Characterization of barycenters in the Wasserstein space by averaging optimal transport maps

摘要: This paper is concerned by the study of barycenters for random probability measures in Wasserstein space. Using a duality argument, we give precise characterization population barycenter various parametric classes with compact support. In particular, make connection between averaging space as introduced Agueh and Carlier (2011), taking expectation optimal transport maps respect to fixed reference measure. We also discuss usefulness this approach statistics analysis deformable models signal image processing. setting, problem estimating from n independent identically distributed considered.