fitellipse.m

Fit ellipses to 2D points using linear or nonlinear least squares

Description

There are two main methods for least squares ellipse fitting:
1) Minimise algebraic distance, i.e. minimise sum(F(x)^2) subject to some constraint, where F(x) = x'Ax + b'x + c

This is a linear least squares problem, and thus cheap to compute. There are many different possible constraints, and these produce different fits. fitellipse supplies two:
[z, a, b, al] = fitellipse(x, 'linear')
[z, a, b, al] = fitellipse(x, 'linear', 'constraint', 'trace')
See published demo file for more information.

2) Minimise geometric distance - i.e. the sum of squared distance from the data points to the ellipse. This is a more desirable fit, as it has some geometric meaning. Unfortunately, it is a nonlinear problem and requires an iterative method (e.g. Gauss Newton) to solve it. This is implemented as the default option in fitellipse. If it fails to converge, it fails gracefully (with a warning), returning the linear least squares estimate used to derive the start value

[z, a, b, alpha] = fitellipse(x)

plotellipse(z, a, b, alpha) can be used to plot the fitted ellipses

• MATLAB release: MATLAB 7.1.0 (R14SP3)
• Other requirements: R14 or later - uses nested functions, true false booleans

[apiwat wisitty]

It's quite fantastic. I'm studying this algorithm. This function help me much. ;-)

[Kristopher White]

Awesome work. Solid implementation, very useful.

[Jenn Risk]

When I run the demo file (using 2007a), I get an error message:

??? Error using ==> minus
Matrix dimensions must agree.

Error in ==> fitellipse at 87
x = x - repmat(centroid, 1, length(x));

Error in ==> ellipsedemo at 58
[zb, ab, bb, alphab] = fitellipse(x, 'linear');

[Richard Brown]

Hi Jenn

I'll investigate this ... I'm not sure if I have access to a copy of 2007a, but I'll see if I can find one. It definitely works on newer versions!

regards,

Richard

[GAURAV]

Hi!! I have one doubt.. Will it work if I have just four points in X-Y system? Because here it said that it has to have more than 5 points?

Regards,
Gaurav

[bear tiger]

good!
Is there any reference for this algorithum

[nancy]

Hi,Richard Brown
       I have read your code( fitellipse.m )on matlabcentral. Now I have some puzzle about ellipse detection in an image:
1) How can I get the point coordinate from an image? I have tried to use the edge function,but the result is not satisfactory.
2) If detect all edge points in an image, there are lots of points ,how can I select suitable points as input of the fitellipse function?
 
       
regards,

                    Lei Q

[Felipe Pedreros]

Incredible implementation Richard, but I'd like to know the errors of the parameters. Maybe these are obvious but I can't find the way to get it.
Could you help me?

Regards,
Felipe

[Richard Brown]

@nancy:
1. Not entirely sure what you mean, but if you've used edge to find the edges of your ellipse, then you can use find on the resulting black and white image to get the coordinates of the edge pixels. 2. You can fit an ellipse to all of the edge pixels if you like, you don't need to choose a subset.

@Felipe: No they're not obvious. I'll get back to you with a better answer a bit later - I'm from Christchurch New Zealand, and my university has its hands full getting our teaching back underway after the earthquake a few weeks ago.

[Felipe Pedreros]

Hi Richard,

I understand your situation very well... my University was also down after our earthquake last year. I hope all is going well now in NZ.
Concerning my question, I'd like to ask if a modification to the inputs is possible, by leave fixed some of the parameters like the center (x0, y0) of the ellipse. The same for the your code fitcircle.m

Best regards
Felipe

[Pierre Roduit]

First, thank you for this code.
Just a comment on this part of this code.

if ishandle(varargin{1})
    hAx = varargin{1};
    varargin(1) = [];
else
    hAx = gca();
end

If a figure 1 is open and you try to draw an ellipse with a center at [1,1], it will take take these coordinates as a reference. Not an obvious error...

[Valeria Rodríguez]

Hi. It seems the code sometimes switch the major and minor axes. This is problematic for plotting. Besides this, the code is very useful.

Greetings.

[Richard Brown]

@Pierre: Thanks, good catch! I'll put a new one up shortly that checks explicitly for an axes handle.

@Valeria: The order of the axes is not specified - there is no guarantee that the first will be the major axis. If you want to enforce this it's a trivial modification.