CircleFit.m

Robust nonlinear least squares fit of exact equation of circle to xy data

Description

Iterative, robust fit of the exact equation of a circle to xy data. Outliers are identified based on multiples of current standard deviation and "set aside". The interative solution proceeds until there are no remaining outliers. Returns xo,yo,R, terminal outlier criterion, and residuals vector.

• Required Products: Optimization Toolbox
• MATLAB release: MATLAB 7.1.0 (R14SP3)
• Other requirements: Requires an approximate starting solution for xo,yo,R (e.g. from Datum2D.m)

[John D'Errico]

I have not tested this one yet, but there were several things which immediately bothered me from only a quick glance through.
- Nowhere did the help tell me what kind of fit is done. Does it arbitrarily assume the errors lie in y? Does it only handle partial arcs of a circle? Or is it a total least squares solution? The latter makes more sense. It is a circle after all. This should absolutely be repaired, as it should never be necessary for a user to delve into the depths of code to learn facts as important as this.
- Naming the function with internal caps is not my own preference. This causes problems on some operating systems, and its harder to type. Yes, I could change the name, but why?
- A ridiculous choice of help system. In order to get help for this function, the author makes you type "CircleFit help", instead of "help circlefit", which is the standard for every matlab function. Not only is the author's choice non-standard, but it took more work to implement as several dozen displays. Nonstandard help like this is not much different from no help at all.
- There are enough optional arguments and flags to supply here that I'd have leaned towards a property/value pair interface.
- Rather than defaulting to fixed numeric starting values for the parameters, a variety of estimators exist which should yield far better choices, while not forcing the user to supply starting values at all if they would prefer not to.
- The author should try mlint on this code. It made some good suggestions here.
- Finally, the author should reference the prior submission FEX 5557, which appears to do exactly the same thing, except for this code's claim to be a robust fit.
I'll stop here without testing the code itself. Its a start anyway.

[Duane Hanselman]

By requiring the Optimization Toolbox you limit the usefulness of this function to a small audience. This problem is easily solved using linear least squares which is in basic MATLAB. I agree with John that your help format is ridiculous. How is this function an improvement over FEX 5557? Your help text and use of the Optim. Tlbx are big weaknesses.

[Richard Brown]

Note: linear least squares doesn't solve the least squares problem for minimizing distance from the circle to points, which is the "best fit" in the geometric sense. Therefore a nonlinear least squares solution is appropriate.