Optimal Transport solver for shape analysis and shape assembly?

[ttsesm]

Hi,

I am interested to use Optimal Transport for shape assembly. My knowledge with OT is really basic though, however from what I understood it can be used for full or partial shape matching and from what I've seen it has been used successfully for shape deformation matching, registration, etc..

The idea in shape assembly is that you have a part of two different pieces which complete each other so that you can assembly a single merged piece. The issue is that you do not have any overlap part but only two fractured parts where there is a bijection between the two.

Thus, I am trying to understand whether any of the OT solvers could be used for such a use case and if yes how. I would appreciate if someone with deeper understanding of OT could elaborate whether something like that would be feasible or not.

Thanks.