Wasserstein barycentric coordinates: histogram regression using optimal transport.

This article defines a new way to perform intuitive and geometrically faithful regressions on histogram-valued data. It leverages the theory of optimal transport, and in particular the definition of Wasserstein barycenters, to introduce for the first time the notion of barycentric coordinates for histograms. These coordinates take into account the underlying geometry of the ground space on which the histograms are defined, and are thus particularly meaningful for applications in graphics to shapes, color or material modification. Beside float: left; overflow: hidden; margin: 0 .4em; padding: 1em; max-width: 30%; border-radius: 3px; background-color: #ece9d8; text-align: left; line-height: 1.5;}.bsa-cpc a { color: #1d4d0f; text-decoration: none !important;}.bsa-cpc a:hover { color: red;}.bsa-cpc .default-image img { display: block; float: left; margin-right: 10px; width: 36px; border-radius: 7.5%;}.bsa-cpc .default-title,.bsa-cpc .default-description { display: block; margin-left: 46px; max-width: calc(100% - 36px);}.bsa-cpc .default-title { font-weight: 600;}.bsa-cpc .default-description:after { position: absolute; top: 4px; right: 4px; padding: 1px 4px; color: hsla(0, 0%, 20%, .3); content: \"Ad\"; text-transform: uppercase; font-size: 7px;}@media only screen and (min-width: 320px) and (max-width: 759px) { .bsa-cpc #_default_ { flex-wrap: wrap; } .bsa-cpc ._default_ { float: none; margin: 0 1em .5em; max-width: 100%; }}