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How consistent is the surface quality, and how consistent is the lighting? I might be inclined to try to isolate the the doughnut shape - the intensity seems pretty consistent. If you get that, then fitting circles to the inside and outside would be fairly straightforward.
I implemented the algorithms in this paper and I think I ended up using the MLS approach. I'm not saying this method is the best, but it worked well for my purposes. I did have to have some parameter searching loops (maybe threshold values, and I think canny parameters) to get it to work in varying lighting conditions.
I would definitely be experimenting with different (controllable) lighting arrangements. That could be a huge help
