How can I detect the two curved lines above and below the black band in the image? I would like to generalize this to a set of similar images so that I can continuously measure the distance between the two curves.

I have tried superpixel oversegmentation, and the output is promising, but I'm not sure how to move on from there. Ideally, the curves would enable me to measure the perpendicular distance between the two curves so that I can find the max, min, average, etc. Thanks in advance.