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Firstly, I'm not sure whether this is the correct site but I also assume the question is not too different:

Assume there are two curves: One is considered as a reference curve and the other is just an another or "measured" curve.

Example

I want to transform the measured curve in such a way that it fits the reference curve. In other words: I want to calibrate.

I stumbled over Procrustes analysis and Fréchet distance which seem to be usable but nevertheless I wanted to ask you completely unbiased how to proceed. Are there commonly known methods or even implementations in common programming languages (C++, Octave, R,..)? Thanks in advance!

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  • $\begingroup$ Procrustes doesn't seem like it would be a good fit for this problem because it only allows rigid transformations, reflection, and isotropic scaling. These operations wouldn't be sufficient to get the example curves to match. $\endgroup$
    – user20160
    Apr 2, 2018 at 4:17
  • $\begingroup$ The problem isn't clear to me. Are these curves continuous functions with known expressions, or finite sets of points that have been measured? Should they be treated as y values at a fixed set of x positions, or as parametric curves (x and y values at a fixed set of t positions)? Is the goal to warp one curve to match the other, to measure their similarity, or to match points on one curve to points on the other? $\endgroup$
    – user20160
    Apr 2, 2018 at 4:35

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Since Procrustes analysis amounts to iteratively updating a mean (here, a mean curve), I think that is not the suitable in your situation. It is common to use the quadratic Wasserstein distance as a metric in such problems (the literature on this is indeed not so sizeable). The following paper discusses what you may want: https://hal.archives-ouvertes.fr/hal-00749519v2/document

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  • $\begingroup$ Thanks a lot for the advice! I'll have a look on it but however: It seems to be a common problem or task to me so I wonder that there isn't something already implemented? But I'll check it out. $\endgroup$
    – Ben
    Dec 25, 2017 at 18:53

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