Circle Fit (Taubin method)

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

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

The author wishes to acknowledge the following in the creation of this submission:
Circle fit

• MATLAB release: MATLAB 6.0 (R12)

[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)

[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);

[jinrong]

 

[David]