See attached demo and adapt at needed. It computes the average radial profile.
Or maybe you just want to use the contour() function but that is so obvious I assume you tried that and didn't like what it did, but you just didn't tell us why you didn't like it.
If you can't figure out my attached demos, and need more help, attach your gray scale image, or the data variable, or "circular structure" in a .mat file.