Algorithm for aligning elliptical shapes

Question

I'm looking for an algorithm to align elliptical shapes that is capable of handling "missing data." Rough sketch:

In this case, we would like to align all shapes to shape #1.

I looked around for "convex shape alignment" and "elliptical shape alignment," but couldn't find anything that would seem to be robust to missing parts (e.g. in the top right corner image) that are outside of the frame.

Is there any algorithm that was designed specifically for this purpose?

Answer 1

You can use the Hough transform to detect the ellipses, plus an ACP in order to have the orientation, and then you have all the ellipses parameters: center, radii, orientation.