What is the state of the art/research metric to compare ellipses but jaccard coefficient?

Im looking for the, if there is one, metric to compare ellipses with each other. Last time a had a similar dataset (malaria cells, now its pupiles) i used jaccard coefficient but that was more because of i didnt had the time to do further research on this topic.

I jused the jaccard coefficient like that: - transform the multi-d data in 1D to make the comparation even possible.

Even tho it worked quite well i didnt like it that much and im quite sure there a better metrics out there for that matter.

I hope you all stay fit in this very challenging time for some