Congratulations on coming up with an interactive method of finding a circle.
I looked again at your example, and have some questions/suggestions. The Question is are all your images similar to this, that is, a series of concentric light/dark circular bands, centered near the middle of the image, with a rectangular obstructing grid running horizontally and vertically? If so, I have some ideas for an algorithm that might (you'd have to test it!) work.
First, you want to find the center of the circles. If you did a histogram along the X axis, and another histogram along the Y axis, I'd expect it to show a pattern that you could use estimate the center. I'd also consider doing a histogram along a line running from the lower left to upper right corner, and from upper left to lower right corner -- that should minimize the effect of the grid.
If the above procedure lets you make a reasonable guess for the center, you might be able to refine your guess by the following procedure -- instead of using the entire picture to form the histogram, just plot the intensity along lines going through what you suspect is the center. Plot from the putative Origin along a fixed-length radius using angles of 0, 45, 90, 135, 180, 215, 270, and 315° -- if you really have started from the origin, these 8 traces should be very similar (have a low standard deviation). You could now move the Origin slightly and see if this measure increases or decreases -- you are looking for a minimum.
Once you have the center, you can use similar "radial intensity plots" to find where the intensity changes on the majority of your 8 radial directions -- this is likely to be a radius of your circle.
I have no idea if this algorithm will actually work, but it seems like something to try. I'd be interested in hearing how it works out for you.
Bob Schor
