How do I detect the centerline of an object

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Hi,

I am writing a program for analyzing chromosome aberrations. I typically get chromosome images that look more or less like a bunch of scattered bananas:

I have figured out how to get the outline and the (rotated) bounding boxes. What I would really like is to be able to get the centerline. By centerline I mean a line going through the geometric center of the binarized object (as shown below), not necessarily through the brightest pixels, which may be on the sides rather than the center.

Any tips on how to code this would be appreciated.