# Least Squares Fitting of Circles

Article

DOI: 10.1007/s10851-005-0482-8

- Cite this article as:
- Chernov, N. & Lesort, C. J Math Imaging Vis (2005) 23: 239. doi:10.1007/s10851-005-0482-8

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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.

### Keywords

least squares fitcircle fittingLevenberg-Marquardt algorithm## Copyright information

© Springer Science + Business Media, Inc. 2005