Ellipse fitting

Question

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

Translating in the plane should lead to a different equation...after all, the best fit is a different ellipse (a translation of the original one). If the original satisfies an equation $F(x, y) = 0$, then the translated one will satisfy $F(x-h, y-k) = 0$ instead. Fortunately, such a substitution doesn't change the eccentricity. if your eccentricity changed, then perhaps there's an error in your code. — John Hughes, Oct 06 '15 at 14:18
Yeah you are right i am sorry, equation is different when you translate — user277519, Oct 06 '15 at 15:33
But eccentricity changes as well. I read that the least square method is not that accurate. Could it depend on that? — user277519, Oct 06 '15 at 15:34
Take a look at http://people.cas.uab.edu/~mosya/cl/index.html for a pile of fitting algorithms, coded up in MATLAB and c++ — Carl Witthoft, Sep 28 '16 at 12:25

score 0 · Answer 1 · edited Apr 13 '17 at 12:56

0

There is a similar question in

https://mathematica.stackexchange.com/questions/60779/fitting-ellipse-to-5-given-points-on-the-plane

See if it is useful.

edited Apr 13 '17 at 12:56

Community

1

answered Oct 06 '15 at 18:27

cgiovanardi

836

score 0 · Answer 2 · answered Feb 24 '17 at 07:40

The process below is valid for exact fitting in case of $n=5$.

If $n>5$ it provides an approximate fit (i.e. Regression).

It is convenient for conics in general. So it is convenient for ellipse (the signs of computed coefficients makes the difference between ellipse and hyperbola).

This comes from the paper (page 16) : https://fr.scribd.com/doc/14819165/Regressions-coniques-quadriques-circulaire-spherique

Ellipse fitting

2 Answers2