I'm a little confused about how significant of information can be derived from a 2d projection of the shell. This sort of mathematical modeling looks like phrenology.

Using PCA on 3d shapes is a proven method for identification. It's nothing like phrenology aside from both involving morphology. Former actually works, latter does not.

(I upvoted, seems a little weird that you were downvoted) So, I spent a little time looking up "Principal Component Analysis" and yeah, this method works well with these forms, and my comment comparing it to phrenology was definitely more out of ignorance!

I was most surprised that you could flatten a 3d structure down to 2d and not lose so much information that it would cause a very high rate of error. Someone else was skeptical enough to do a study as a critique on it, only to have it retracted. (funny in light of this post)

https://elifesciences.org/reviewed-preprints/94685v1/pdf