  We propose Gaussian optimal transport for Image style transfer in an
Encoder/Decoder framework. Optimal transport for Gaussian measures has closed
forms Monge mappings from source to target distributions. Moreover interpolates
between a content and a style image can be seen as geodesics in the Wasserstein
Geometry. Using this insight, we show how to mix different target styles ,
using Wasserstein barycenter of Gaussian measures. Since Gaussians are closed
under Wasserstein barycenter, this allows us a simple style transfer and style
mixing and interpolation. Moreover we show how mixing different styles can be
achieved using other geodesic metrics between gaussians such as the Fisher Rao
metric, while the transport of the content to the new interpolate style is
still performed with Gaussian OT maps. Our simple methodology allows to
generate new stylized content interpolating between many artistic styles. The
metric used in the interpolation results in different stylizations.
