Collection Variational methods and optimization in imaging
Organizer(s)
Date(s)
19/04/2024
Sliced Partial Optimal Transport
Sliced optimal transport is a blazing fast way to compute a notion of optimal transport between uniform measures supported on point clouds via 1-d projections. However, it requires these point clouds to have the same cardinality. This talk will show a fast numerical scheme to compute partial optimal transport in 1-d : this corresponds to solving an alignment problem often solved with dynamic programming, though our solution is much faster. We integrate this 1-d alignment algorithm within a sliced transport framework, for applications such as color transfer. We also make use of sliced partial optimal transport to solve point cloud registration tasks such as those traditionally solved with ICP. I'll show results involving hundreds of thousands of points computed within seconds or minutes. I'll also show preliminary results on sliced partial Wasserstein barycenters.
