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stat.ME2025
Monge-Kantorovich quantiles and ranks for image data
Gauthier Thurin
This paper defines quantiles, ranks and statistical depths for image data by leveraging ideas from measure transportation. The first step is to embed a distribution of images in a…
stat.ME2024
Regularized estimation of Monge-Kantorovich quantiles for spherical data
Bernard Bercu, Jérémie Bigot, Gauthier Thurin
Tools from optimal transport (OT) theory have recently been used to define a notion of quantile function for directional data. In practice, regularization is mandatory for applicat…