error measurement of points fitted to a circle

Question

I have a bunch of points where the best circle is fitted into them. The algorithm is based on the least squares approach to fit a circle.

Numerical way to solve for the curvature of a curve

My question is, how would error analysis be performed. I am thinking of something like:

$\sum_{i} (r_i - r_{(\text{actual})})^2 $ where $r_i$ are the distances from the center of the fitted circle to the point, and $r_{actual}$ is the actual radius of the circle.

Any suggestions or insights on how to proceed?

Answer 1

Given $f(x,y) := a(x^2+y^2) + b(xy) + cx + dy + e,$ a circle is determined by $f(x,y)=0.$ For error analysis of a list of points $[(x_1,y_1),\dots,(x_n,y_n)]$ that should be on the circle, you can use $\sum_i f(x_i,y_i)^2.$