Correcting for concentricity after perspective correction

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I'm working on a project with Python + OpenCV for automatic target scoring. The problem I'm facing is with perspective correction of concentric circle target.

Long story short: Is it possible to correct image to get perfect concentric circles out of concentric ellipses?

Long story: I managed to compute the transform matrix and use warpPerspective function to correct the ellipses back to perfect circles. This worked, except that concentric ellipses do not wind up in concentric circles after correction. Given the literature I could find, that looks like a well known problem... See the target image with a perfect circle fitted on the biggest circle: See target here The center of each scoring circle area is shifting in the direction of the original perspective (right, slightly down)

Is it possible to correct image to get perfect concentric circles?

If not, it seems I will not be able to perform proper decimal scoring. Should I use a completely different approach?

Thanks a lot!

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