Circle fit

Fit a circle to a set of measured x,y points.

Description

Revival of a 14 years old code (written in 1991 for MATLAB 2.x).

Given a set of measured x,y pairs that a re supposed to reside on a circle, but with some added noise. A circle to these points, i.e. find xc,yc,R, such that (x-xc)^2+(y-yc)^2=R^2

The method minimizes the sum of squared radial deviations.

• Acknowledgements: This submission has inspired the following:; Ellipse Fit, Circle Fit (Kasa method), Circle Fit (Pratt method), Circle Fit (Taubin method)
• MATLAB release: MATLAB 5.2 (R10)

[Yuri Slobo...]

Can someone please enlighten me where one meets such distributions to be fitted by a circle ?

[Yogesh Mehta]

Yuri,

It can be extremely useful. For example, trying to fit a nyquist plot to an experimentally acquired FRFs... Ideally, nyquist plot is supposed to be a circle, but is not due 'noise'

[Bjorn Hemming]

I have used this function to verify a feature in a Metrology software giving correctly first 4 digits, so it seems OK

[Knut C. Naue]

Nice tool for data covering almost a complete circle. But if data exists describing only an arc, circfit fails identifying the assumed center and radius.

[Hedi Kawano]

http://www.math.niu.edu/~rusin/known-math/99/circlefi tells you that the equation used in this "circle_fit.m" gives an approximate solution.

[Hedi Kawano]

Sorry, it is
http://www.math.niu.edu/~rusin/known-math/99/circlefit
 (last "t" was missing)

[Tomaz Pepelnjak]

Very useful if you need to fit measured points to the circle function and compare it further to reference value.

[Luigi Rosa]

High-quality code, simple and effective

[shmi braun]

Re: Hedi Kawano

  see also
http://www.pitchup.com/matlab/print.aspx?article=168

[Sanjeev Sharma]

I found it to be very effective.

[Hendro Nurhadi]

Just... Excellent.. thanks.
:-)

[Richard Brown]

Note: This code doesn't minimise the sum of squared radial deviations - that is a nonlinear least squares problem

This code minimises sum((x.^2 + y.^2 - R^2).^2)

[Sebastian Laechele]

Works very well!
I don't really know how, but it works! :D
You saved me a bunch of hours there.
Thank you very much!

[Darren Hewett]

 

[Mehmet Alpay]

Works like a charm :-)

[Nikolai Chernov]

This circle fit has been first published by P.Delogne and I.Kasa in the 1970s and is known as "Kasa method" in statistics. It works well when points cover a large part of the circle but is heavily biased when points are restricted to a small arc. Better fits were proposed by Pratt and Taubin.

[SengChoy Liew]

I have come to a death end in Image processing toolbox to evaluate the circles in a gray scale image.

Anyone how how to use the codes given to fit into those circles in the image so that an histogram for the distribution of circles diameter can be plot ?

[Yasmine]

Hi,

Does anyone know how to calculate deviation from circularity of the measured points compared to the fitted circle using this code?