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Measuring the ellipticity is an important task to ensure the quality of steel coils before they are shipped out. In this paper a new algorithm to measure the ellipticity of steel coils using a machine vision system is presented. Traditional algorithms for ellipse detection based on least squares fitting can not be directly applied to this problem, since they lead to ellipses with a very high ellipticity if the amount of fitting data is small. In our new concentric ellipse fitting least squares algorithm the additional information, that the elliptic input curves are concentric, is used to increase the amount of available input data, to estimate the ellipticity even if the curve segments are very short. In this paper the results of a traditional ellipse fitting algorithm are compared to those of the new concentric ellipse fitting algorithm. Furthermore the preprocessing tasks (Hough transform, edge detection, curve filtering), which lead to the fitting data, are described in detail. Finally a simulation of the radius dependency of the ellipticity is done, which is compared to the results of the algorithm.