Optimal transport with 3D shapes

par M. Jean Feydy (Inria)

lundi 18 déc. 2023, 10:00 → 11:00 Europe/Paris

Université Paris-Dauphine

 

 

The optimal transport problem has many different uses: a generalized sorting problem in dimension D>1 ; a nearest neighbor projection with an incompressibility constraint ; a foundational example in operations research... In this talk, I will present modern algorithmic advances on the topic, articulating the differences between low- and high-dimensional transport problems. We will see that in 2D and 3D, at least, the estimation of Wasserstein distances, transport maps and barycenters is now a solved problem. This opens the door to easy non-linear manifold learning for statistical shape analysis and model order reduction.