Change point detection on curve segments

Question

I have a time series of trajectories with X,Y coordinates, with a known start and finish. And I need a change point detection algorithm able to detect changes in the "curve" of each series (one algorithm for all series and future ones that may come). The problem is that the curves are quite different between them, nevertheless most of the time a human eye can easly spot the change point.

The CPD should be bases in the curve, so not mean nor variance. I have tried creating a basic regression + cost minimitzation algoithm with poor results. I am using python. Any ideas of algorithms/libraries I could use?

An example of the data: The green cross is the change point.

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