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I tried to find out circle center for noisy data. For computation sake I implemented this algorithm https://dtcenter.org/met/users/docs/write_ups/circle_fit.pdf It works fine but sometimes data is more similar to the line rather than circle. I need some parameter which would show me that data is more likely an arc of circle. example

Gleb
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  • I would propose a regularized second degree polynomial level set. It is very easy to fit using normal least squares fitting. And with some tweaking and re-weighting you can make more robust fits also (other than the 2-norm). – mathreadler Apr 18 '18 at 11:43
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    Note that in a certain sense (which can be made rigorous), a line segment is an arc of an infinitely large circle. –  Apr 18 '18 at 12:36

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Perhaps read up on model selection. A circle has more parameters than a line (3 vs 2), and indeed a circle can, locally, approximate a line arbitrarily well. You should thus expect that a circle always gives a better fit than a line (i.e. the fitting error is always lower), even if the data really is a noisy line.

In order to choose between models with varying numbers of parameters, you need to penalize the models with more parameters.

Wouter
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