Finding center of circle and eccentricity

Question

Jeff 2011-3-18

0
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https://ww2.mathworks.cn/matlabcentral/answers/3439-finding-center-of-circle-and-eccentricity

I have what amounts to an xray image of a circular xray field - the xray beam is a cone. The beam is supposed to be aimed at a metal ball with the shadow of the ball hopefully centered on the xray beam. So you basically have two concentric circles with inner one a lighter shade of grey and the outer basically black (the exposed part of the film). I hope you're still with me.

What I want to do is (1) find the centers of both circles and (2) find the eccentricity of the two circles. My first approach was to try to find the boundary of each circle and then perform some measurements on those. However, today I began thinking maybe I could simply locate two points on each circle, form a chord, and determine the center. This assumes a perfect circle, which may not be the case. I could do this several times and calculate a standard deviation.

Now to my question. Which way would you pros attack this. Perhaps there is a completely different way I need to look at this.

Thanks, Jeff