fit_ellipse

Find the best fit for an ellipse using a given set of points (a closed contour).

Description

This function uses the Least-Squares criterion for estimation of the best fit to an ellipse from a given set of points (x,y). The LS estimation is done for the conic representation of an ellipse (with a possible tilt).

Conic Ellipse representation = a*x^2+b*x*y+c*y^2+d*x+e*y+f=0
  (Tilt/orientation for the ellipse occurs when the term x*y exists (i.e. b ~= 0))
 
 Later, after the estimation, the tilt is removed from the ellipse (using a rotation matrix) and then, the rest of the parameters which describes an ellipse are extracted from the conic representation.

For debug purposes, the estimation can be drawn on top of a given axis handle.

Note:
1) This function does not work on a three-dimensional axis system. (only 2D)
2) At least 5 points are needed in order to estimate the 5 parameters of the ellipse.
3) If the data is a hyperbola or parabula, the function return empty fields and a status indication

• MATLAB release: MATLAB 6.1 (R12.1)

[Larry O'Neill]

This method works excellent with all my noisy data. Also well written and extremely easy to use.

[Peter Delahunt]

Thanks Ohad - it works well with color discrimination data. Best wishes, Peter

[P F]

Does what it claims to. Quite helpful!

[Chaiyanan Sompong]

Thank you. In present-day, i do my research about face detection in color image.

[Eric Tittley]

 

[Antje _]

Thanks!

[Gita Adur]

Execellent!!! Very well written and extremely easy to use.

[Willem Van der Merwe]

Great. The plot function was a great help as well.

[Heikki Suhonen]

Works well for me. Easy interface, and nice optional visualization.

[Sophie Jarlier]

It's grest to have your code! Just a question: I randomly selected 5points and execute your function but I get the following error:
In fit_ellipse at 155
stopped because of a warning regarding matrix inversion
But I have 4 points that have same y=320 which is the maximum size of my image.. Should these 5points have 5different y and 5different x?
Thanks for your answer
Sophie

[Raimund Leitner]

Incredible useful and practical m-file

[Roy Pur]

THANKS

[a s]

 

[Daniel Nilsson]

Awesome! I just had to modify the program to plot the non-rotated ellipse instead, otherwise this was perfect!

[Dave Peake]

Exactly what I was after, perfect. Does what it says, does it well and easily.

[Kevin Shaw]

Love it. Works as advertised.

[Samuel]

Hi, I have one question.... When a run the code the program shows the ellipse result, but don't plot the graphic with the points and ellipse fit curve (the same graphic above). I would like to see the fit curve, but I don't know whats is the problem... Please, anybody help-me.... (sorry my english)

[Sophie]

Thanks a lot for this script which is really useful!
I have one question because I get into trouble: I would like to get all pixels that are inside the ellipse.. I was doing something like that but it does not work:

x0 = ellipse_t.X0_in;
y0 = ellipse_t.Y0_in;
a = ellipse_t.a;
b = ellipse_t.b;
t = ellipse_t.phi;
for x=1:size(I,1)
 for y=1:size(I,2)
        X = (x-x0)*cos(t)+(y-y0)*sin(t);
        Y = -(x-x0)*sin(t)+(y-y0)*cos(t);
       if (X^2/a^2+Y^2/b^2)>1 % outside ellipse
            I(y,x) = 0;
        end
end
end

Any idea? Thanks in advance!

[Sophie]

@Samuel: did you resolve your problem?
I do not know your exact problem but maybe what you want is this:
handle= subplot(221); % or something like this
ellipse_t = fit_ellipse(x,y,handle); % the ellipse should be drawn on the subplot else your ellipse is out of range if I am not wrong

[Sophie]

I found.. it's just a question of angle: should have done:
t = - ellipse_t.phi;

[Raymond Cheng]

Thanks for your sharing.

[Sieun]

thank you :D

[Evgeny Pr]

 

[Mustafa]

 

[scaramanga]

I'm using your function in a loop, is it possible to draw ellipses with a different color at every iteration of the loop ?

[Rafal]

Hello. I get all the ellipse parameters.I load two orthogonal signals as a x=b1ch3(:,1), y=b1ch4(:,1), there is problem because it's not drawing and fitting ellipse to this points.

[Roy]

thanks for sharing.

[Rakesh]

Thanks a lot!! nice work!

[Rafal]

Hello i use this script and it's working perfectly,but unfortunately i have one problem ...

I load signals ,it draws an ellipse , when i want to put near ellipse points to which there is aproximation they are moved. I think it could be connected with new coordinates for ellipse. cause i use cmd plot(x,y,'b'); and there is ideal bow as ellipse has,but it's moved. Could anyone helps me?

[Rafal]

Hello. Can someone help me and give description of algorith used in this matlab code. Maybe a link to publication. If someone has also block scheme of this algorithm send it to me please. My mail :
[e-mail]

Best Regards

[bear tiger]

 

[Thanos]

Hi, I am using the script and it works fine for my data. I am trying to work the math a little bit and I am struggling at one point. why we assume that the f=-1? As far as I can see from the code, the value we assign to f affects the a, b, c, d, e which in turn affect the ellipse properties. Is that something mathematically trivial? I am looking forward for your answers
Cheers
Thanos

[Tima Tima]

Thank you. It is vary helped for my work

[Mohammed El-Said]

Works Great,
Thanks for sharing...

[Hassan Naseri]

Excellent deployment, easy to use and well commented ... THANKS

[Steven Dakin]

Works out of the box. Very useful. Thanks.

[David Scaduto]

 

[Paulo]

How to use this? I mean, the inputs x and y? Can I have an example? Thanks! This is very useful for my project!

[Amit Ruf]

Nice code, however, you probably have a bug related to the orientation of the ellipse, see:

http://www.mathworks.com/matlabcentral/fileexchange/22423

I fixed it and added a computation of the residual of the fit which provides a quality measure for the fit.
If you want my version, please mail to:
[e-mail]