Curve Matching Techniques for Rotated Curves in Geometric Analysis

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klau
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I need to perform geometry matching of curves (see http://www.tiikoni.com/tis/view/?id=c54d9b8 ). As it can be seen, the big problem is that curves might be rotated, though they have similar shape.

Do I need to make curve fitting and look at the parameters of analytical models? But, I guess, it's very complicated to fit these curves.

How can I solve this problem? Any ideas is highly appreciable.
 
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You didn't give any information about what the curves represent. People could read your other posts and guess, but it would be a good idea to make a coherent statement of the problem in this thread.