods.

The new algebraic fit outperforms geometric and other algebraic methods.

The analysis guides the design of more accurate circle fitting algorithms.

Abstract

We study the problem of fitting circles (or circular arcs) to data points observed with errors in both variables. A detailed error analysis for all popular circle fitting methods -- geometric fit, Kasa fit, Pratt fit, and Taubin fit -- is presented. Our error analysis goes deeper than the traditional expansion to the leading order. We obtain higher order terms, which show exactly why and by how much circle fits differ from each other. Our analysis allows us to construct a new algebraic (non-iterative) circle fitting algorithm that outperforms all the existing methods, including the (previously regarded as unbeatable) geometric fit.