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Circle Fit (Taubin method)

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Fits a circle to a set of data points on a plane; returns the circle center (a,b) and radius R.

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File Information
Description

This is a robust and accurate circle fit. It works well even if data
points are observed only within a small arc. This circle fit was
proposed by G. Taubin in article "Estimation Of Planar Curves, Surfaces And Nonplanar Space Curves Defined By Implicit Equations, With Applications To Edge And Range Image Segmentation", IEEE Trans. PAMI, Vol. 13, pages 1115-1138, (1991). It is more stable than the simple Circle Fit by Kasa (files
#5557 and #22642) and slightly faster than Circle Fit by Pratt (file #22643).

Acknowledgements

Circle Fit inspired this file.

MATLAB release MATLAB 6.0 (R12)
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Comments and Ratings (6)
19 Apr 2013 Marta

Can anyone help me with using this function in the Curve Fitting App ? I need to get Goodness of Fit and RSME values..

04 May 2012 Pascal

Nice ! Would be nice to input sigma error on data points and output resulting error on center and radius.

01 Dec 2011 David  
09 Aug 2011 jinrong  
02 Jul 2010 Manuel Lopes

Works nicely, can be easily extended to 3D data.

%project 3D data to a plane
[U,S,V]=svd(XYr);
XYp = U'*XYr;

Pare = CircleFitByTaubin(XYp(1:2,:)')

%estimated center
UU = U * [Pare(1:2)';0];
%estimated radius
RR = Pare(end);

23 Dec 2009 Scott Graybill

Nice function. Very clean and easily implemented in any language. Was wondering if it could be extended to a sphere. I can't follow how you wrote the function from the article (G. Taubin, 1991)

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