Brief

Researchers have developed a new framework for barycentric projections of optimal transport plans on Riemannian manifolds. This method addresses the challenge of converting probabilistic optimal transport couplings into deterministic maps, which is complicated by the curvature and cut loci of manifolds. The proposed framework includes an intrinsic projection that maps source points to conditional Fréchet means and a tangential log-exp projection that acts as a local displacement surrogate. Experiments on various datasets demonstrate the effectiveness of these projections. AI