Ellipse fitting

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I am not a mathematician and I don´t know much about it but i need help to fit an ellipse to a series of points and calculate its eccentricity. I have coordinates in the cartesian plane. I managed to do that using Matlab and the least Square approximation but i got many inconsistencies (transalting all the points in the plane led to different ellipse equation).

Serching the net I found out that Fitzgibbon, Pilu, Fisher fitting technique might be more reliable. Can someone who know better then me confirm that? Do you have a function in matlab i can enter to use that kind of fitting?

Thanks

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