[scilab-Users] Least squares fit to a circle

[Stephane Mottelet]

Hi,

there seems to be a bunch of different ways to fit a circle, did you  
consider the various methods compared in this paper

www.emis.de/journals/BBMS/Bulletin/sup962/gander.pdf

?

S.

Mike Page <Mike at Page-One.Waitrose.com> a écrit :

> 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
>
> No virus found in this incoming message.
> Checked by AVG - www.avg.com
> Version: 9.0.791 / Virus Database: 271.1.1/2763 - Release Date:  
> 03/22/10 07:33:00
>
>