[scilab-Users] Least squares fit to a circle

[Mike Page]

Hi Vladimir,

Thanks for your email and your interest in this problem.  I have attached a CSV file with the experimental data in it.  Fitting a circle to the whole data set works OK, but if you look at the data, you can see a region of different curvature at the right hand side.  It is specifically this part that I want to fit to the nearest circle.  This is approximately the last 12 data points in the file.

Let me know if you want me to send some code as well.

Regards,
Mike.


-----Original Message-----
From: Vladímir Rodríguez [mailto:vladimir.rodriguez at reduc.edu.cu]
Sent: 23 March 2010 13:51
To: users at lists.scilab.org
Subject: Re: [scilab-Users] Least squares fit to a circle


El mar, 23-03-2010 a las 09:19 +0000, Mike Page escribió:
> Hello,
> 
> Does anybody have a good suggestion for fitting a circle to a set of
> experimental (x,y) data?  The data are measured electrically as a set of
> complex numbers and I want to find the centre and radius ([x0, y0, r]) of
> the circle that fits the data best in a least squared error sense.
> Typically the data spans somewhere between 0.2 and 1.0 radians of arc and is
> not very noisy (say 1%).
> 
> I have tried using the nonlinear solver fsolve, by defining a loss function:
> 
> L = (r^2 - (x-x0)^2 - (y-y0)^2)^2
> 
> and finding the vector [r, x0, y0] for which dL/d[r, x0, y0] is zero.  I
> have tried both with and without a Jacobian, but find that often the method
> fails to converge to a solution (maybe works 8 out of 10 times).
> 
> Next I tried the Box method of the Nelder Mead toolbox (I have constraints
> since physically, the centre has to be in the ++ quadrant of the complex
> plane).  This is better and always converges to a solution.  However, the
> solution is not always very good.  I can often fit a better circle by eye.
> 
> It may be that the algorithms are converging to a local minimum rather than
> the global one, but I don't know a good way to change this behaviour.  I
> seem to remember that simulated annealing was a way to solve this problem -
> does anybody know anything about that?
> 
> So, what I would like to know:
> 
> - Is there a better way than fsolve or Nelder Mead for fitting a circle to
> the data?
> - Is there a way to tune the performance that might give me a better fit?
> 
> I can post some code if it helps.
> 
> Thanks for any help.
> 
> Regards,
> Mike.
> 
If you can send the data (or a sample) I would like to try.
-- 
                      MSc. Vladímir Rodríguez Diez
                  Departamento de Ingeniería Eléctrica
                        Universidad de Camagüey

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