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Comparing patterns on coins.

Hello. I'm having a trouble comparing patterns on coins. I have fully working comparison of diameters, but some coins sadly have the same diameter. How can I accurately compare these patterns. I'd like it to be rotation invariant. It doesn't have to be scale invariant, because camera is always on the same height. I tried many things. I tried feature detectors like SIFT, SURF, FREAK, but i couldn't get anything to work properly. I don't want to use learning machine.

What would be the best method to use in comparing images like these? All help appreciated.

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