Wasserstein Style Transfer

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. More- over, interpolating between a content and a style image can be seen as geodesics in the Wasserstein Geometry. Using this in- sight, we show how to mix different target styles, using Wasserstein barycenter of Gaus- sian 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 us- ing other geodesic metrics between gaussians such as the Fisher Rao metric, while the transport of the content to the new interpo- late style is still performed with Gaussian OT maps. Our simple methodology allows to generate new stylized content interpolat- ing between many artistic styles. The metric used in the interpolation results in different stylizations. A demo is available on https: //wasserstein-transfer.github.io.