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Some ideas here (hu moments should already be an option for this pipeline):
https://www.learnopencv.com/shape-matching-using-hu-moments-c-python/
https://docs.opencv.org/master/d5/d45/tutorial_py_contours_more_functions.html
Perhaps, contour / convex hull calculation and then wasserstein distance estimation:
http://scipy.github.io/devdocs/generated/scipy.stats.wasserstein_distance.html
Other:
https://github.com/jl626/torch_shape_measure
http://www.kernel-operations.io/geomloss/_auto_examples/optimal_transport/plot_optimal_transport_2D.html?highlight=wasserstein
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