, Volume 23, Issue 3, pp 239-252

Least Squares Fitting of Circles

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Abstract

Fitting standard shapes or curves to incomplete data (which represent only a small part of the curve) is a notoriously difficult problem. Even if the curve is quite simple, such as an ellipse or a circle, it is hard to reconstruct it from noisy data sampled along a short arc. Here we study the least squares fit (LSF) of circular arcs to incomplete scattered data. We analyze theoretical aspects of the problem and reveal the cause of unstable behavior of conventional algorithms. We also find a remedy that allows us to build another algorithm that accurately fits circles to data sampled along arbitrarily short arcs.

Nikolai Chernov PhD in mathematics from Moscow University in 1984, scientist in Joint Institute for Nuclear Research (Dubna, Russia) 1983–1991, professor of mathematics in UCLA 1991–92, Georgia Tech 1992–93, Princeton University 1993–94, University of Alabama at Birmingham since 1994.
Claire Lesort MS in mathematics from University of Limoges in 1994, MS in mathematics from University of Alabama at Birmingham 2000, PhD in Statistics from University of Alabama at Birmingham 2004. Statistician at BellSouth Telecommunication Inc. since 2003.