Least Squares Fitting of Circles

Authors:
N. Chernov;C. Lesort
Affiliations:
Department of Mathematics, University of Alabama at Birmingham, Birmingham, USA 35294;Department of Mathematics, University of Alabama at Birmingham, Birmingham, USA 35294
Venue:
Journal of Mathematical Imaging and Vision
Year:
2005

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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.